You have already learned that matter is the stuff that everything in the universe is made of. In chemistry, scientists study matter and the changes associated with it. For example, water is matter that can exist in three different states: a solid, a liquid, or a gas. You can freeze liquid water, and it will change into ice (a solid), or you can heat liquid water, and it will evaporate into water vapor (a gas). What distinguishes these forms of water from one another, and how do they behave differently?
that has mass and takes up space. Mass is a measure of the amount of matter a substance contains; volume is the amount of space a substance takes up. Even gases that you cannot see, such as water vapor, have mass and volume. Like solids and liquids, gases are matter.
All matter is made of atoms, the smallest particles of a substance that still have the properties of that substance. Atoms combine to form molecules; a molecule consists of two or more atoms joined by chemical bonds. A molecule of water always contains two atoms of hydrogen and one atom of oxygen. This molecule is the same whether it is an ice cube, a drop of liquid water, or a puff of water vapor. When matter changes state—for example, from solid to liquid or gas—it does not form different kinds of molecules.
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atom and element. An atom is an individual unit of matter. An element is elements. All of the atoms of an element contain the same number of protons, which are a type of subatomic particle. There are other subatomic particles as well. Electrons orbit the nucleus in the electron cloud and have almost no mass while carrying a negative charge. Protons and neutrons are found in an atom’s nucleus and carry 99% of the atom’s mass. Protons are positively charged while neutrons have no charge
1. How is water both a molecule and a compound?
Also, do not confuse the terms molecule and compound. A molecule consists of two or more atoms joined through chemical bonds. A compound consists of two or more elements joined through chemical bonds. Hydrogen gas (H2) and oxygen gas (O2) are molecules—each consists of multiple atoms of only one type of element. Water (H2O) and carbon dioxide (CO2) are both molecules and compounds.
physical property of matter include color, smell, melting and boiling points, magnetism, and density. You can observe the color of water by looking at it and the smell of water by smelling it. You can measure the melting and boiling points of water by heating it; you may cause a change of state, but you do not produce new kinds of matter. You can observe whether water is magnetic by holding a magnet beside it. You can calculate the density of water by dividing a sample’s mass (measured using a balance) by its volume (measured using a graduated cylinder). None of these observations or measurements change the water into a different kind of matter.
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chemical property can be observed only when the matter changes as a result of a chemical reaction. In other words, you observe chemical properties only when one type of matter changes into molecules of two different chemicals—for example, hydrogen and oxygen—creates molecules of a new wood produces new substances, such as carbon dioxide and ash
Under different conditions, the properties of a substance can change. During a physical change, the chemical composition or identity of a substance does not change. In other words, only the substance’s physical properties change during a physical change. For example, a physical change occurs when you break ice into many small pieces. Additionally, all state changes are physical changes. For example, a physical change occurs when you freeze water to form an ice cube or when you melt ice to form water.
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chemical change results from the formation of a new substance. In other words, the substance’s chemical properties change. (These are usually accompanied by physical changes.) If you dissolve an antacid tablet into water, a chemical change occurs. The gas bubbling through the water as the tablet dissolves is a sign of this change. The properties of the gas are different than the properties of the tablet or the water.
2. The picture shows a measurement of the length of a paper clip. Record two ngth of a pap gth of p physical properties of the paper clip.propert hysical prop
The movement and arrangement of particles is different in solids, liquids, and gases. The atoms and molecules in matter are in constant motion, but some particles move more quickly and farther apart than others. Because of this, solids, liquids, and gases have different properties. Remember that a molecule of a substance (such as water) is the same whether it is in a solid, liquid, or gaseous state. molecules move and interact.
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Solids: Of the three states of matter, a solid has particles that move the least. The particles that make up a solid have relatively little energy. As a result, they are packed closely together, vibrating slightly incompressible. In other words, if you press down on a solid, it does not move as much as a liquid or gas cube has the same shape and volume whether it is sitting in a square box, in a round pitcher, or upon a
Liquids: The particles in a liquid are not as closely packed as the particles in a solid. They have more containers. However, the particles in a liquid have less energy than the particles in a gas. As a result, they are still quite attracted to each other. Liquids are more compressible than solids but less a round pitcher, the water will take on a round shape. If you pour liquid into a square box, the either container.
Gases: Of the three states of matter, a gas has particles with the most energy. Gas particles can move
If you press down on the lid of the container, the gas will decrease in volume as its particles are forced closer together. If you have ever watched steam rising from a boiling pot of water, you might have noticed that the steam diffuses or spreads out—into the air as the water molecules move as far from each other as possible.
There is a fourth state of matter: plasma A plasma is similar to a gas, but it is made up of ionized—or free electrons (in other words, electrons that are not attached to a nucleus). Plasmas are important
For most types of matter, the particles are more closely packed in the solid state than in the liquid state. These solids are denser than the liquids they become when they melt. (In other words, a sample of the solid contains more particles than the same volume of liquid.) Water is an important exception. Molecules of solid water are spaced farther apart than molecules of liquid water. As a result, ice is less
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States of Matter
Solid Liquid Gas Plasma
This phenomenon is caused by hydrogen bonds: weak interactions between the hydrogen and oxygen atoms of neighboring water molecules. Oxygen atoms have slightly negative charges, while hydrogen atoms have slightly positive charges. Recall that opposite charges attract and like charges repel. When water molecules come together to form ice, the hydrogen atoms attract the oxygen atoms and repel the other hydrogen atoms. The result is a crystal, or lattice, structure, with large gaps between neighboring water molecules
Does Ie Float on ater
Ie moleules
drogen onds eteen ie moleules allo tem to e spaed urter apart
ater moleules
densit ater densit
Ie
3. How do the particles behave in a solid compared articles behav s to a gas? olid comp
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The heat of your hand quickly causes an ice cube to melt, and your hand begins to feel very cold. You notice the same thing in a glass of ice water. If you leave the glass of water out long enough, the ice will your hand? What is heat, and how does it affect temperature?
To explain these macroscopic, or large-scale, properties of matter such as heat and temperature, you have to consider matter at the microscopic, or molecular, level. When you describe the kinetic energy (energy of motion) or potential energy (stored energy) of an object such as a ball, you probably mean its macroscopic energy. If the ball is moving, for example, it has kinetic energy. If you lift the ball above the ground, you increase its potential energy. All substances have energy associated with the motion and interactions of their particles. This internal energy is composed of kinetic energy due to the motion of the particles and potential energy due to the forces and interactions among the particles. Another name for internal energy is thermal energy.
Thermodynamics is the study of this internal energy and its effects on macroscopic properties of a substance. Thermal energy is a measure of the total energy—both kinetic and potential—of the particles of a substance. Temperature is a measure of the average kinetic energy of the particles. Heat is transferred thermal energy. For example, when you hold an ice cube in your hand, the heat moves from your hand into the ice. The thermal energy in your hand decreases and the thermal energy of the ice increases. The increase in thermal energy can increase the temperature of the ice to the point where the ice begins to melt. A tiny amount of energy actually transfers back and forth between the ice and your hand, but generally heat moves from a region of higher temperature to a region of a lower temperature.
4. Describe the energy transfers that occur when energy trans t liquid water is boiled.
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ancient Greeks debated the divisibility of matter, and Democritus developed the idea that tiny, indivisible particles called atoms could explain the properties and behavior of matter.
English schoolteacher carried out experiments that provided indirect evidence of atoms. He showed that matter how much oxygen and nitric oxide he combined, the two always reacted with one another in a constant weight ratio.
made another discovery about the nature of matter. Thomson used a device called a cathode ray tube the tube—one with a positive charge and the other with a negative charge. These plates were positioned above and below the path of the cathode rays. Thomson found that the cathode rays bent away from the negatively charged plate. Therefore, he concluded that the rays were composed of particles that carried a negative charge. His work established that there were much smaller particles than atoms. He proposed a structure of the atom similar to an English dessert known as plum pudding. He envisioned a model in which the negatively charged particles are embedded in a sphere of positive charge, much like raisins are embedded in a plum pudding.
Changes in the Atomic Model
One of Thomson’s former students, Ernest Rutherford, came up with the nuclear model. Rutherford had he worked with his own research students to study the nature of a type of radioactivity known as alpha of alpha radiation at squares of thin gold foil. His students carried out the experiments and reported that
Democritus
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nuclei. If an alpha particle collided with an atom’s nucleus, the particle bounced off the gold foil. Because most particles passed through the foil, however, Rutherford concluded that the area around the nucleus the plum pudding model.
Rutherford’s work shed light on the presence of an atomic nucleus (which has been discussed before), but it did not reveal any new information about the positions of electrons in an atom. Niels Bohr, a student in Rutherford’s lab, worked on extending Rutherford’s model to explain how electrons were arranged in the atom. Bohr built on the idea of different elements emitting patterns of light based on a mathematical relationship. He developed a model of an atom with a central nucleus surrounded by electrons moving in orbits. His model allowed that electrons could move from one orbit to another when now think of electrons as occupying electron clouds rather than atomic orbitals but continue to use previously discussed.
5. Summarize how the properties of matter were used in the properties the development of the atomic model. he developmen
during this time that he developed much of his work, which led to the quantum model of the atom from a dissatisfaction with the Bohr model. He did not agree with the generally accepted model of both wave and particle behavior for electrons and worked to mathematically interpret the behavior in terms that year, he chose to leave Germany for England, where he accepted a post at Oxford and later moved some of Einstein’s work on electromagnetism and gravitation.
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Atoms are the building blocks of matter, but matter can take many forms. When heat is applied to matter, the particles move faster, which registers as an increase in temperature or average kinetic touchable level. For example, the transfer of energy between particles can transform matter between matter, creating chemical changes that rearrange the very atoms. The observations of good scientists can impact the future of science itself through discoveries based on these properties and the changes of matter.
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Everyday Matter
We observe many different types of changes in everyday activities. From dicing apples and boiling water to cooking eggs, matter is changing before our eyes. Physical changes can alter the phase of matter without affecting its identity or the internal arrangement of molecules. However, chemical changes always result in a new substance being formed by breaking and forming chemical bonds between the atoms of molecules. These observations can lead to new discoveries in science when built on the solid foundations of notable scientists in our past.
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1. What happens to the particles in a gas when it is heated?
A. They break apart.
B. They get smaller.
C. They become more dense.
D. They move faster.
2. Which of the following best describes temperature?
A. Average molecular kinetic energy
B. The amount of heat given off
C. Atomic structure and arrangement
D. Total relative electric charge
3. Which of the following properties of sodium metal is a chemical property?
A.
B. Readily reacts with water
C.
D. Is denser than water
6. List the names of the following scientists who contributed to the development of atomic theory in chronological order with a note describing the contribution of each scientist next to his name: John Dalton, Ernest Rutherford, Niels Bohr, J.J. Thomson.
Graphing Motion
How long can you stand still? Think about every time you stand up, get in the car, or go to sleep at night. Even if you are standing in one spot, are you still moving?
Even if you are to stand perfectly still where you are now, we are constantly moving around the universe at 30 kilometers every second. That’s 67,000 miles per hour! When describing an object’s motion, we also need to think about its position, velocity, and acceleration and for how long it was moving. How can we predict an object’s speed? How are an object’s velocity, acceleration, and position related? Can we tell where an object is with this information?
1. If you got into a car and went to your friend’s . house, how would your d fr position, velocity, and ouse, y acceleration change? a tion,
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Sir Isaac Newton described three laws of motion.
law of force and acceleration, and the third is the law of action and reaction. Each of these three laws describes how forces acting on an object change the motion of that object.
When we describe the motion of something, we might say where the object is, how fast it is moving, whether the object is speeding up or slowing down, and where the object is going.
describe an object’s position and how that changes over time. Consider if you are meeting your friend at their house. You know that the house is 5 km away, and it will take you 20 minutes to walk there, but you do not know how to get there from your house. Knowing just the distance from your house or how long it would take you to reach your friend’s house is the scalar quantity.
However, you also know that your friend’s house is directly north of your house. Now, you can describe the direction as well as your speed and distance when moving. Knowing the velocity, both the speed and direction, of your motion is the vector quantity. The reason why velocity, and not speed, is a vector quantity is because a
direction. When we measure the speed of an object, we only measure the distance that an object travels over time.
2. Describe why velocity is considered a vector y quantity and not a scalar quantity. uantity
How do we measure these changes in the velocity and acceleration of an object? Using a stopwatch
motion detector. A motion detector uses high-frequency sound waves to track the changing position of a moving object. Based on the object’s change in position over time, motion detectors can then determine the object’s velocity and acceleration.
The second is a photogate. Instead of relying on sound waves to track an object, photogates rely on infrared beams by measuring when the beam is blocked by an object as it passes through. By setting up multiple photogates, one can determine the time that it takes for an object to travel between two
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The position of an object is always in reference to something else. In many cases, the starting position is where we begin measurement over time. How far an object changed position during that time is the object’s distance. When we measure an object’s distance, the number will always be positive or zero. However, because objects can move backward and forward, position can be either positive or negative.
When graphing the position over time of an object, we need to consider the object on a horizontal axis, moving backward and forward. In the following graph, the object moved from its starting position of 0 m to 0.5 m in 1 second and then to 1 m in 2 seconds. The position of the object at 4 seconds is once again at the starting position of 0 m.
In addition, we can interpret from the graph that the object stayed at the same position (3 m) from 7 seconds to 9 seconds. This means that for 2 seconds, the object did not change positions. We can interpret that the object also remained at rest at 4 m from 10 seconds to 11 seconds on the graph before returning to the starting position at 0 m
distance
This would be the same as walking forward 1 m and backward 1 m. While the total distance traveled was 2 m, the object is back at the original starting position. The difference between the object’s starting displacement. In this example, the displacement of the object would be 0 m
Displaement s Distane
Displaement traightline distance eteen start and end sitins Vetor
Distane tal distance traveled Line
In this example, we see that the displacement of the car is the straight-line vector from points A to B, where distance is the path that the car actually drove. This is the addition of the lines from A to X to Y to B
3. Draw a graph of you moving forward 3. Draw a graph grap 5 m for 5 s, pausingforw for 2 s, and then m for 5 walking back to your starting position for 5 s. ting p
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Both speed and velocity are a measure of distance over time; therefore, the same equation that is used to calculate speed is used to calculate velocity. However, like distance, speed can only have a positive or zero value to tell you how many units of distance were traveled over time. Because velocity is both speed and direction, velocity can be either positive or negative. Pretend that we want to see if we are walking at a constant speed. To do so, we need to measure the distance over a period of time. Consider the two graphs shown.
and this stays constant for the entire 14 second walk. Therefore, to graph the constant speed or velocity of an object, we graph our speed as 1 m/s for those 14 seconds. If we knew that we were walking forward for 14 seconds, then we could say that the velocity was 1 m/s. Within a one-dimensional graph,
1. Choose two points on the line, and determine the coordinates.
2.
3.
4. Divide the difference, or change, in the y-coordinates by the change in the x-coordinates.
Because the difference in time measured is small, we consider this the instantaneous speed or velocity of an object. However, because the object is moving at a constant speed or velocity the entire time, the
We can assume that the starting velocity (vi) of the car is zero and the starting position (xi) is also zero, so the velocity of the car is the distance traveled over time.
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speed all the time. Sometimes we might slow down, and sometimes we might speed up. This change in velocity is known as acceleration. Acceleration is caused by an unbalanced (net)
of motion that an object at rest will remain at rest, and an object will remain at the same speed and motion unless acted upon by an unbalanced force.
Think about driving a car. The car initially is not moving, but as you press the gas pedal, the car starts to move faster. In this case, the car has a positive acceleration and is increasing in velocity. Now, you come to a red light, and you slowly press on the brake. The car begins to slow down (decrease velocity), and the acceleration is now negative. If the car is moving at a constant velocity (if you are driving on the interstate, for example), then the acceleration is zero
Acceleration is a vector quantity because it describes an object’s change in velocity. Acceleration can also be positive or negative depending on the change in velocity. In the picture, the soccer ball moves up and down. During this time, the force of gravity changes the velocity of the soccer ball at an acceleration of 9.8 m/s2. As an object accelerates at a constant rate, the velocity of the object begins to increase, and position increases exponentially.
The soccer ball is at rest.
The foot acts as the unbalanced force, and the ball moves.
graph that the object is accelerating because the velocity is changing, but by how much?
area under the graph. Without accounting for the change in velocity, displacement (x) would equal velocity (v) multiplied by time traveled (t). Between time 20 seconds and 30 seconds, the object
4. Two cars are traveling at a constant speed to their eling c car travels 30 m in 6 s, and the second car travels 50 m in 10 s. Which car has greater velocity? Which car has greater acceleration?
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If we are to graph an object’s motion and the relationship between the object’s displacement, velocity, and acceleration versus time–
a. At v=0
b. Motion with constant velocity
c. Motion with constant acceleration
d. Motion with constant deceleration
A. where v = 0, the position of the object remains constant and acceleration remains at zero.
B. where the object has no acceleration, the object moves at a constant velocity. Displacement (x) is calculated by adding the object’s starting position (xo) plus the object’s initial velocity (vo) and multiplying by time (t).
C. as the object maintains a constant acceleration, velocity increases at a constant rate. Displacement then increases exponentially.
D. as the object maintains a constant negative acceleration, velocity decreases at a constant rate. The resulting displacement change of the object begins to decrease until the object is at rest.
5. Examine graphs C and D with theirgrap relative equations for distance. Which graph shows the objects traveling a t sh greater distance over time? Explain your reater distance er d reasoning.
Vectors are able to be represented mathematically by using scaled lines with arrowheads to depict the direction and magnitude of the object’s motion. Until now, we have worked with understanding motion
direction to determine the direction in which the object will move.
one street (y direction) and then east along the second street for 1 km (x direction). Overall, you walk 3 km, but what is the displacement of your travel?
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direction, magnitude, and angle.
cos(60), which gives us 5.0 m/s. In the y direction, because it is opposite of our angle, we multiply 10 m/s by sin(60) to get 8.66 m/s. However, because the velocity is decreasing, the velocity in the y direction is -8.66 m/s
objects move, we need to think about all the forces that are acting in multiple directions. Imagine that you throw a baseball. Once thrown, the ball moves along the horizontal (x) axis, but it is also falling along the vertical (y) axis.
We know this to be the case because the ball won’t move in a straight line forever, but how can we angles, like projectiles. As the baseball is thrown, it will eventually start to go down toward the ground. This is because the acceleration of gravity continues to act in the vertical y-axis direction. However, once the ball leaves your hand, unless another force acts on it, there is no acceleration in the horizontal x-axis direction. While the equation for vertical and horizontal motion remains the same, because there is no acceleration in the horizontal direction, the equation can be abbreviated.
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Circular Motion
er form of two-dimensional motion is circular motion, which occurs when an object travels around ular path. A special case of circular motion is uniform circular motion. An object that is moving with
y-go-round, and the rotating hands on an analog watch are examples of circular motion. Some
s a curved exit ramp, it may travel around a portion of a circular path, but it still undergoes circular n during that time.
n calculate the average speed (v) of an object traveling in uniform circular motion around a circle a radius of r. To do this, recall that the average speed of an object in one-dimensional motion is to the total distance traveled divided by the total time of the journey. The equation for this is as
v = d/t
an object travels around a circular path, the total distance that it travels in one complete loop is to the circumference of the circle. The equation for the circumference (C) of a circle with a radius
C = 2 r
which is also called the period of the motion. We can plug these variables into the equation for ge speed to determine the equation for average speed in uniform circular motion. The equation for
v = 2 r/t
ugh the object moves with a constant speed, its direction of movement is constantly changing the object is accelerating. The acceleration of an object in uniform circular motion is called petal acceleration. This vector points inward, toward the center of the circle. The magnitude of petal acceleration (a c
a c = v2/r
elocity vector of an object that is exhibiting uniform circular motion always points tangent to the of the motion. The centripetal acceleration vector always points inward, toward the center of the as shown in the diagram below.
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object is accelerating in two dimensions, we can conclude that its velocity is changing—either in magnitude, direction, or both. However, the acceleration of objects that are undergoing projectile motion or uniform circular motion can be described with some general rules.
In projectile motion, an object always accelerates in the vertical direction, but it never accelerates in the horizontal direction.
In uniform circular motion, an object constantly experiences centripetal acceleration that keeps the object moving in a circle. In other words, the direction of the object is constantly changing as it moves. Be careful! While the speed of an object in uniform circular motion is constant, its velocity is constantly changing because it is always changing direction.
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All moving objects have momentum (p). This is a measurement of an object’s motion. The more
p = mv
This equation shows us that momentum is directly proportional to both the mass of an object and the velocity of an object. The mass and velocity of the object are inversely proportional to each other. This equation also shows us that if an object is at rest, with velocity equaling zero, the object will have no momentum regardless of its mass.
A spinning object, too, has momentum. But because it is a two-dimensional, rotating system, we give it a different name than linear momentum. We call it angular momentum. Angular momentum (L) is a measurement of how much an object in rotational motion will resist having its rotation changed. It is
L = rmv
Here, r is the radius of the rotation, m is the mass, and v is the linear (or tangential) velocity. Again, like for linear momentum, mass and velocity are directly proportional to the momentum, but so, too, is the radius. The bigger the radius for a given mass and velocity, the greater the angular momentum. Again, just like for linear momentum, if velocity drops to zero, angular momentum drops to zero.
Angular momentum is demonstrated by gyroscopes. A gyroscope, like the one in the image below, can spin upright, balanced on its tip, because of its angular momentum. The amount of force that is required to change the gyroscope’s momentum greatly exceeds the force of gravity, enabling the gyroscope to balance seemingly against the force of gravity.
Bicycles, too, are demonstrations of angular momentum. Because they are wheels that are spinning, the bike tires have angular momentum and enable the bike to balance upright as it moves. This also explains why bikes become wobbly and hard to control as they slow down. As the tangential velocity of the bike tire decreases, its angular momentum decreases and it becomes easier for gravity to overcome it and cause the bike wheel to fall over, bringing the bike with it.
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René Descartes (1596–1650) was a mathematician and natural scientist. Notably, he was recognized as one of the founders of modern philosophy. His best-known statement is, “I think; therefore, I am.” In mathematics, he developed Cartesian (or analytic) geometry, which is how algebra is used to describe geometry. This became the conventional way to represent unknown numbers using x, y, and z and known numbers using a, b, and c. We continue to use Cartesian coordinates when graphing on the x and y axes. In addition, Descartes pioneered a standard notation using superscripts for exponents and powers (for example, 2 being used to represent x2 or x squared) It is this standard notation and Descartes’s work that laid the foundation for calculus, which was developed by Sir Isaac Newton, and theory regarding the law of conservation of momentum, in which he thought of motion on a straight line instead of as circular motion, as was previously described by Galileo Galilei. Descartes further described two additional laws of motion, and these became the bases for the laws of motion that we know today.
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Motion in physics describes the position of any object in relation to time. The distance that an object travels is the position where that object is in relation to time whereas the displacement of an object is the vector quantity that an object traveled. Speed is one way to describe the motion of an object as a scalar quantity. Once we know the speed and direction that an object is traveling, we use the term “velocity” to describe how much distance is traveled per second. Because the direction of the object is known, velocity is a vector quantity. An object maintains a constant velocity if there is no acceleration acting on the object. If an object maintains a constant acceleration, then the object’s velocity will increase or decrease exponentially. Because vectors are graphed using right angles, the Pythagorean are unknown.
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Even if you stand still, are you still moving?
When we describe motion, we use our relative position. However, even Earth itself is continuously moving in the universe. The force of gravity from the Sun and surrounding planets also has an impact on Earth’s velocity and motion. So even if we are standing still, we are continuously moving. While many in physics will use this information to determine how planets are moving or how the universe is expanding, when we calculate our displacement, velocity, and acceleration, we use our relative changes in distance here on Earth
6. How would calculating the velocity of a car that is culating v moving at a constant rate be different oving cons at than calculating the velocity of a ball thatt an is being thrown? elocity ball ty bal
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1. A car that is traveling for 15 seconds increases its velocity from 2.3 m/s to 4.5 m/s. What is the magnitude of the car’s acceleration while it travels for 15 seconds?
A. 6.8 m/s2
B. 0.68 m/s2
C. 0.44 m/s2
D. 0.15 m/s2
2. Which of the following graphs shows an object decelerating at a constant rate?
3. Which of the following is a scalar quantity and not a vector quantity?
A. Velocity
B. Acceleration
C. Speed
D. Displacement
4. If an object moves south for 10 m and east for 5 m, what is the overall displacement of the object? x 2 + AB y 2 2 + 52
5. A car moves at a constant velocity of 15 m/s for 2 minutes. How far does the car travel?
T = 20 x 60 = 120 X = X o + V o t = 0 + (15)(120) = 1,800 m
6. Two runners begin a race. Runner 1 is running at 1.5 m/s and accelerating at 0.2 m/s2 while runner 2 is running at 1 m/s and accelerating at 0.6 m/s2. After 10 seconds of sprinting, which runner is farther ahead?
o + V o t + 1/2at2 = 0 + (1.5)(10) + ½(0.2)(10)2 = 15 + 10 = 25 m o + V o t + 1/2at2 = 0 + (1)(10) + ½(0.6)(10)2 = 10 + 30 = 40 m Runner 2 is ahead.
Newton’s Three Laws
Objects stay at rest or in motion due to forces acting on them.
A force acting on an object can be calculated if you know the object’s mass and its acceleration.
Forces always come in pairs that are equal in size and opposite in direction.
1. Name and/or describe all the forces at work in the given situation.
2. How will the forces you named change the motion of the car? nge ge
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Sir Isaac Newton (1642–1727) was a brilliant mathematician and physicist. His work Mathematical Principles of Natural Philosophy (published in 1687) is considered one of the most important books in modern science. In it, Newton laid out an orderly world that behaved according to a single set of laws.
These laws, known as Newton’s laws of motion, are exact, quantitative descriptions of how objects move. Newton’s three laws of motion demonstrate the relationships between force, motion, acceleration, mass, and inertia.
3. Describe how an activity in your daily life would be y n iny different if the aily motion of objects could not be predicted. tion ts
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states that objects at rest will stay at rest and objects in motion will remain in motion at a constant velocity unless they are acted upon by an unbalanced force law is also called the law of inertia because it describes an object’s resistance to change in motion. In unless an unbalanced, outside force causes a change.
In order to understand the law of inertia, you need to remember that forces have magnitude (size) and direction. When the forces are equal in size and opposite in direction, the net force is zero, or balanced.
Consider an apple sitting on a table. An apple weighs about 1 newton (about 0.22 lbs.), which means that gravity is pulling down on the apple with 1 N of force, but the table is pushing back with the same amount of force. You can think of it as a math problem: 1 + -1 = 0. Therefore, the combined force, or net force, on the apple is zero. When the net force is zero, we say that there is equilibrium. Because there is equilibrium in this situation, the apple will not move until an inertia: objects at rest remain at rest until acted upon by an unbalanced force.
If an object at rest is to be put in motion, an outside force must be used to create an imbalance. In the pictures, you see two people pushing a heavy box from opposite sides. If they are pushing with equal force, the object will not move because the net force on the box is zero. If the two people were not pushing with equal strength, the box would move in the direction of the greater force because the net force would be greater than zero. Likewise, if they combine their forces and push in the same direction, then the net force will be greater than zero and the object will move in the direction that it is being pushed.
The soccer ball could potentially stay at rest forever unless an outside force—in this case, the kick—put it into motion. Once it is in motion, it does not need to be continually kicked because it will stay in motion until a force causes it to slow down or change direction. In this case, gravity pulls it down and the net stops its motion.
Force of gravity
Table force
An ect at rest stas at rest.
An ect at rest stas at rest.
An ect in tin stas in tin.
An ect acted n an nalanced rce changes seed and directin.
An ect acted n an nalanced rce changes seed and directin.
An ect acted n an nalanced rce changes seed and directin.
An ect acted n a alanced rce stas at rest.
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experiences, we do not usually witness something remaining in motion at a constant velocity because something is always acting to slow down the motion of objects. That something is friction. On Earth, friction will always be the unbalanced force that causes objects in motion to slow down and eventually stop. However, according to the law of inertia, objects in motion have the potential to stay in motion in a straight line and at a constant speed forever unless an outside force causes a change. One way to visualize this is to think about rockets.
The rocket boosters provide enough force to propel the rocket upward faster than the force of gravity can act to pull it back to Earth. As the boosters use up their stores of fuel and fall back to Earth, the space capsule atop the rocket continues traveling until it escapes the pull of Earth’s gravity. Once the capsule is in space, where it is no longer encountering friction with air, it will continue traveling in a straight line and at a constant speed without needing the engine to continue supplying force. If the engine to create an unbalanced force.
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equipped with safety belts, padded dashboards, and airbags. Consider driving along the highway at 60 mph. Your body is not in motion relative to the car. You might be sitting quite still inside the car, but in actuality, your body is traveling at a rate of 60 mph in the same direction your car is heading. But what happens if you slam on the brakes, causing a sudden unbalanced force that stops the car’s motion? Because of inertia (that tendency of objects to resist change in motion), your body wants to continue traveling forward at a rate of 60 mph. A seat belt or an airbag can provide an unbalanced force to slow and stop your forward motion. Without the seat belt or airbag, your body would continue moving forward until it encountered the dashboard. If the dashboard is padded, it might soften the impact somewhat. You might even continue traveling forward through the front windshield. Theoretically, you would then continue traveling forward through the air forever except that, on Earth, gravity would eventually provide the force to pull you down, and friction would eventually provide the force to stop your motion.
4. If a basketball is motionless in the aisle of a moving school bus, explain of a m how the ball will move when the bus stops.
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The law of inertia explains how and why objects stay at rest or in motion. Even toddlers know intuitively that forces are needed to set objects in motion. When a young child learns to stack blocks, they instinctively knock their tower down for the sheer joy of seeing the blocks scatter. Soon, they learn that if they hit the tower with more force, the blocks scatter even farther. Without even going to a high school physics class, a toddler knows the basic idea of Newton’s second law of motion, which describes the effect of net force on acceleration. Newton’s second law of motion states that a force that is applied to an object is equal to its mass multiplied by its acceleration. The law can be stated as a formula: force = mass x acceleration (F = ma).
• Forcenet is measured in newtons (N).
• Mass is measured in kilograms (kg).
• Acceleration is measured in meters per second squared (m/s2).
The second law is also called the law of constant acceleration. As long as a net force is acting on an object, it will experience constant acceleration. When the force is no longer applied, the object will stop accelerating in relation to that force.
you. Friction, which was mentioned earlier, is the force that resists the relative motion of two objects or substances sliding against one another. There is friction between two solid surfaces that are in contact air resistance, or friction with the air. Friction always works in the opposite direction of an object’s motion, and for this reason, it is the force that keeps objects from staying in motion forever at a constant velocity. Static friction is the friction between two surfaces when there is no relative motion between them. If you have ever tried to push a stalled car, you know how stubborn static friction can be. You pushed and pushed,
move. In that moment, you overcame static friction. Once the car was moving, you probably noticed that it was easier to push; that is because static friction is the hardest type of friction to overcome.
Tension
when it is pulled taut from opposite ends. Think of pulling on a rope during a game of tug-of-war. While tension is a pulling force, compression is a pushing force that squeezes an object together; think of pushing down on a spring. Gravity is another force with which you are very familiar because gravity is always at work here on Earth. In the earlier example of the apple on the table, you saw the downward arrow representing the pull of gravity. The equal and opposite force in the picture is called the “table force.” Actually, there is a name for that force; we call it the normal force, and it is the force of one surface that pushes back against an object that is pressed upon it. If you have watched clothes spinning in a front-loading dryer, you have seen the effect of another force. Objects can apply forces on each other as well. These forces are called applied forces. Think of a bowling ball hitting pins; the moving ball applies a force to the pins, putting them in motion.
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We can calculate the effect of forces on objects by using free-body diagrams. A free-body diagram shows an object and the directions and magnitudes of all the forces acting on it. A force is a vector quantity, meaning that it has magnitude (size) and direction. Because of this, we can represent forces with arrows, showing their direction and relative magnitude. Below are some examples of freebody diagrams.
Let’s review these diagrams a little closer and utilize them to calculate different types of forces. In diagram A, notice that the vertical arrows are equal in size and opposite in direction (note that the force labeled “weight” is the force of gravity). Because the normal force and the weight (force of gravity) are equal and opposite, their net force is zero, and they have no effect on the object’s motion. If these were the only two forces acting on the object, it would be stationary.
Notice that the arrow labeled “friction” is opposite in direction when compared to the applied force that the person is exerting as they push the crate, but the force of friction is smaller than the applied force. Because the applied force is greater than the force of friction, the object is in motion.
We can calculate the net force that is acting on the crate by adding the two forces.
100 N + -30 N = 70 N
The crate will accelerate to the right with a force of 70 N.
Using the formula F = ma and the example in diagram A, if we know that the net force that is moving the crate is 70 N, and if the mass of the crate is 14 kg, we can calculate the acceleration of the box by rearranging the formula F = ma to a = F/m. Then, acceleration would be calculated as follows.
a = 70 N / 14 kg
a = 5 m/s2
The force results in an acceleration of 5 m/s2.
FT
FG = mg
Diagram A
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Diagram B shows a stationary object suspended by a rope. The FG arrow shows the force due to gravity, and the FT arrow shows the tension force. Because the object is stationary, we know that the forces that are acting on it must be balanced. If we know the mass of the object, and the only other force that is acting on the object is gravity, we can calculate the tension force that is acting on the object using Newton’s second law (F = ma).
Diagram B
Given that the object has a mass of 10 kg, and acceleration due to gravity is 9.8 m/s2, calculate the tension force. First, calculate the force due to gravity using F = ma.
F = (10 kg) x (9.8 m/s2)
F = 98 N
Because the object is stationary, we know that the tension force is equal to the gravitational force in the opposite direction. Because FG is 98 N, FT must be -98 N. The free-body diagram shows that the forces have the same magnitude but opposite directions.
Analyze diagram C, which shows FG and FT. Based on our knowledge of free-body diagrams, we can make the following observations: There is a force due to gravity acting on the object, and there is a force due to tension acting on the object. Based on the magnitude of the arrows that indicate the forces, the tension force is greater than the force of gravity.
The examples in diagrams A-C show us what happens when objects have linear motion (move in a straight line). Imagine instead a mass (m) moving in a circle. Even if it is moving at a constant speed, the object is accelerating. How do we know that the object is accelerating? Remember that acceleration means change of velocity over time. And velocity is a vector quantity, meaning that it has both size and direction.
For an object that is moving around a circle at a constant speed, the size of the vector will remain the same, but the direction constantly changes. Therefore, the object is accelerating. In this case, the acceleration is directed toward the center of the circle. If an object is accelerating, then Newton’s second law of motion tells us that the object is experiencing a net force (F = ma). Because we know that objects accelerate in the direction of the net force, we know that when an object travels in a circular path, there must be an inward force acting on it. This phenomenon is called centripetal force and explains everything from the rotation of bicycle wheels to planetary motion.
FT
FG = mg
Flift
F g
Diagram C
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body diagram, which is shown in diagram D. In this diagram, an object (the small blue circle) follows a circular path (the dotted line). The blue arrow indicates the velocity of the object, the black line indicates a force that is acting on
force is indicated with the orange arrow. There are several formulas that can be used to calculate centripetal force.
centripetal force is F c = mv2/r, where m is the object’s mass, v is its speed, and r is the radius of the path that the object is following. This formula can be used when searching for the centripetal force that is acting on an object and the other known variables are mass, velocity, and radius.
The next formula calculates the centripetal acceleration of an object. This formula is a c = v2/r, where a c is the centripetal acceleration, v is the velocity, and r is the radius. The centripetal acceleration is needed when applying Newton’s second law to circular motion.
objects that are moving in a circle. That formula is Fnet = mac, where Fnet is the net force that is acting on the object, m is the mass, and a c is the centripetal acceleration.
Let’s review a couple of examples.
F = m v r ac = v r
Diagram D
Centripetal Fore
Centripetal ore Veloit is rit
Diagram E
Cirular Motion
Analyze the free-body diagram in diagram E to calculate the centripetal force of the yo-yo using the formula F = mv2/r. Plug in the values, and you get the following calculation.
F = (0.1 kg) x (2 m/s)2 / 1 m
F = 0.4 N
Another way to calculate centripetal force is to use Newton’s second law for centripetal force (F = mac). c) using the formula a c = v2/r.
a c = (2 m/s)2 / 1 m a c = 4 m/s2
Using the a c of 4 m/s2, you can calculate the centripetal force.
F = (0.1 kg) x (4 m/s2)
F = 0.4 N
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motion is that they explain things that we have
know intuitively that if a soccer ball is kicked with 270 N of force, it will accelerate more than if it were kicked with a force of 100 N. It is important to remember that when a force is applied to an object, it will accelerate for as long as the force is applied. When kicking a ball, for example, the force is applied for only a split second. As soon as the applied force is no longer acting on the object, it will begin to slow down due to friction. With a more forceful kick, creating more acceleration, the ball will travel longer and farther before friction stops it.
Intuition also tells us that if we use the same force on objects with different masses, the object with the smaller mass will accelerate more. A force of 270 N exerted on a soccer ball that weighs 450 g (0.45 kg) will result in an acceleration of 600 m/s/s (270 = 0.45 x 600). A 270 N force exerted on a 5 kg bowling ball will result in an acceleration of only 54 m/s/s (270 = 5 x 54). Among other reasons, this is why soccer is not played with a bowling ball!
5. To make a three-point shot in basketball, you have to shoot the ball with more force than n sh sketball, if you shoot an inside shot. How does Newton’s second law of inside motion prove that this is true?
6.
What supplies the centripetal force that keeps satellites in orbit around Earth?
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Newton’s third law of motion describes what happens when objects exert force on one another. The law states that for every action force there is an equal, opposite reaction force. In other words, when two objects interact, there will always be two forces at work: the action force and the reaction force. We call these forces an action-reaction pair.
Action-reaction pairs can be seen in the free-body diagram below:
forces should cancel each other out because they are equal and opposite. But this is a misunderstanding because although the forces are equal and opposite, they operate on objects of different masses, and Newton’s second law of motion tells us that the same force that is acting upon different masses will cause different accelerations. Therefore, action-reaction pairs can cause objects to start moving, stop moving, speed up, slow down, or change direction.
Action-reaction pairs make motion possible. Think about swimming. In order for a sea turtle
the water away from itself. This movement
reaction force is when the water pushes the turtle in the opposite direction (in this case, forward). The same is true of walking. To move forward, you must exert a force on the ground. Your foot pushes backward while an equal and opposite force—in this case, friction—pushes your foot forward.
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shuttle produce a force of around 5.5 x 106 N. Exhaust gases are produced in the rocket engine from the combustion of fuel, and the mass of the burning gases is expelled through the engine nozzles. This is the action force. The reaction force, which is equal in magnitude and opposite in direction, propels the space shuttle forward. Because the action force acts on the exhaust gases and the reaction force acts on the space shuttle, both accelerate in opposite directions. The acceleration of the exhaust gases and the space shuttle differ because their masses are very different.
These forces can be shown using a free-body diagram. In this case, the diagram shows that the action and reaction forces are equal in magnitude but act in opposite directions, resulting in the acceleration of the gases and the space shuttle.
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is to imagine jumping on a trampoline. As the child in the picture exerts a downward force on the trampoline (the action force), the trampoline exerts a reaction force that is equal in size and opposite in direction, causing the child to accelerate upward.
Or you can imagine a basketball bouncing off the
a reaction force that is equal and opposite. We see the ball bounce because the reaction force is strong enough to cause visible acceleration in the ball, which has a relatively small mass compared to Earth. We do not, however, see or feel Earth “bounce” off the ball because while the force is enough to cause visible acceleration of the ball, it is not enough to cause visible acceleration of Earth, which is much more massive.
7. What other action-reaction pairs are at work in the picture of the basketball game?
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of motion when he was only 23 years old. Like all scientists, his work was based on discoveries and theories that were made by earlier scientists, such as Aristotle and Galileo Galilei. Often, we think of scientists as being important because of their discoveries. In a sense, Newton did not discover the laws of motion because they already existed. He did, however, discover the means for expressing the laws using mathematics. Because the laws are founded on mathematics, they allow scientists to correctly predict how objects will behave when they are acted upon by forces. The laws formed the basis for what is known as classical mechanics: the theory that the motion of any observable object can be calculated with mathematical precision. Because of Newton’s laws, we can determine how long it will take for a car to stop if it is traveling at 55 mph. (On dry pavement, it takes about 300 ft., which is why your driver’s education instructor advises you to abide by the “3-second rule” when you are following another vehicle.) Newton’s laws allow us to understand and predict the motion of everything we can observe, whether we want to improve our golf swing or send a probe into deep space.
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Newton’s three laws of motion are evident all the time in the world around you. If your desk and all the rest remain at rest. Imagine a small earthquake occurring at the exact moment that you are reading second law: when net forces are greater than zero, masses accelerate in relation to the size of the net force. If, during the imaginary earthquake, you took shelter under your desk (which is a wise thing to do during earthquakes), you would be relying on the action-reaction pairs that are described in Newton’s third law. You would hopefully be protected as you hid beneath your desk because if an object fell down on your desk (action force), your desk would exert an equal, opposite reaction force (pushing upward on the fallen object), and that would prevent the object from landing on you.
Connect It
8. Which of Newton’s laws are at work in the image?
9. Predict what will happen to the motion of the car based on what you observe in the image.
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Summarize It
1. Which of the following describe(s) the way that a force can affect an object’s motion?
A. It can cause the object to speed up.
B. It can cause the object to stop.
C. It can cause the object to change direction.
D. All of the above
2. If a force of 500 N acts on an object that weighs 0.5 kg, what will the acceleration be?
A. 250 m/s2
B. 100 m/s2
C. 1,000 m/s2
D. 2,500 m/s2
3. If you jump from the back of a small rowboat into the water, how will the boat move relative to your motion?
A. The boat will move away from you.
B. The boat will move toward you.
C. The boat will stay still.
D. The boat will rotate 90°.
4. Using Newton’s second law of motion, explain why an overhand serve in volleyball is harder to return than an underhand serve.
The overhand serve uses more force than the underhand serve, so the volleyball accelerates more (travels faster), making it harder to hit.
5. Explain how diving off a diving board demonstrates all three of Newton’s laws of motion.
Answers may vary. A possible student response could include the following. Law 1: The diver or diving board are at rest until the diver jumps, and the diver stays in motion until gravity pulls them down. Law 2: If the diver jumps with greater force, they will accelerate more. Law 3: The diver exerts a force on the board that is equal and opposite to the force that the board exerts on the diver.
6. When an insect splatters on your windshield as you are driving, which of Newton’s laws best explains the results? Explain your reasoning.
Answers may vary; all three of the laws can be used to explain the situation. A possible student response could include the following: The insect was in motion until it hit the car (law 1). The force with which the insect hit the car was equal to its mass multiplied by its acceleration (law 2), or the force of the car hitting the insect caused its body to accelerate so much that it burst (law 2). The insect and the car experienced equal and opposite forces, but the reaction force caused the insect to accelerate more because it had a smaller mass than the car (law 3).
The Four Fundamental Forces
Imagine It
When astronauts went to the Moon, they had to learn to walk differently. They had to take steps that were more of a hopping motion. The reason for this change in walking was the gravity on the Moon. The Moon’s gravity is just of the gravity that we experience on Earth.
However, if we went to Jupiter, the gravity we experience would be much higher.
1. What if we lived in a world without gravity?
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Gravitational force and electromagnetic force were discovered long before the strong and weak nuclear forces that exist between all objects. Each of these forces acts on and governs the universe around us. Gravitational force governs the attraction between two masses whereas electromagnetic force governs the interaction between charged particles. Strong and weak nuclear forces govern the interaction between subatomic particles and particles in the nucleus. Nuclear forces work only over very small distances; gravitational and electromagnetic force can work over any distance but have less forces were thought to be separate from each other, but over time, they came to be viewed as parts of one unifying force.
The Standard Model seeks to describe all the interactions of subatomic particles. Force carrier particles caused by an exchange of these force-carrying bosons and has a boson that is particular to that force. Electromagnetic force is carried by the photon. Strong force is carried by the gluon, and weak force is carried by the W and Z bosons. Gravitational force’s carrier, the graviton, has been theorized but not
Carriers of the Four Fundamental Forces
2. How do nuclear forces differ from gravitational forces andgvitationalelectromagnetic forces?troma roma
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Nuclear forces were discovered in the 20th century, when we began to work with the atom. Strong nuclear forces are between protons and neutrons. Weak nuclear forces occur between radioactive particles and electrons that do not experience strong nuclear force.
Strong nuclear force is the strongest force of the four. It holds the fundamentals of matter together. Part of the strong nuclear force keeps protons and neutrons, the nucleons, together in the nucleus of the atom even given the strong repellent force of the positively charged protons. This force acts over a very small distance, though particles have to be within the diameter of a proton of each other.
This force differs from the other forces in that it gets weaker as the particles get closer together. This force is actually strongest when the particles are farthest apart. Force-carrying particles called bosons, in
3. Why do protons stay together in the nucleus ygether even though they all have a positive charge? yall
Nucleons: held together by nuclear binding energy
Neutron Proton
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get close enough to each other, the nuclei fuse with each other. This process causes the nuclei to lose mass and release large amounts of energy and is called fusion. This is different from the process of
two new nuclei break apart, they cause other nuclei nearby to break apart, creating a chain reaction. This releases massive amounts of energy, like what is found in an atomic bomb. The nucleus can be broken apart when it is bombarded with a neutron or gamma rays. These processes take advantage of a mass defect. The mass of the nucleus is less than the mass of the protons and neutrons. The binding energy actually accounts for the extra mass. The idea is that small amounts of mass can be converted into large amounts of energy.
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Weak nuclear force is responsible for particle decay or turning one subatomic particle into another. If a neutrino comes too close to a neutron, the neutron turns into a proton and the neutrino turns into an electron. When subatomic particles come very close to each other, they can exchange bosons, or force-carrying particles. This exchange of W and Z bosons, which are found in weak forces, causes the subatomic particles to decay into new particles. This force is attractive only and is the secondweakest force.
Carbon dating by archaeologists to determine the age of formerly living artifacts measures this decay. Naturally occurring carbon-14 has six protons and eight neutrons in the nucleus. Over time, one of those neutrons decays into a proton to make nitrogen-14, which is made of seven protons and seven neutrons. The decay rate of carbon-14 is predictable and can be measured. Weak nuclear force initiates the fusion reactions that power the Sun. Two protons are smashed together, and the strong force binds them into a helium atom that is unstable because the nucleus is missing two neutrons. The weak force caused by the pair of protons initiates beta decay that eventually creates the more stable helium atom with two protons and two neutrons. Weak nuclear force is different from the other forces also. When the distance increases, the force decreases exponentially. There is no inverse proportionality with distance and force, even of the square of the distance.
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Gravitational force acts between all objects that have mass. This is why pecans fall from trees and why the Moon orbits Earth. Sir Isaac Newton is thought to have come up with the idea of gravity based on an apple falling from a tree. He described this force as the attraction between two objects. Based on the theory of relativity, Albert Einstein had a different theory. He said that as you approach a large object in space, it will bend space and time around it, creating a sort of hole that other objects fall into. Imagine a mattress with a bowling ball in the middle. Anything placed on the mattress that is smaller than the bowling ball will roll toward the bowling ball. Anything with more mass than the bowling ball will create its own indentation that objects will roll toward.
Gravity is only an attractive force. The farther away from an object you get, the less pull it has on you. Gravitational force is inversely proportional to the square of the distance between two objects. If you double the distance, you quarter the force exerted. The larger the mass of the object, the more pull it has. The closer you get to the bowling ball on the mattress, the more likely you are to fall or slide toward it. Gravitational force is directly proportional to mass. If you double the mass, you double the force. No matter how strong gravity feels, it is the weakest of the four forces. Think about how easy it is to lift your shoe from the ground.
4. What are some ways that gravity is overcome daily? ay
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Electromagnetic force is the attraction between unlike electric charges and the repulsion between like electric charges. This force is also called the Lorentz force. This is the force that causes positive protons to be attracted to negative electrons. If the positive or negative charge is large, then the attraction will be large. Theoretically, this attraction continues no matter the distance, but the farther away the objects get from each other, the smaller the effect of the attraction.
This force is the interaction of the electrical force and magnetic force, which are now considered components of electromagnetic force. Electrical force is experienced by objects even if they are stationary, but put the objects in motion and they experience the magnetic force. As the objects move, a magnetic force is created around them. This force is carried by the photon, just like the particle component of light. They are the same particle, but one is visible and the other is not.
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get pulled down to the ground due to gravity because of the repulsion between the atoms of the pan and atoms of the stovetop. Friction is the repulsion of two objects rubbing against each other. Solid objects hold their shape because the negative and positive charges of the atoms hold them together. Air resistance between an airplane and the atmosphere helps keep the plane in the air. Elasticity, molecular bonds, tension, air drag, and normal force are all phenomena that are related to electromagnetic force
5. How do magnets attach papers to a refrigerator?
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Physicists are trying to unify all four forces under a unifying theory. They theorize that all four forces scientists would have a theory of everything. The theory of everything would explain the entire universe. to be correct. They are just looking for proof that they are correct. They have been able to unify gravity that acts on a macro level within the universe and quantum mechanics that act on a microscopic level.
Stephen Hawking (1942–2018) is generally thought of as one of the most recognized scientists of the current era. In 1963, he was diagnosed with amyotrophic lateral sclerosis (ALS), which is a motor neuron disease. In 1966, he obtained his PhD in applied mathematics and theoretical physics specializing in cosmology and general relativity from Trinity Hall, of the University of Cambridge. Hawking was initially controversial. His idea that black holes emit radiation, generally called Hawking radiation, was
Brief
History of Time spent 237 weeks on the bestseller list
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There are four fundamental forces of nature. Gravitational force, according to Einstein, is a force that bends space and time around objects and is dependent on mass and distance. Electromagnetic force is dependent on the charge that particles carry and the distance. Particles with the same charge repel each other, and particles with opposite charges attract each other. Strong nuclear forces bind protons and neutrons together. Lastly, weak nuclear forces govern the radioactive decay of subatomic particles. Scientists hope to unify all four forces into one force in the theory of everything to explain the universe.
Connect It
How does force impact our universe?
The four fundamental forces—gravitational, electromagnetic, and strong and weak nuclear forces—and their interactions govern the entire universe.
6. How does force impact our universe?
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1. Which of these is not a fundamental force?
A. Gravitational force
B. Normal force
C. Electromagnetic force
D. Weak nuclear force
2. Gravity is due to–
A. the pull between Earth and the Moon.
B. the pull between an electron and a proton.
C. the pull between objects with mass.
D. the pull between positive and negative charges.
3. What is the ranking of the forces from strongest to weakest?
A. Strong nuclear, gravity, weak nuclear, electromagnetism
B. Weak nuclear, electromagnetism, gravity, strong nuclear
C. Gravity, electromagnetism, weak nuclear, strong nuclear
D. Strong nuclear, electromagnetism, weak nuclear, gravity
4. What is the correlation between gravitational force and distance, and how does it differ from the correlation between gravitational force and mass?
5. How are magnetic force and electric force connected? 6.
Universal Gravitation
Have you ever wondered about the forces between objects? Consider a game of billiards. What forces are acting between the balls during the game?
Effect of Mass
Stronger Weaker
Effect of Distance
Stronger Weaker
1. Use the graphic to guide your thinking. What scenario would create the most gravitational pull between ost gravita g two objects?
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Newton’s laws of motion discuss the forces experienced by bodies here on Earth but can be applied to celestial bodies. states that a body must remain at rest or move in a straight line at constant speed unless it is acted upon by an outside force. Neither the object at rest nor the one traveling at constant speed are accelerating; therefore, objects do not accelerate unless acted upon by an external force. states that if such a force acts upon a mass, then acceleration occurs. This relationship is given by the formula F = ma where the force produced is the product of both mass and acceleration. This also explains why a force applied to a more massive object would accelerate less than one with less mass. states that when one body exerts a force on a second body, the second body exerts an equal and opposite second one, it is exerting a tension force on the second canoe. The second canoe exerts a force back
force for falling objects and the motion of the planets. Newton made the great discovery of , or the mutually attractive physical force between any two masses. He then went on to apply this concept to what is known as , which states that every object in the universe attracts every other object with a force directed along the centers of the two objects. His universal law of gravitation further states that the amount of gravity that something possesses is proportional to its mass and distance between it and another object. Newton used this law, along with his laws of motion, to explain motion of various types such as falling objects and planets. The universal law of gravitation coupled with circular acceleration keeps objects, such as Earth, in orbit. The law of universal gravitation can be explored mathematically using the following formula where F is the attractive gravitational force between two objects of mass m1 and m2 separated by some distance r; the constant G is called the universal constant of gravitation with a value of 6.67 x 10-11 m3kg-1s-2.
F = force measured in newtons (N)
G = gravitational constant (6.67 x 10-11 m3kg-1s-2)
m1
m2 = mass of second object in kilograms (kg)
r = distance between two objects in meters (m)
You and your best friend each have a mass of 60 kg. You are standing 20 cm away from each other. Calculate the gravitational attraction force between you.
G = 6.67 x 10-11
m1 = 60 kg
m2 = 60 kg
r = 20 cm (convert to meters)
2. What would happen to Earth’s gravity if we were closer to the Sun?we ravity if we we
3. Notice how small the force is between you and your best s betweeny etw friend. How could b y you increase the force?incre cre
G =6 67 x 10-11
m1 = 40 kg
m2 = 20 kg
r = 10 m
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G = Universal gravitational constant = 6.67 x 10-11 N • m2 kg2
m
What gravitational force does the Moon produce on Earth if Earth has a mass of 5.98 x 1024 kg, the Moon has a mass of 7.34 x 1022 kg, and their centers are 3.88 x 108 m apart?
G =6.67 x 10-11
m1 = 5.98 x 1024 kg
m2 = 7.34 x 1022 kg
r = 3.88 x 108 m
4. What units need to be used for force, mass, and distance?
The between two objects is directly proportional to their masses. More mass means more force. If the mass of one object is doubled, so is the force. The gravitational force between two objects will decrease as you move the objects farther apart and increase as you move them closer together.
Direct and Inverse Relationships in the Law of Universal Gravitation
Mass and gravitational force are directly proportional. When the mass is doubled, the force of gravity is doubled.
Gravitational force is inversely proportional to the square of the distance between objects. If distance is doubled, the force of gravity is ¼.
5. How could you change the mass of y hange the mas e t give you four times the force? you four fou
this time, Earth was accepted as the center of our solar system. Copernicus further described the orbits of planets around the Sun as traveling in a circular orbit at constant speeds. Johannes Kepler wrote his Brahe. After further observations, he added a third law ten years later. was explains how every planet revolves around the Sun with the Sun as one focal point of its elliptical path. As the planet follows this path, its distance to the Sun is constantly changing , or second law, states that there is a line segment connecting the planet and the Sun that sweeps down when they are farther away from the Sun along their orbits. Therefore, the orbital speed changes depending on the distance from the Sun. that the square of the time it takes a planet to orbit the Sun is proportional to the cube of its average distance to the Sun. This ratio is the same for every planet and is used to estimate orbital periods or the average distance from the Sun for planets in our solar system. Collectively, describe the motion of planets traveling around the Sun.
The law of universal gravitation states that every piece of matter is attracted to every other piece of matter and the force is directly proportional to their masses but inversely proportional to the square of the distance between them. This law applies to all objects with mass, big or small. The law of universal gravitation applies to the planets as much as it does to the falling of an apple to Earth’s surface. Recall Newton’s second law of motion. Forces cause acceleration. Gravity is a force with an acceleration of 9.8 m/s2. The law of universal gravitation is based on the balancing point of the masses of two objects in a straight line. When that line becomes curved, the center of mass does not change, but the distance between the objects may vary, as it does with the planets in our solar system
Kepler’s Three Laws of Planetary Motion
applying uniform circular motion. Objects traveling in a circular path are constantly accelerating toward on the planet that is directed toward the center of its orbit, the Sun. Newton’s second law allows for determining the magnitude of this force in terms of mass and acceleration of the circular motion (a = v2/r), which is the force required to keep Earth traveling on its circular path. Newton’s third law implies that if Earth is attracted to the Sun, then there must be an equal and opposite force attracting the Sun to Earth. Since the Sun’s movement is so minuscule that it can be neglected, the force of attraction between Earth and the Sun must be dependent upon mass.
Orbitals may be altered due to collisions with or gravitational effects from other objects in the solar system. Asteroids and comets have been observed to change course in response to traveling too close to planets or their moons. In 1994, the Shoemaker-Levy 9 comet was traveling too near Jupiter, which into Jupiter’s atmosphere.
6. How do you think planetary orbits y impact planetaryeclipses? orb orb
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Katherine Johnson (1918–2020) was a female African American many spacecrafts. She loved math and studied geometry for the purposes of space travel. The National Aeronautics and Space Administration (NASA) hired Johnson as one of its “human computers” in 1953. In 1962, the United States decided to send humans to the Moon, but there were many mathematical obstacles during their journey. Johnson was part of a dynamic mathematical team whose calculations helped send astronauts to the Moon and back. The movie Hidden Figures highlights the story of the team of female African American mathematicians who served a vital role in NASA during the early years of the US space program.
The Big Picture
Gravitational interactions exist not only between Earth and other objects but between all objects. The amount of gravitational attraction that is present is directly proportional to the product of the objects’ masses. In Newton’s law of gravity, we also notice that mass is a crucial quantity. More mass means more force.
Connect It
7. Solve the given equation using the law of equat universal gravitation. using the law
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What variable(s) can change the force between objects using the law of universal gravitation?
Mass of objects
Distance of objects
Both A and B
None of the above
The gravitational force between two objects will _____________ as you move the objects farther apart.
increase
decrease become inverse vary
Which of the following has an incorrect unit?
Mass = J
Force = N
Distance = m
All are correct.
Explain how mass can change the amount of force that is present between two objects using the law of universal gravitation.
The more mass an object has, the more force it will have. The law of universal gravitation has two objects present. The larger the mass(es), the larger the force that will be present.
How can the law of universal gravitation apply to all objects on Earth?
All objects that exist have mass. Objects on Earth are also all experiencing a gravitational pull toward Earth and other objects.
How does the gravitational force change as objects become closer together or farther apart?
The closer together that objects are, the stronger the gravitational force; as the objects get farther apart, the gravitational force becomes weaker
Coulomb’s Law
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If you rub a balloon on your shirt then hold it near your hair, your hair will be attracted to the balloon, as shown in the picture. Would the balloons still attract your hair if your hair were shorter? How far away will you be able to hold the balloons and still have your hair be attracted?
1. What factors do you determinethinkhow th hair is attracted to a balloon?
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You have probably heard the phrase “opposites attract.” This is the concept that explains why hair is attracted to balloons in the picture above. But what is opposite about the balloons and the hair?
The balloons and the hair, like all matter, are made of atoms Atoms are made of positively charged protons, neutral neutrons, and negatively charged electrons. Neutral atoms have no electric charge and are composed of equal numbers of protons and electrons. However, not all atoms are neutral. While the protons and neutrons are tightly held in the nucleus of the atoms, the negatively charged electrons on the outside of the atoms can be removed, resulting in an imbalance of charges. Atoms with fewer electrons than protons have a positive charge, but if there are more electrons than protons, they will have a negative charge. All charges are the result of moving electrons, and the resulting electric charges exert forces.
Electricity cannot be seen directly, but it is a physical phenomenon associated with the movement of charged particles. Therefore, lightning or sparks are the by-product of this movement. Charged particles are tiny particles that carry an electric charge that can be positive or negative, such as protons and electrons.
When you rub a balloon on your shirt, electrons are transferred from your shirt to the surface of the balloon, giving it an overall negative charge. This accumulation of electric charge on the surface of an object is called static electricity When this negatively charged balloon is brought near a neutral object, like hair or a wall, it will draw the opposite (positive) charge toward it, causing the two objects to be attracted to each other. This is called electrostatic attraction. Eventually, the accumulated charges will dissipate, resulting in the objects returning to their neutral state and no longer being attracted.
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You may have experienced this same phenomenon when removing clothes from the dryer. As clothes tumble together, electrons are rubbed from some and onto others, creating an opposite charge and causing them to “stick” together. Sometimes, the charge dissipates quickly. Have you ever felt a small shock when touching something after walking across a carpet? When your shoes rub on the carpet, electrons are rubbed off the carpet and accumulate on the surface of your body. When you touch something conductive, the electrons can be suddenly transferred to the object, resulting in a small shock
2. Why will a balloon not attract 2. Why w hair unless it has been rubbed on
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Like Charges Repel
What would happen if two negatively charged balloons came near each other? If opposites attract, what would happen if the charges were the same?
Though opposite charges attract, like charges repel. A Van de Graaff generator is a machine that removes electrons from an inner belt, causing an accumulation of static charge on a metal globe. If you get too close to the metal globe while it is charged, the charge could be suddenly attracted to you and you could get a shock as the charge transfers to you. But if you were to stand on something to insulate you from the ground and touch the globe as it is starting to charge, the charges would accumulate on the globe and on you.
As the static charge accumulates on the hair of the student in the picture, the strands of hair all accumulate the same charge and repel each other, causing the top hairs to move as far apart from each other as they can. This electrostatic repulsion is the principle behind how an electroscope works.
Charges within matter can be altered by separating positive and negative particles or removing electrons from one medium and transferring them to another by means of friction or other methods. However, charges are not created or destroyed through these processes. The total charge remains constant, thus obeying the law of conservation of charge.
As shown in the top of the diagram, if the two leaves that are hanging near each other are neutral, they neither attract nor repel. When the leaves have the same charge, whether positive or negative, they repel. If the leaves are attached to a metal ball when in the presence of static electricity, the electrostatic charge will be transferred to the leaves and the leaves will repel.
The force of attraction or repulsion between objects with stationary electric charges is called the electrostatic force.
3. How do you think the amount of static charge would affect the leaves static charge w atic chag of an electroscope?
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Charles-Augustin de Coulomb was a French physicist who studied electrostatic attraction and repulsion in the 1700s. His work resulted in the description of electrostatic force known as Coulomb’s law, which states that the force of interaction between charged particles is based on the strength of the charges and the distance between the particles.
The electric charges we have discussed come from protons and electrons. These particles and their charges are very small. The SI unit used to measure the charge is a coulomb (C). One coulomb is equal to the quantity of electricity conveyed in 1 second by a current of 1 ampere. This is equal to the charge of 6.24 x 1018 protons or electrons. Therefore, the charge of just one proton is 1.6 x 10-19 C, and the charge of an electron is -1.6 x 10-19 C.
According to Coulomb’s law, the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The accumulated static charge on objects is usually much less than 1 coulomb, so it is measured in microcoulombs (μC = 10-6 C) or nanocoulombs (nC = 10-9 C). If the objects are repelling each other,
are sometimes dropped when they are entered into an equation to avoid confusion, and it is simply noted if the force is one of attraction or repulsion. The distance is measured between the centers of the objects, not their surfaces, and is measured in meters.
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balloons were both rubbed on the same shirt and accumulated the same charge of -5.20 nC. If the distance between the centers of the balloons is 42.3 cm, what is the electrostatic force of repulsion between them? Note: Convert nC to C and cm to m to use in the equation
k c q1q2 d2 F =
2:
charged balloon with a force of 0.0597 newtons. How close are the two balloons? Note: Convert nC to C; the value for force is entered as a negative because it is an attractive force.
(8.99 x 109 Nm2/C2) (-5.20 x 10-9 C) (-5.20 x 10-9 C) (0.423 m)2 F = 2.43 x 10-11 Nm2 0.19 m2 F = F = 1.36 x 10-6 N k c q1q2 F d2 =
k c q1q2 d2 F =
0.0 d2 = d2 = 4.19 m2 d = 2.05 m
Example
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If you are familiar with Newton’s law of universal gravitation, you may notice that Coulomb’s law is very similar.
Both forces act on protons in a nucleus. They are attracted to each other because of their masses (Newton’s law of universal gravitation), but they repel each other due to their like charges (Coulomb’s law). It would seem that the gravitational force must be stronger than the repulsive force because the protons stay together in the nucleus. But this is not the case. The repulsive force between two protons in a nucleus due to their charges is 4.1 × 1042 times stronger than the attractive gravitational force between them due to their masses. Protons staying together in the nucleus despite this strong repulsive force is what led scientists to propose that strong nuclear force binds together protons and neutrons in a nucleus.
4. What is the difference between a positive force value and a negative force value in negat nd ag Coulomb’s law?
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he electric ield directin is alas directed aa r sitive srce charges and tard negative srce charges.
Charged particles exert forces on each other, and the strength of those forces depends largely on their distance apart, much like Coulomb’s law. When electrons move closer to the region around other electrons, the charges repel. When they move closer to the region around protons, the charges attract. The repulsion or attraction is greatest when these regions are close together. An is the region surrounding each charged particle and is indicated by arrows to signify the amount of force experienced by each particle. Arrows point toward negative charges and away from positive ones. The length of the arrows indicates the relative strength of the electrical force and depends on the distance
together but would diminish when that distance increased.
The potential energy of any object on Earth is a product of its mass, height, and the gravity experienced by the object. Therefore, gravitational potential energy is the energy stored within an object due to its position and useful for doing work. As an object is lifted higher, work is done to the object, and it increases its gravitational potential energy, which can then be transferred to do work by the object. In a very similar way, the electric potential energy of a particle is the product of its charge, distance
together, much like a falling object increases velocity due to gravity. The difference in electric potential energy charges are brought together, the potential energy increases. However, if two different charges are brought together, then the potential energy decreases. This should make sense, since similar charges repel each other, which produces kinetic energy due to an increase in that potential energy.
produced by these interactions. Both gravitational and electric potential energy are inversely related to the distance between objects or particles. While gravitational energy depends on the mass of both objects, electric potential energy is contingent on their charges.
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all ravitatinal tential nerg lectric tential nerg lectric tential energ increases. A
ravitatinal tential energ increases.
5. How might mig . How mg be similar to
Fabiola Gianotti, PhD, and the CERN Particle Accelerator
Fabiola Gianotti was born in Italy in 1960. She received her PhD in experimental particle physics from the University of Milan in 1989. Gianotti began working as a research physicist at the European Organization for Nuclear Research (also known as CERN) in Switzerland in 1994. She worked on detector development and construction, software development, and data analysis. In 2009, she was promoted to project leader and spokesperson for the ATLAS Experiment. She played a major role in the discovery of the Higgs boson and presented its discovery to the world in 2012. For her work, Gianotti has received many prestigious honors and awards. She became an honorary professor at the University of Edinburgh
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Protons and electrons have opposite charges. When objects rub against each other, they accumulate static charges. Charged objects exert an electrostatic force on each other. Like charges will repel while opposite charges will attract. The strength of the electrostatic force depends on the charges of the objects and the distance between them, as described by Coulomb’s law.
Connect It
What factors do you think determine how hair is attracted to a balloon?
attract hair. Because the balloons and hair are attracting each other, they must have opposite electrostatic charges.
6. According to Coulomb’s law, what . Ac factors affect how strongly a balloon and hair will be ba ngly attracted to each other?
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Summarize It
1. When two objects rub together, which atomic particle is being transferred?
A. Protons
B. Neutrons
C. Electrons
D. Nucleus
2. For a Van de Graaff generator to work, which charge(s) must accumulate on the metal globe?
A. Positive only
B. Negative only
C. Either positive or negative
D. Both positive and negative
3. Which charge would create the greatest electrostatic force?
A.
B. -6.42 μC
C.
D. -9.03 nC
4. Explain why a balloon that is electrostatically attracted to a wall will eventually fall away from the wall.
The balloon is electrostatically attracted only if it has accumulated a static charge Once in contact with the wall, the static charge will begin to dissipate. When the balloon and wall are no longer oppositely charged, they will no longer be attracted to each other, and the balloon will fall away.
5. Why does an electroscope operate by electrostatic repulsion and not attraction?
The two leaves of an electroscope receive the same electric charge when in the presence of static electricity. Because they both have the same charge, they repel and not attract.
6. What is the electrostatic force of repulsion between two objects with charges of 2.48 μC and 4.31 μC that are located 3.92 cm apart?
Electric Circuits
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Think about things you might use in your daily life that contain electric circuits. This list can get long very quickly because circuits are everywhere around us. Circuits light lamps, cook food, open automatic doors, and send and receive calls on mobile phones.
1. Where do you see electric circuits . y in the room around you right now?
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A current
current is measured in units of amperes (A), or amps, and can be calculated if you know the amount of charge (measured in coulombs) divided by the amount of time (measured in seconds) it takes for a charge to move a given distance. So, 1 A = 1 C/s.
the number of free electrons available in the material. These electrons can move from a valence band into a conduction band when excited. Conductors free electrons within the material. Conductors have a full valence band, a conduction band with free electrons, and many empty energy levels. When energy is added to a conductor, the electrons move easily between energy levels. This means that an electric current can also move easily within the conductor. Common examples of conductors include metals such as copper, aluminum, brass, tin, gold, and silver.
Semiconductors
valence band of semiconductors is full, but they have an empty conduction band at low temperatures. Electrons can jump from the valence band to the conduction band when thermal energy or light energy is added. The conductivity will increase as temperature increases, since more electrons are jumping bands. Common examples of semiconductors include crystalline solids such as silicon, germanium, and gallium arsenide.
Insulators
the electrons to make the jump between the bands. Also, the electrons within an insulator are tightly bound and do not move easily. This means that an electric current cannot move easily with the insulator. Common examples of insulators include plastic, rubber, glass, and wood.
A circuit provides a path for a current to travel and can be described as either open or closed.
on. There is a starting line, a lane for the car to closed circuit that a current travels on. Circuits can also be described as alternating current (AC) or direct current (DC). An AC circuit has a current in a given cycle. For example, wall plugs in the United States are AC circuits that have 60 cycles of oscillation per second. AC circuits in Europe and Asia have 50 cycles of oscillation per second. DC circuits only allow the current to travel in one direction. The remainder of this scope will focus on DC circuits.
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The only way for an object to move is if an unbalanced force is exerted on it. The same is true of
look closely enough, you can see a “+” and a “–” on opposite ends of the battery. These signs indicate the two terminals of that battery. These terminals are the origin of the force that is needed to get charges moving
The terminals of a battery have an electric potential difference between them as a result of chemical reactions happening in the battery. The terminal with the “+” has a high electric potential while the “–”
diagram, you see a battery indicated with the symbol below.
is referred to as voltage and measured in volts (V). Voltage is always positive as it measures the difference between high electric potential and low electric potential.
2. How is electric potential important in electronspushingthrough n pushg a tronscircuit? t
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test charge, not an electron. Electrons, however, are the actual carrier of the charge in a circuit. Think back to chemistry and how metals have a sea of electrons that are able to move from place to place. This is why metal is a good conductor; it allows the electrons the ability to move easily. However, the path an electron has to take as it moves is not so easy. As the electrons move, they collide with the atoms of the wire, resulting in a change in the direction of the motion. This results in resistance, letter omega).
Resistance is impacted by several factors. These include the length, thickness, and type of wire. The longer a wire is, the more atoms that an electron will encounter, resulting in higher resistance. Have you ever noticed how some electric cords are really thin while others are much thicker? Which wires have high resistance? The thin wire has much higher resistance because an electron has less space to travel.
versus a small pipe. Some metals, such as silver and copper, have much lower resistance while others, such as lead, have higher resistance. This is why most electric wires are composed of copper.
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So, we know now that voltage provides the energy that is needed for a charge to move from a low–electric-potential terminal in a battery to a high–electric-potential terminal, which, in turn, allows a current, and resistance in a circuit. His experiments proved that there was a proportional relationship between the current and resistance and the voltage. Essentially, if you were to increase the resistance and keep the current the same, the voltage would have to increase. This led to the mathematical relationship of voltage, current, and resistance called Ohm’s law
Voltage = Current x Resistance
V = IR
law allows us to manipulate the formula so that the current can be determined if the voltage and resistance are given.
Current = Voltage/Resistance
I = V/R
found that, for many materials, the resistance is constant over a wide range of voltages. For these materials, a graph of applied voltage versus current shows a straight line. Resistors that stay constant into a circuit, we can increase the voltage through the circuit and the current will increase, but the resistance will always stay the same.
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through a wire provides no use for a household. However, adding components to the wire, such as a light bulb, allows for the transformation of the energy in the current into energy that we can use. This leads to power into different energy by an element in the circuit. Electric power is the rate at which energy moves through a circuit. The moving current in a circuit provides power that we can use in many devices. This power can appear as light, heat, or mechanical power, such as in an automatic door.
consumed by an element in a circuit as well as the amount of time needed for the consumption to (1 watt = 1 joule/second).
Power = Energy/time
P = E/t
Power can also be calculated using current and voltage by multiplying the two measurements
Power = Current x Voltage
P = IV
3. Explain the difference between voltage, power, and voltage,resistance. pow
Types of Circuits
By adding different elements to the circuit, you have lots of different ways that you can set up those circuits as long as there is a closed path for the electrons to travel. Elements that can be added to circuits can be resistors, capacitors, or light bulbs because they are good indicators of as resistors.
Circuits are drawn using diagrams with symbols. Here are the symbols you will need to be familiar with to interpret and draw your own diagrams. Common devices have complicated circuits inside them. We can break many circuits down, though, series circuit
parallel circuit, a current two points.
A series circuit may have several circuit elements in it, but the elements connect one after another along a single path. That is, the current must a series circuit.
As discussed earlier, electrons transfer energy as they move from the beginning to the end of the circuit loop. We call this a voltage drop. We can use an instrument known as a voltmeter to measure the voltage drop through different locations in a circuit. For example, if one end of the voltmeter is placed on the positive terminal of a battery and the other end is placed on the negative terminal, a voltmeter should show a voltage drop that is equal to the total voltage of the battery. However, there will be a voltage drop as electrons move across each element in the
drops across each element in the circuit equals the total voltage in the circuit. This property is due to the conservation of energy. Essentially, you can summarize it by saying that the total energy that is transferred from the charges that are traveling in the circuit is equal to the voltage drop at each element
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R1 and R2, the voltage drop across each resistor is V1 and V2 circuit is V, then you can calculate with the formula below.
V = V1 + V2 +...
R1 and R2, the current would be the same.
1 2
When we think of the resistance of elements in a circuit, we can think of many resistors combining to act like one big resistor. This idea is known as equivalent resistance. The equivalent resistance, R eq, of resistors in a series circuit is the sum of the individual resistances.
R eq = R1 + R2
The total resistance increases as you connect more resistors in a series.
To solve problems in series circuits, it may be helpful to follow these steps:
• Calculate the equivalent resistance, R eq, of the circuit. This is the sum of each resistor in the circuit.
R eq = R1 + R2
• I, in the circuit is equal to the voltage, V, of the power source divided by the equivalent resistance, R eq, of the series resistors.
eq
• with resistors R1 and R2, the voltage drop across each is calculated individually. Remember that 1 2 and V = V1 + V2.
V1 1R1
V2 2R2
• Power (W) equals current multiplied by voltage.
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multiple paths between two points. The two paths are said to be parallel.
What is the voltage across a parallel pair of resistors? Conservation of energy tells us that voltage changes by the same amount along each parallel path. Therefore, the voltage across parallel resistors is the same for each path and is equal to the applied voltage from a battery or other source.
For example, in a parallel circuit with two resistors, the total voltage in the circuit, V, is equal to the voltage drop across each resistor, V1 and V2, such that Vtotal =V l V1 =V2V .
= 6V, V1 = 6V, and V2 = 6V.
Equivalent resistance in parallel circuits is different than in series circuits. For parallel circuits, adding more resistors on more branches will decrease the equivalent resistance of those resistors. To help you
road with the same number of cars traveling on it, the road will not seem as busy because cars have a choice of lanes to drive in. The same is true of parallel circuits. The current has several paths it could travel on while still getting to the same destination.
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the equivalent resistance equals the sum of the reciprocal of each individual resistor in parallel circuits. The equation is below.
of the equivalent resistance equals the sum of the reciprocals of all the resistances. Consider a parallel circuit containing two resistors: R1 2 is 9V.
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circuit has no resistance, all the current will follow that path and the other elements will not receive any current, meaning that they will not work.
Itotal
current on one branch of the circuit, you will use the resistance for that individual branch.
Based on what we have calculated so far, Itotal, I1, and I2 for our 9V circuit would be calculated as shown below.
The total current is also equal to the sum of the current through each branch of the circuit.
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• Calculate the equivalent resistance, Req, of the circuit using the reciprocal relationship.
• equivalent resistance, Req, of the series resistors.
4. How are series and parallel circuits different from each other?
Magnets, Magnetic Force, and Magnetic Fields
A magnet, or magnetized material, is an object with a north pole and a south pole that produces a Magnetism results from the movement of electrons in a material. Usually, this movement is in the form exert forces on other magnets. As a rule, like poles repel each other and opposite poles attract each magnet. As Earth spins, the core generates a magnetic north pole and a magnetic south pole. A compass
and Magnetic Fields
electricity and magnetism are fundamentally related to one another. This relationship is known as
This principle can be used to create an electromagnet. An electromagnet is a temporary magnet that is created by an electric current. An electromagnet typically has a ferromagnetic core, such as iron. A simple electromagnet can be made by wrapping wire around an iron nail, as shown in the image above. produced. You can also increase the strength of the electromagnet by increasing the number of windings
observe these electromagnets on cranes in junkyards.
induction because a moving magnet can induce a current in a wire even if no battery or other voltage source exists. The induced voltage in a circuit can be measured with a voltmeter (voltage is measured in volts). The induced current, or amperage, in a circuit can be measured with an ammeter (the current is measured in amperes). As you will learn in the next section, electromagnetic induction plays an important role in the generation of electricity around us.
Battery +
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application is a motor. Motors are devices that cause objects to move when electricity is applied. For example, a motor causes the blades of a fan to spin and the wheels of a car to rotate. Motors transform technology on Earth.
A basic motor consists of a rotating loop of wire and a magnet. The loop of wire is placed between the electrical energy is transformed into mechanical energy when the loop begins to rotate. The image below shows an example of this.
While a motor converts electrical energy into mechanical energy, a generator is a device that performs electricity from a moving source of energy.
different for a generator. This time, the magnet is placed in the center of the loop of wire, and it can of wire. Thus, the rotating mechanical energy of the magnet is transformed into electrical energy. A to a larger, spinning apparatus called a turbine.
Diret Current DC Motor
simple DC eletri motor is used en te oil is poered a magneti ield is generated around te armature e let side o te armature is pused aa rom te let magnet and dran toard te rigt ausing rotation
e armature ontinues to rotate
en te armature eomes orizontall aligned te torque eomes zero t tis point te ommutator reerses te diretion o urrent troug te oil reersing te magneti ield
e proess ten repeats
At nuclear power plants, nuclear energy heats water, and the water evaporates into steam. At other power plants, the energy for heating water into steam comes from burning fossil fuels, such as coal or
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An important application of electromagnetism is a computer hard drive. When a computer stores data to a hard drive, it actually uses the principle of magnetic force. A simple mechanical hard drive, like the one in the image below, is composed of a plate with a thin, ferromagnetic coating. To store data on the plate, a tiny magnet is moved over a region of the plate. The magnetic force of the magnet causes all of the spinning electrons in a tiny region of the plate to become aligned in a particular direction. For example, the electrons may align pointing upward. Then, the tiny magnet moves to another region, causing the electrons in that region to be aligned in another direction. For example, the electrons in the next region may align pointing downward. An electronic signal from the computer tells the magnet how to align the electrons in different regions.
Computers store data in binary code, which is composed of zeros and ones (called bits). So, the upward alignment of electrons in a region may correspond to a one, and the downward alignment of corresponds to a binary code of data that can be stored or retrieved by the computer. Computers, mobile phones, and tablets all contain hard drives that store data. However, in many cases, these hard drives are in a solid state, in which there are no moving parts. Engineers are constantly creating new, denser technologies that allow more data to be stored in the same amount of space. This has allowed computers to become increasingly smaller and more powerful. However, no matter how small the hard drive, the basic principles are the same: magnets are used to store information.
speaker, a coil of wire is attached to a cone-shaped object. This assembly is called a speaker cone. The at the middle of the cone, next to the coil of wire. When a musical electric signal (alternating current) speaker cone becomes an electromagnet! Then, the permanent magnet exerts attractive and repulsive forces on the electromagnet as the musical signal changes. This causes the speaker cone to vibrate according to the signal from the music, producing sound.
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he received a doctorate degree. He accepted a post as a mathematics professor at the University of unique at the time because he used a mathematical approach to the study of electricity
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only by understanding all of these properties of circuits that we can understand circuits as a whole.
Connect It
Circuits are present in our everyday lives and come in one of two categories: series and parallel.
5. Can you categorize the types of categorizecircuits, t either as series or parallel, that are present in the room around you right now? m aroundy y
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1. What happens to equivalent resistance in a series circuit as you add more resistors?
D. None of the above
2. What happens to equivalent resistance in a parallel circuit as you add more resistors?
D. None of the above
3. Which of the following would result in a broken circuit?
A. Closed switch
B.
C. High resistance
D. High voltage
4. 5. Why is equivalent resistance different for series and parallel circuits?
resistor having a much smaller impact on the equivalent resistance for that circuit.
Work and Power
Work involves using a force to move an object over a distance.
Power is a measure of how much work is done in a certain amount of time.
Both work and power can be calculated using mathematical formulas.
In the picture above, a tractor is attempting to pull a truck out of the mud, but the truck does not seem to be moving
1. Is the tractor doing work on the truck? Why or oing work on why not? WouldWhy you say that the tractor is powerful t in this situation? Why or why not?
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When we think of the word work work in general terms, such as doing a job (like selling cars) or completing a task (such as writing an work as the measure of the energy transfer that occurs when an object is moved over a distance by an external force that is exerted in the direction of the object’s motion. In other words, work means in one day and technically do little, if any, real “work” if they did not use a force to move anything Now, if the salesperson lifted the hood on any of those cars so that a potential buyer could take a look at the engine, then we can say that work was done because a force was used to move the hood over a distance. You may feel that you worked really hard on an essay for your literature teacher, but the words. If your pencil had not been sharpened recently and you had to push so hard to make marks on the page that you got writer’s cramp, then your hand was probably tired from the work. Now, if you used the computer to write your essay, you probably did less work because it takes less force to move the keys on your keyboard, and each key does not move very far!
entire object from one place to another. For example, work is done when a force is used to compress a stationary spring or rotate a shaft. A force can sometimes cause motion that we cannot see, such as when magnetic force causes an imperceptible alignment of particles inside a magnetic material
Alternatively, it is important to remember that, transferred to an object. For example, if you pick up your backpack before you go to school, you are doing work because you are using force to move it over a distance. In moving the backpack, you have transferred kinetic energy (the motion of lifting the backpack) to the backpack so that, once lifted, it has potential energy due to gravity. However, if after lifting the backpack you simply stand there holding it, you are no longer doing work because you are no longer transferring energy to it. True, you are exerting a force on the backpack, and if it is full of books, you might be exerting a large force to hold it against the pull of gravity. However, if it does not move, then work is not being done.
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back and begin walking horizontally, you are not doing work on the backpack. Why? The force you are exerting to keep the backpack on your back is an upward force against the pull of gravity that is perpendicular to the direction that the backpack is moving. In other words, the force you are using to keep the backpack on your back is not the force that is causing it to move over a distance. On the other hand, if you carry your
done on the backpack because the backpack is changing position, moving upward, due to the force you are using to move yourself in the same direction.
speaking, what work is involved in w reading a book?
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We can calculate exactly how much work is done if we know how much force is used and how far an object is moved. If we assume that the force that is acting on an object is constant, we can express the work (W) as the product of force (f) and the distance (d) that the object traveled. Thus, the mathematical formula for work is W = f x d.
When calculating work using the formula W = f x d, the International System of Units (SI) dictates that we use standard metric units for measuring force and distance. Thus, force is measured in newtons (N), distance is measured in meters (m), and the unit for work is the joule (J)
1 meter. Using the formula for work, W = f x d work is not that much energy!
of your bunk bed. If your sibling weighs a little more than 64 lb., it would take 300 N of force to lift them of work.
3. Imagine standing still while holding a Imagine cinder block with a w force of 133 N. How can you use the formula W = f x d t you us to prove that no work is being done?
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4. Calculate the work in each situation:
You lift a 50 lb. bag of dog food (222 N) to a shelf that u is
You use a pulley system with a movable pulley. The force syst that is needed to lift the dog for f food is now 111 N, but you must that is needed pull 6 m of rope. now 111 N, but y ow 111
weighing 360 lb. that you need to lift from the ground up to the bed of a pickup truck, which is a distance of 1 m. Converting pounds into newtons to move the refrigerator. You would probably need a friend to help you lift it! Together, you would do
Now, let’s imagine that your friend is not available to help you, so you decide it would be easier to push the refrigerator up a ramp that pushing the refrigerator up the ramp instead of lifting it straight up, you spread the force over a larger distance, allowing you to use less force. This is true because when calculating work, force is inversely proportional to distance. That is, if W=f f x d half the original force if you spread it out by exerting the force over twice the distance that is actually needed to get the refrigerator from the ground to the bed of the truck. The work would feel easier because you use less force, but you would still be doing the same amount of work as if you lifted the refrigerator straight up. The formula for work proves that this is true. In the the refrigerator. By using the ramp, you cut that force in half but doubled the distance; therefore,
This is the principle behind simple machines. Simple machines spread the force that is needed to move an object over a greater distance, which makes the work feel easier but does not decrease the amount of work that is actually done. In general, we prefer doing work that feels easier (uses less force) even though we are actually exerting the force over a greater distance.
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We live in an automated world. For much of the work that we need to do, we have machines to do it for us. A food processor uses force to turn a shaft containing blades that chop your vegetables for you. An take the stairs. Machines are advantageous not only because they do work for us but also because they do the work faster than we could do it. When we discuss how much time is involved in doing work, we are discussing the concept of power.
volleyball player as having a powerful serve if they are able to hit the ball with enough force that it speaking, power is the amount of energy that is transferred or converted per unit of time. In other
How Is Power Calculated?
amount of work by the time it took to do the work. The formula for power is
P = W/t.
Because we know that the formula for work is W = f x d, we can also express the formula for power as P = f x d/t.
Using the International System of Units, if we measure work in joules and time in seconds, then the unit for power is the watt (W).
What makes one machine more powerful than another? If two machines do the same amount of work, but the second machine can do the work faster, then the second machine is more powerful
P = W/t t
Now, suppose that you attach a second, pulley, like other simple machines, allows you to use less force but spreads it out over a greater distance. In fact, a movable pulley will cut the the distance. You would still do 1,000 J of work you could probably lift the load in less time,
situation resulted in 66.7 W. Using the movable pulley made the work feel easier, and because it resulting in more power.
Likewise, if two machines work for the same amount of time, but one machine does more work, then it is the more powerful machine. For example, imagine that you have two battery-operated cars
capability. If you set both cars in motion and time them for 30 seconds, the car with a fully charged battery would probably travel the greater distance. Because the cars are identical, we know that the we know that it is more powerful. This makes sense because there was more power available in the fully charged battery.
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using P= f x d/t. You might remember that distance divided by time (d/t) is the formula for velocity. power, we can express that a powerful machine is strong and fast. Modern cars have stronger engines than the old Model A’s, which means that they can travel faster. Modern cars are more powerful than their ancestors because they are both stronger and faster.
Horsepower
When describing powerful machines, we describe their power using the term “horsepower” (hp). One 1 foot t = 1 second 1 hp = 550 ft.-lb. f/s
5. Which athlete is more powerful? Calculate the power for each:
Athlete A carries 300 lb. (1,334 N) uphill for a distance of 100 m. It takes them 60 seconds.
Athlete B carries 350 lb. (1,557 N) uphill for a distance of 100 m. It takes them 70 seconds.
Scientists in the Spotlight: Leonardo da Vinci
whose painting the Mona Lisa is one of the most well-known pieces of art in the world. But da Vinci’s genius went well beyond painting.
Besides being considered a master artist, da Vinci was an amateur scientist and mathematician who did pioneering work in the geometry, pyrotechnics, optics, hydrodynamics, and mechanical engineering. His boundless imagination, coupled with his fascination with the world around him, led him to design all sorts of theoretical inventions that, when viewed today, demonstrate the depth of his intuitive understanding of physical principles that would not be articulated until centuries later. Most of his designs were sketched in the margins of the notebooks in which he took copious notes describing and analyzing the phenomena he observed in the natural world.
Among his sketches is a design for something that we recognize today as a helicopter. He called it the aerial screw, and it used the power of four people rapidly turning cranks to create the force that is needed to lift it off the ground. Another invention resembles a prototype for the modern tank. Shaped like a turtle shell and made of wood and metal plates, it was powered by four strong people who turned two internal cranks.
Da Vinci was particularly fascinated with through pipes or channels as a source of mechanical force. Among his many sketches was one for a hydraulic saw. He imagined a movable cart with a vertical blade that, when connected to a water wheel, would move up and down to cut a log. The machine he envisioned was similar to the bandsaw that we use today, but of course, today’s saw uses electric power to do the work.
Like most of da Vinci’s ideas, the hydraulic saw was never actually invented, but it did demonstrate that he understood the relationship between work and power and the need for machines that could do more work in less time than doing the work by hand.
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distance by an external force that is exerted in the direction of the object’s motion. The formula for work is W = f x d. When force is measured in newtons (N) and distance is measured in meters (m), the unit for work is the joule (J). Simply exerting force on an object does not mean that work has been done. The object must move over a distance.
Power is the amount of energy that is transferred or converted per unit of time. In other words, power P = W/t When work is measured in joules (J) and time is measured in seconds (s), the unit for power is the watt (W). Machines
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What is the relationship between work and power?
The image shows a tractor trying to pull a truck out of the mud, but the truck does not seem to be moving.
6. If the truck is not moving, is work being done? How ot w do you know? WhatH should be changed o W u know? W to pull the truckchang out successfully?
A. 3,000 J
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2. If you push against a wall with 400 N of force for 10 seconds, but the wall does not move, how much work is done?
A. 4,000 J
B. C. 40 J
D. 0 J
3. What is the standard unit for power?
A. Watt
B. Newton
C. Joule
D. Horsepower 4. Why or why not?
No work is being done because the jug is not moving.
1,000 W. How much more powerful is a food processor than a blender?
Impulse and Momentum
You hear a screech of tires and the crash of a collision. Two cars have just gotten into a head-on collision. But neither driver was hurt. How is this possible?
How can physics help us better understand how some car wrecks injure passengers and drivers while other wrecks are completely survivable and everyone walks away without a scratch? The answer lies with momentum.
1. We say that a moving car has momentum. But what is momentum? What does it describe?
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Have you ever heard someone discuss the momentum of a team or maybe the momentum of a program? For example, “The space program gained momentum in the late 1960s . . . ” or, “The football team had momentum going into the last quarter.” In this case, the program or the team is moving forward and making progress. The more momentum there is, the harder it will be to stop progress. This applies to objects as well. An object with great momentum will take more effort to stop; why is that?
Momentum is a quantity that is based on both size and direction. Momentum is a measure of motion
p = mv
This equation shows that momentum is directly proportional to both the mass of an object and the velocity of an object. The mass and velocity of the object are inversely proportional to each other. This equation also shows us that if an object is at rest, or velocity equals zero, the object will have no momentum regardless of its size.
Momentum = mass x velocity
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The law of conservation of momentum states that if objects collide, the total momentum before the collision must equal the total momentum after the collision. Total momentum refers to the momentum of all the objects involved in the collision. When a tennis racket strikes a tennis ball, an impulse is applied to the ball. The racket puts a force on the ball for a short time period. By the way, according to Newton’s third law of motion, every action has an equal and opposite reaction. So, the ball also puts a force on the racket, and the racket therefore has an impulse applied to it. The key fact is that the share of the momentum between the objects that are involved in a collision may change, but the total value always remains the same. It is important to note that this is only true if there are no other external forces, such as friction, acting on the system. This law also only applies to the momentum values of closed systems.
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Within a closed system, the total momentum of the closed system before a collision equals the total
same as the amount of momentum that the second car gains. Each car had a different velocity and the system did not change, so the difference in momentum equals zero and therefore remains constant. This is because forces act in pairs. Newton’s third law of motion states that for every action, there is an opposite and equal reaction. From the point of view of momentum conservation, there are two types of collisions.
Elastic collisions are collisions in which both momentum and kinetic energy are conserved. The system’s total kinetic energy before the collision equals the system’s total kinetic energy after the collision. These types of collisions may be characterized by several factors, including large changes in momentum and impulse caused by large forces. Elastic collisions occur when particles rebound against each other with the same kinetic energy and momentum that they had before the collision. If objects bounce off each other, the collision is considered elastic.
lasti Collisions o Deormation ot Momentum and ineti nerg re Consered
Elastic collisions are not limited to microscopic objects, such as atoms and molecules. Elastic collisions can occur with larger objects. One such example is billiard balls. As a moving billiard ball collides with a resting billiard ball, the moving ball will come to a
collision is said to be perfectly elastic if the total kinetic energy at the end of the collision is exactly the same as the total kinetic energy at the start of the collision. Elastic collisions also occur during collisions permanently distorted.
etns cradle sheres transerring energ
illiard alls clliding n a l tale
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the impact is considered to be an inelastic collision. Inelastic collisions are encounters between objects in which some of the kinetic energy is converted into other forms of energy, such as sound, light, or heat. In the image, two cars collide and one car appears much more damaged than the other; this is an example of an inelastic collision.
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is an energy conversion in which heat is produced by the friction between the objects that are involved in a collision. Recall that heat is the transfer of thermal energy between two objects.
Reshaping is a form of conversion in which one or more of the objects involved in a collision are permanently altered from their original shape, especially if those objects become stuck together.
Sound and light energy are forms of conversion are produced during the collision.
A car crashing against a tree is an example of an inelastic collision as the kinetic energy is not conserved. The energy from the car is transferred into sound energy when the car stops. Another example of this type of collision would be a bullet that is shot into a piece of wood. The energy from the bullet is transferred in the form of thermal energy.
2. What are the two types of collisions, and how the two types e typ are they different from each other?differ re
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Force is a very important variable, but time is just as important. There are situations in which it is necessary to know how long the force acts on an object. For example, if you push a stack of books
amount of time the force acts. This is called impulse, or a force acting on an object for a given amount of time. Impulse can be calculated using the force applied to the object multiplied by the amount of time
Impulse is actually seen in everyday phenomena. There are several examples in sports. When a baseball bat hits a ball, the amount of time the bat is in contact with the ball is an example of impulse. For instance, if a ball is hit with the top edge of the bat, the amount of time the ball and bat are in contact is shorter than if the ball is hit with the middle of the bat. The result impacts the change in momentum of the baseball and could be the difference between a foul ball and a home run. What about kicking a soccer ball? Would a kick with the tip of the toe or the inside arch of the foot provide greater impulse? The inside arch of the foot allows for more time in contact with the ball and therefore greater impulse.
You have probably experienced impulse in a car. A car traveling at a certain velocity is coming upon
the brakes are applied hard and quickly over a very short distance. In both scenarios, the car slows down to the desired speed, but what would be different for the passengers in the two scenarios? With scenario A, the passengers would most likely notice very little change as the car is slowing down; however, in scenario B, the passengers probably felt a quick jolt and may have moved a little as the momentum of the car changed quickly.
3. What are some other examples of impulse at work in daily life?
Impulse = force x time
J = Ft
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the impulse and momentum. Impulse and momentum are also impacted when a force acts in the same direction as the object’s motion, such as pushing the gas pedal to accelerate a car that is already moving. In both events, a force changes the velocity of an object. When the velocity of the object is changed, the momentum of the object changes.
the acceleration of the object. F = ma
The acceleration of an object can be calculated using the change in velocity divided by the change in time.
If the formula for acceleration is substituted in Newton’s second law of motion formula, it looks like this.
If the change in time is multiplied on both sides of the equation, the formula becomes this.
In other words, because impulse is calculated as force multiplied by change in time, and change in momentum is calculated as mass multiplied by change in velocity, the equation shows that impulse equals a change in momentum.
Impulse = change in momentum
Application of this is important for many aspects of science. It is important to understand that an object’s change in momentum is based on mass and change in velocity. Because an object’s mass generally will not change, the change in velocity determines the change in impulse. When you know those two variables, you are able to determine how time and force can be manipulated in the equation. It is easier to see this in an example.
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that the ball was in contact with the person for 0.02 s. Using this information, determine the change in momentum, impulse, and force exerted when the dodgeball made contact with the person’s leg.
Change in momentum = mass x change in velocity
Impulse = change in momentum
Because we calculated the change in momentum and impulse, we can now calculate the force.
Impulse = force x change in time
To demonstrate how protective equipment in sports helps, the same scenario is used except the person is wearing protective padding. The time-lapse video shows that this time, the ball was in contact with the person for 0.05 s. How does the padding impact this scenario?
Impulse = force x change in time
the mass and change in velocity did not change. The padding allowed for more time for the dodgeball to stay in contact with the person, changing the time; therefore, the force was reduced. This concept is one that engineers use when designing protective equipment.
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When a car gets into an accident or when a shipping box is dropped, the objects inside the car or box go from an initial velocity to a different velocity, meaning that there is a change in momentum. In most cases of accidents or drops, the objects involved need to come to rest in such a way as to reduce damage to those objects. One way to do this is to increase the time it takes for those objects to come to rest from their initial velocity. Remember, the longer it takes for momentum to change, the smaller the force that is applied to those objects. It is known that less force causes less damage. Whenever we want to minimize the force, we extend the time. For example, if the time is extended 100 times, the force of impact is reduced 100 times. This has allowed for the development of many different features to reduce damage during collisions, such as padded equipment and helmets in sports, airbags in vehicles, and arrestor beds for semi trucks.
Safety Features in Vehicles
During a car crash, everything inside the car, including the passengers, goes through a rapid change in momentum. For example, the passengers in the car that is hitting another car will go through rapid deceleration. The passengers in the car that is being hit may go through rapid acceleration. Either way, the passengers in both cars will be subjected to great force during the change in momentum, and these forces can cause tremendous injury. One way to reduce these forces is by increasing the time it takes for the change in momentum to occur. Some of the most effective ways to increase this time include the use of seat belts, airbags, and crumple zones in the car.
Padded dashboard
Crumple zone
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body to change from an initial velocity to zero. In this way, seat belts decrease the forces placed on the body during collisions. They also prevent the passenger from moving around inside the car.
Airbags also increase the time it takes for the passenger’s body to change from an initial velocity to zero. During a car accident, the driver is propelled forward by incredible force, causing the forward velocity of the passenger to increase rapidly. If there were no airbag on the steering wheel of the car, the forward velocity of the passenger would be stopped suddenly by either the steering wheel or the windshield. This sudden stop would create a huge force over a very short time period. Airbags greatly increase the time it takes for impact, which in turn greatly decreases the force that is felt by the passenger. Airbags also prevent secondary injuries, such as abrasions, as well as cushion the head and upper body of the passenger.
Crumple zones are exterior areas of the car that absorb impact. The greater the amount of time it takes for the car exterior to crumple, the less force is exerted on the occupants. This is why crumple zones work. Because it is the force of the collision that harms passengers, anything that can be done to extend the time of impact will reduce this force. For example, if cars bounced off each other, or rebounded in an elastic collision, there would be a greater change in momentum and therefore a larger impulse. Larger impulses mean greater force. Luckily, most cars are designed to crumple, which means that the change in momentum is reduced, and this greatly reduces impulse.
Padded dashboards are another safety feature that increases the time to impact and thereby reduces force. Dashboards that are made from soft materials and have some type of cushioning may be found in many modern cars. These dashboards are much safer than the older models’ rigid metal or wooden dashboards.
Impact attenuators include setups such as rows of barrels that are full of water or emergency pull-off ramps that are softer than the road. If a runaway truck hits these setups, the amount of time that it truck. This decrease allows the truck to slow down
4. What are the safety features in a car, and how do ture they increase the time of impact? hey increase crease
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Padding extends collision time, which impacts impulse. The extra thickness of gymnastic mats extends the time of momentum change and impacts impulse. In some sports, such as football, players use padded helmets and shoulder pads. In other sports, players have padded gloves, shin guards, and batting helmets. The padding in these types of equipment is compressible, which reduces the force experienced from collision with a fast-moving object or person. This is why skydivers land on bent knees. By bending their knees, less impact force results as bent knees provide a longer time to change the person’s momentum
Follow-through motion extends collision time, which reduces force. In most racket or bat sports, the athlete is trained to “follow through” when making contact with the ball. This follow through increases the time over which the collision between the racket or bat and ball occurs. This increased time on the impulse side of the equation has an effect on the velocity of the ball, which changes the momentum. This is true, as the mass of the ball or racket does not change. In other words, follow through causes the ball to rebound from the racket or bat faster than if there were no follow through. This is important in many sports that use rackets and bats, as increased velocity of the ball is advantageous.
Netting absorbs forces by extending collision time. Nets are used in tennis, volleyball, and acrobatics, for example.
5. What are some other examples of impulse and momentum in athletics?
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the ball forward, you would be propelled backward. This is due to the conservation of momentum. Momentum that is applied to an object going one direction is canceled out by momentum that is reactively applied in the opposite direction.
Rockets utilize conservation of momentum in their engines. They push matter out the back of the engine at high speeds. The rocket’s exhaust has low mass compared to the rest of the rocket but high velocity. This translates to a low velocity for the higher-mass rocket in the opposite direction from the rocket exhaust!
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designing new technology. Two of the inventors of the automobile airbag came from very different family in what is now Slovenia in 1919 and succeeded at many things early in his life. He was on the Olympic ski jumping team when he was only 16, made a harrowing escape from the Nazi police to avoid sized perfume pump, plastic ice skates, and an industrial plastic injection pump. However, his design and prototype for the automobile airbag was not so successful as it kept exploding, and he moved on to other ideas only to see his idea become standard in nearly every vehicle on the road before his death in 2020.
The other inventor was Yasuzaburou Kobori. Born into a family without privilege in Japan in 1899, Kobori had to go to work after elementary school, but he worked hard to learn from his experiences and worked up to a position developing cutting-edge machinery for coal mining. After many years, Kobori left the coal industry and started his own “Good Ideas Center” for inventing. Along with an automatic sandwich-making machine, he designed a car airbag system that extended not only to occupants but net to prevent them from falling onto the hood or under the car. Unfortunately, the airbags were never Service Act at that time. Kobori was awarded patents for his design all over the world, but he died in 1975 before the system was widely used.
Many people do not know the importance of it in everyday life or even recognize it. The truth is that we use momentum in just about every activity that involves motion, from driving a car to participating in various sports or activities. We must remember that momentum is observed when there is any interaction between two objects occurring in an isolated system.
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Now, how could it happen?
The graphic below shows two different collisions right before they happen. use both of these collisions to prove the law of conservation of momentum?
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Which variable is momentum not dependent upon?
Mass Velocity Force
None of the above
Which is not an example of an elastic collision?
A game of billiards
A tennis match
A game of darts
A bowling match
Explain how kinetic energy is conserved in an elastic collision but not in an inelastic collision. Inelastic collisions change some of the kinetic energy that is present into other forms of energy or use it to do work on the other object involved in the collision Elastic collisions do not use kinetic energy and maintain the total amount during the collision.
Explain whether a tennis ball that is dropped from a high distance experiences an elastic collision or inelastic collision.
Because the tennis ball would not return to the original drop height, some of the kinetic energy that was present during the collision must be transferred away from the tennis ball. This means that this collision must be inelastic.
Which has greater momentum, a train at rest or a moving skateboard? Explain.
rest and therefore has no momentum.
Conservation of Energy
You just built a toy-brick space station or a toy-brick house made of more than 500 pieces. After a couple of weeks, some friends come over; one accidentally knocks the toy-brick sculpture off its display area, and it explodes into parts. Unfortunately, you threw away the instructions that allow you
1. How is this the same as the amount of matter or energy in the world and how it rgy is utilized?
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Energy is the ability to do work, and it comes in two main forms, kinetic and potential. Kinetic be found in objects, electrons, atoms, waves, and one example of which is gravitational energy,
Potential Energy (stored energy) Kinetic Energy (moving energy)
2. What are some other examples of potential and kinetic energy?
The pitcher winds up, ready to throw the ball.
The pitcher throws a fastball toward home plate.
friction energy transformation. law of conservation of energy. This law states that us. Someone uses mechanical energy to allows electricity
chemical energy
transformed from one form to another, and heat is lost in every transformation.
3. Why is it important to understand that when electronicspowering and cars? en powering
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system is closed with them, then the system is open coaster example, this is an open system. There every run of the roller coaster. A cup of coffee
the coffee is now limited to the cup; no mass is the pan, but put a lid on the pan, and the system becomes closed.
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Heat transfer plays a major role in the transfer is also important to many systems, such as weather and homeostasis in animals. Heat always moves from the warmer object to the cooler object. This indicates that cold is just the coffee, the spoon heats up because heat travels from the coffee to the spoon.
What is this thermal (or heat) energy Molecules in substances are in motion. The colder contain, so the slower the molecules move. The the warmer it is, the faster the molecules move. Surely all of the molecules in the substance aren’t Temperature the molecules.
4. Explain why cold doesn’t exist. plain why
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Heat can be transferred between substances and objects in three ways. Conduction, convection, and radiation power systems and do work.
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and-spoon example from earlier, the heat moves from the coffee to the cooler spoon. The molecules of down a little, and the spoon molecules speed up a little. This continues until the coffee molecules and speed up. This is how conduction works.
Pot handle
Frying pan
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rises. The cold water at the top of the pot sinks because cold water is more dense than warm water. convection current.
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electromagnetic rays. Think radiant energy
have felt the radiant heat from the street before you even put your foot down
5. How do convection,conduction, and radiation work to melt chocolate using a double boiler? (A t hocolate usin double boiler boils water in a pot, and a bowl is suspended above the water to melt the chocolate.)
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experiences heat transfer from the surface. Hot air rises, and cool air sinks. As the air above the surface heats up and the cool air in the upper atmosphere sinks, a convection current is created that moves heated and cooled air around the planet. These convection currents move
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eat to be used to keep our bodies in homeostasis at a constant 98.6°F. When we touch items that are cooler than our bodies, we lose heat to the object. Most of the time, the air around us is cooler than we
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because the oven is a closed system, all of the air in the oven will be the same temperature eventually. ovens, called convection ovens, actually use forced convection currents via a fan to circulate heated air, the house to the outside.
6. How would breezes at a beach be connected to convection currents?
Dr. Douglas Casa and the Korey Stringer Institute
from exertional heat stroke (zero fatalities).
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substance. Heat can be transferred by conduction, convection, and radiation. Conduction happens
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How is energy conserved in every energy transformation and heat transfer? the world, it drives myriad processes.
7. How is conservedenergy in w is ener every transformationenergyand ery energy heat transfer?
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1.
A. Radiation
B. Convection
C. Conduction
D. Thermal
2.
A. Ball at the top of a hill
B. Pear
C.
D. Rubber band stretched out
3. Heat always moves from an object of ______________ temperature to an object of ________________ temperature.
A. cooler, warmer
B. zero, warmer
C. cooler, zero
D. warmer, cooler
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Energy in Systems
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Energy is always conserved in a system, but how is this done? How does energy transform from one type to another?
Energy
Energy is the ability of a system to do work or produce heat. The law of conservation of energy states that energy cannot be created or destroyed, but it can change forms. There are many forms of energy, as shown in the diagram above.
• Mechanical energy is the sum of the potential energy and kinetic energy of an object.
• Radiant energy involves the electromagnetic waves that are given off by a source into the surrounding environment.
• Chemical energy is the energy that is stored in chemical bonds.
• Electrical energy is the energy that is produced as a result of moving electric charges.
• Thermal energy is the internal energy of a system, including the kinetic energy and potential energy of its particles.
• Sound energy is energy that is made by vibrations traveling as waves and requires a medium (air, water, or solids) to travel.
• Nuclear energy is energy that is released by fusing or splitting the nucleus of an atom.
There are many ways in which these forms of energy can be transformed from one to another, but the energy itself is not destroyed and no new energy is created during these transformations.
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1. Think about your use of an electronic device your use today. What is the series of energy oday. t eriestransformations eries of that is necessary for that device hat is hat is n to function?
Some energy transformations are direct. Radiant energy from the Sun is transformed into thermal energy to heat our planet. Solar panels transform radiant energy from the Sun directly into electrical energy. Plants transform the Sun’s radiant energy into chemical energy through photosynthesis.
Some transformations take several steps. The chemical energy from batteries is transformed into electrical energy and can then be used for several different transformations. It can be transformed chemical energy that is stored in food is transformed by different body processes to provide mechanical energy for you to move, thermal energy to maintain your body temperature, and chemical energy for cellular functions.
and then into electrical energy for homes and businesses. There are different ways that a turbine gets its energy. It can come directly from moving wind or water (mechanical energy) or from thermal energy that is created by burning fossil fuels (chemical energy) or from splitting atoms (nuclear energy). This thermal energy is used to heat water and create steam to turn a turbine. The electrical energy that is produced is further transformed into radiant and thermal energy when you turn on a light and into mechanical, sound, and thermal energy to run appliances and machinery.
Mechanical Energy Transformations in Systems
One of the easiest energy transformations to observe and calculate is that of potential energy and kinetic energy in different systems, like a swinging pendulum or a roller-coaster car. In these examples, friction and air resistance are ignored to simplify the calculations. The mechanical energy (ME) of a pendulum at any point along its swing is the sum of the potential energy (PE) and kinetic energy (KE) of the pendulum at each location.
Gravitational potential energy is the energy that is stored in an object due to its position. The higher an object is above a surface, like the ground, the more potential energy the object possesses because it has the potential to fall a greater distance.
Kinetic energy is the energy of motion. As the pendulum swings downward, it transforms its potential energy into kinetic energy. As it swings upward, the kinetic energy is transformed into potential energy. While the potential and kinetic energies are continuously changing, the total mechanical energy is the same, demonstrating the law of conservation of energy.
2. Where is the potential energy greatest for the ntial eg swinging greatestpendulum? th reatest fo Why? Where inginggingppendu is the kinetic energy greatest for the swinginggreate energy g pendulum? Why? the swingig
Advanced Topics Potential Energy Diagrams
Potential energy diagrams are used to show the measure of potential energy and changes throughout a situation. This helps us better understand the trends. Potential energy diagrams can be used to show chemical reactions, orbital motions, or pendulum swings.
Chemical Reactions: A potential energy diagram, also called a reaction curve, shows how potential energy changes during a chemical reaction. The diagram shows how potential energy changes as reactants are converted into products. Note that there are two kinds of reaction curves: endothermic and exothermic. In an endothermic reaction, energy is absorbed by the reaction or system, resulting in products that are at a higher energy level than the reactants. In an exothermic reaction, energy is released by the reaction or system, resulting in products that are at a lower energy level than the reactants. It is important to not confuse the two reaction types. All chemical reactions fall into one of the two categories
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Consider a satellite orbiting Earth. Most satellites orbit in a circular motion. These
constant. Because the kinetic energy (KE) depends on the speed of an object, the KE will also be constant throughout the motion. The potential energy (PE) is dependent on the height of an object, so the PE will also remain constant. The total amount of mechanical energy remains the same.
Like with circular motion, the total amount of mechanical energy of a satellite remains the same in elliptical motion. Unlike with circular motion, the energy of a satellite changes form in elliptical motion. The force of gravity is constantly doing work on a satellite and slowing it down as it moves. The gravity pulls the satellite toward Earth. The motion of the satellite keeps it moving in a forward path. As the speed changes, the KE also changes. When the satellite is closest to Earth, the speed is the greatest. When the satellite is farthest, the speed is the least. As the satellite gets farther from Earth, it loses KE and gains PE. Conversely, as the satellite gets closer to Earth, it gains speed and loses height. This causes a gain in KE and a loss of PE. Throughout this process, the mechanical energy still remains constant.
Pendulums: The kinetic energy of an object is the energy that it possesses due to its motion. Recall that KE depends on mass and speed, where KE = (½)mv2. The faster an object moves, the more KE it has. The KE of a pendulum increases until the ball is in equilibrium position. The KE decreases as it moves farther away from equilibrium. The potential energy of the object is the stored energy based on the position of the ball. This PE is a gravitational potential energy because gravity is the force that causes the movement. The amount of PE is dependent on the mass and height of the ball’s swing, where PE = mgh.
The equilibrium position is where the pendulum would rest—its lowest position (location 3). At this point, the height would be zero and the PE would be zero as well. As the pendulum swings back and forth, there are times when it moves away from the equilibrium. As it does this, and height increases, PE increases. As it moves toward the equilibrium position and height decreases, the PE decreases. However, the total mechanical energy of the pendulum will remain the same at all times. Therefore, if the PE is increasing, the KE is decreasing and vice versa. When PE is lost, it appears as KE. There is a transformation of PE and KE as the ball of the pendulum moves.
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Energy is measured in joules. A joule (J) is the SI unit (in the international system of units) for energy, and it is equal to one newton of force applied over one meter of distance. Mechanical energy is the sum of potential energy and kinetic energy.
Mechanical Energy (J) = Potential Energy (J) + Kinetic Energy (J)
ME = EP + EK
Potential energy is the energy that an object has stored due to its position.
Potential energy (J) = mass (kg) x gravity (9.8 m/s2) x height (m)
PE = mgh
Kinetic energy is the energy of motion.
Kinetic energy (J) = ½ x mass (kg) x velocity (m/s)2
KE = ½ mv2
Example Problem 1
dip, which is 15 m above the ground.
PE = mgh
PE = (450 kg) (9.8 m/s2) (15 m)
PE = 66,150 J
KE = ½ mv2KE = ½ (450 kg) (30 m/s)2
KE = 202,500 J
ME = PE + KE
ME = 66,150 J + 202,500 J
ME = 268,650 J
Note: A large amount of energy makes sense with a roller coaster.
Example Problem 2
A 5 kg object is moving downward at a speed of 12 m/s. It is currently 2.6 m above the ground.
a.What is its kinetic energy?
KE = ½ mv2
KE = ½ (5 kg) (12 m/s)2
KE = 360 J
b. What is its potential energy?
PE = mgh
PE = (5 kg) (9.8 m/s2) (2.6 m)
c. What is its mechanical energy?
PE = 127.4 J
ME = PE + KE
ME = 127.4 N + 360 N
ME = 487.4 J
Note: A small amount of energy makes sense with a smaller mass.
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Systems
A system is a group of interacting, interrelated, or interdependent elements forming a complex whole. A system is something that we identify or prepare in order to do experiments and make observations. It is a part of the universe that we wish to study. Anything that is not part of the system is considered the surroundings. The system and surroundings together make up the universe. The solar system is comprised of all the celestial bodies that are revolving around the Sun or are held by its gravitational attraction. An ecosystem is characterized by the interactions of the biotic and abiotic factors in a given
Isolated Systems: Nothing is perfectly isolated from its surroundings, but we can get quite close even though, eventually, all barriers break down. An isolated system does not exchange matter or energy with its surrounding environment; nothing can enter or leave. The energy and matter remain the same. Any changes that occur happen inside the system. Examples of isolated systems include a closed
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negligible and can be ignored. This allows us to use conservation laws in problems, and it helps us gliding on an air table.
Closed Systems: A closed system will not exchange matter but does exchange energy with its surrounding environment. A closed system has a constant amount of mass, but energy can cross the border in the form of heat or work. Therefore, the volume of the system does not necessarily remain the same if the system expands or contracts with the energy changes. Examples of closed systems include a balloon being heated or cooled, a pot boiling with a lid to trap the steam, and a pressure cooker being heated.
Open Systems: An open system will exchange matter and energy with its surrounding environment. Examples of open systems include boiling soup on a stove where both heat and steam can leave the system while ingredients can be added. A pond, where water can be added by rain or removed by evaporation and animals can come and go, is also an example of an open system.
3. What are some examples of isolated, closed, and open xamples iso es systems that you have observed at y s thy home or in school?
Entropy
that then shattered into pieces? A solid piece of material may break into smaller pieces, but you rarely observe small pieces of material form back into a whole piece. Similarly, you may have noticed that cream will dissolve into coffee and a fragrance will diffuse (or spread) into the air of a room. However, the reverse never happens; dissolved cream does not spontaneously separate back into its original form, and a diffused fragrance does not return to an isolated region of the room.
The explanation for these phenomena is entropy. Entropy is a measure of the disorder in a system, and it is a key part of the laws of thermodynamics. What is the law of entropy?
The Second Law of Thermodynamics and Entropy
As discussed earlier, cream dissolves into coffee and a fragrance diffuses into a room, but we never observe the reverse process. In both cases, a system becomes less ordered. That is, the particles always spread out and exchange energy until they come to equilibrium.
We observe this whenever one substance is at a greater temperature than another. A hot substance has more thermal energy than a cool substance. The two substances are said to be ordered because one has more energy than the other. When these substances interact with each other, we always observe the hotter substance transfer thermal energy to the cooler substance. After they come to equilibrium, they have the same energy and are more disordered. The measure of disorder in a system is called entropy. More disorder equals greater entropy.
For example, when a block of ice melts, the molecules of water spread out and become more disordered. The entropy increases.
Consider many gas particles moving at high speed on one side of a chamber. If there is a barrier between the two sides of the chamber, the system is closed. In this case, the entropy of the system will remain constant. However, if a door is opened to the other side of the chamber, the particles will spread out until there are equal quantities of particles in both chambers. In this case, the energy of the particles spreads out and the entropy of the particles increases.
likely to evolve into more disordered states than into more ordered states. For example, a system in an ordered state, like a solid block of ice, is more likely to evolve into a disordered state, like liquid water. Because states of a system with greater disorder are more probable, the entropy of a closed system always stays the same or increases. That is, the entropy of a closed system does not decrease. This is the second law of thermodynamics, also known as the law of entropy. This law is a statement about the direction of thermodynamic processes. It is one of the few laws in physics that indicates an asymmetry in nature.
Note that the entropy in a system will decrease if we remove energy from it. For example, freezing a cup of water lowers the entropy of the water. The solid ice has less disorder and less entropy than the liquid water. However, the fact that we can add energy to or remove energy from the water means that it interacts with the environment, so it is not a closed system. We never encounter a truly closed system on Earth.
The entropy of individual systems increases or decreases as energy is added to or removed from them. But the entropy of the universe as a whole cannot decrease because it is a closed system. There is no place outside the universe from which energy may be added to the universe. The entropy of the universe always increases.
Summary of Energy Flow and the Second Law
transferred, the temperature eventually equalizes by a heat source’s temperature falling and a heat sink’s temperature rising. When temperatures are equalized, no more heat is transferred even though objects still contain heat. When heat is converted into work, the heat source’s temperature falls, approaching that of the heat sink. If there is no temperature difference, no heat can be converted into work. But if there is a temperature difference, some of the heat will be used to raise the temperature of the sink. If some of the heat goes into raising the sink, it cannot all be converted to work. Therefore, it
James Prescott Joule, Physicist g
In the mid-1800s, James Prescott Joule (1818–1889) proposed that mechanical energy, electricity, and heat were all forms of energy and such energy transformations could occur. Joule conducted experiments to determine the amount of heat that was generated by an electric wire, resulting in Joule’s law, which states that the heat that is generated in an electric wire is proportional to the current squared multiplied by the resistance. He did further experiments to determine the amount of mechanical work that is needed to generate a unit of heat. The SI unit
(also known as Lord Kelvin) resulted in the discovery that when a gas expands freely, it changes temperature; this is known as the Joule-Thomson effect. This discovery was a basis for refrigeration.
The Big Picture
Energy exists in several different forms. Forms of energy can be transformed into other forms of energy by different processes. Some transformations are simple while others are more complex. During these transformations, no energy is destroyed and no new energy is created; all energy is conserved.
Connect It
There are several energy transformations in the picture below.
4. What different energy transformations fferent fferent are found in the camping scene?
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1. Which choice below is not a form of energy?
A. Chemical
B. Mechanical
C. Fossil fuel
D. Thermal
2. What does the law of conservation of energy state?
A. Energy comes from the Sun.
B. Energy cannot be created or destroyed.
C. Energy transformations can be simple or complex.
D. There are several different forms of energy.
3. What type of energy is stored in batteries?
A. Electrical energy
B. Radiant energy
C. Mechanical energy
D. Chemical energy
4. Describe the energy transformations that are needed to be able to watch a TV.
5. How does a roller coaster demonstrate the conservation of energy?
6. How do the three types of systems differ? Explain
Characteristics of Waves
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You perceive the world around you with your senses. Two of those senses rely on waves. The image below shows the different types of waves that are needed for your senses of hearing and sight.
1. Describe what you notice about the waves that are needed for you to hear and see. eeded y
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What is a wave
It means that waves move energy through something. There are two main types of waves. One type is a transverse wave.
A transverse wave is a wave that is propagated in a direction that is perpendicular to the displacement medium This means that the wave energy moves in one direction while the particles that are disturbed by the wave move at a right angle to that direction. In the image, the wave energy moves from left to right while the particles that are disturbed by the wave move up and down.
The highest point of the wave is called the crest, and the lowest point is the trough. The midpoint between the crest and trough is the equilibrium point, also called the resting position. The distance from the resting position to the crest or the trough is the amplitude. This can be considered the height of the wave. The amplitude is determined by the amount of energy that created the wave. A wave with greater energy will have a larger amplitude.
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The image below shows waves with the same frequency but different amplitudes. A higher amplitude is caused by greater energy.
wavelength. The symbol for wavelength is frequency of the wave and is measured in hertz. One hertz is one wave per second. Because each wave propagates energy, the more waves there are, the more energy that is transferred. Therefore, a higherfrequency wave carries more energy than a lower-frequency wave of the same amplitude
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Examples of Transverse Waves: If you wiggle a rope up and down or side to side, it will produce a transverse wave, as shown in the picture.
But there are transverse waves that cannot be seen. These are the waves of the electromagnetic spectrum, which is shown in the diagram below. These electromagnetic waves, or light, do not need a medium to travel through, so they can be transmitted through space. They include the radio waves that are needed for TV and cell phone signals, medical X-rays, and the waves of visible light that are needed for you to see. Indeed, light is a wave that is generated by the oscillation of particles, such as electrons and protons, create the light wave can be transmitted. This is why light can travel through the vacuum of space.
wavelengths and frequencies of visible light stimulate cells in your eye, allowing you to detect the colors of the visible spectrum.
Different types of EM waves are characterized by their wavelengths and frequencies in the electromagnetic spectrum image.
2. Why can you see visible light y but not the otherlg types of waves on the typeselectromagnetic spectrum? electromg g
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The second main type of wave is a longitudinal wave. A longitudinal wave is a wave that is propagated particles that are disturbed by the wave move in the same direction that the wave energy moves. In the diagram below, the coils of the spring that is disturbed by the wave are compressed forward as the wave energy moves forward. Longitudinal waves are also called compression waves.
There is no crest or trough in a longitudinal wave as there is no high or low point. Instead, the characteristics of a longitudinal wave are compression and rarefaction. The compression is the part of the wave where the particles are pushed closer together by the energy of the wave. This is also how amplitude is measured. The amplitude is how close together the particles are in the compression. The closer together the particles are in the compression, the greater the amplitude of the wave. The rarefaction is the less dense, more spread-out region of a longitudinal wave. The wavelength of a longitudinal wave is the distance between equal parts of the wave that includes one compression and one rarefaction. Like a transverse wave, the frequency of a longitudinal wave is the number of waves that pass a point in a given amount of time.
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The coiled spring toy is one common example of a longitudinal wave as the compressions are easy to observe. There are longitudinal waves that cannot be seen, such as sound waves.
Vibrations from the speaker in the image above create a disturbance in the air particles that transmits sound energy.
Sound is produced by vibration. The energy of the vibration causes the air particles at the sound source to be compressed. Those particles bump into the particles next to them, passing the energy through the air particles to your ear. The energy is then passed to your eardrum, causing it to vibrate and allowing
Quicker vibrations cause a greater frequency of compressions and create a higher-pitched sound. The same process occurs through liquids and allows you to hear underwater. It also happens through solids. Put your ear on your desk and tap on the desk. The sound wave will propagate through the desk to your ear. Because longitudinal waves require particles to be compressed, they require a medium and cannot propagate in space, where there are no particles or the particles are too far apart to be compressed.
3. Do you think sound waves travelth faster through gases, like air,throg or through solids?rougExplain. g
Wave speed, also called wave velocity, is a measure of how fast a wave is moving. It is calculated using the wavelength and frequency of a wave.
Example 1: Determine the speed of the wave in the box below.
Wavelength: The distance from crest to crest is 4.0 cm = 0.40 m.
Example 2: Determine the speed of the wave in the box below.
Wavelength: The distance from crest to crest is 4.0 cm = 0.40 m
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The speed of most waves depends on the medium through which they are traveling. Waves of different frequencies traveling through the same medium will have different wavelengths.
All three waves above are traveling at 1.0 m/s through the same medium.
Example 1:
Rearrange the wave speed equation:
wave speed = frequency x wavelength wavelength = wave speed/frequency wavelength = 0.11 m
Example 2:
Rearrange the wave speed equation:
wave speed = frequency x wavelength frequency = wave speed/wavelength
frequency = 3.0 Hz
4. Describe the relationship between frequencyrequencywavelength.and
LIGO Scientists and Gravitational Waves
This is a photo of the LIGO facility in Livingston, Louisiana.
Washington state and the other in Louisiana, working in unison to detect gravitational waves that are created by cosmic events such as black holes or colliding neutron stars. The LIGO facilities use laser interferometry and multikilometer-scale detectors to measure minute ripples in space-time that gravitational waves that were created when two black holes collided 1.3 billion light-years away. Many awarded the Nobel Prize in Physics.
LIGO scientists are a diverse group working not only at the facilities in Washington and Louisiana but observation, and data analysis.
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Waves transfer energy through substances and space. Different types of waves transfer different types of energy. Not all waves can be seen, but all waves can be described by their characteristic properties.
Connect It
How do waves allow you to hear and see?
Your ears detect the sound waves of a music system. Your eyes detect the light and colors from a TV. Both sound energy and light energy are transmitted by waves.
5. Why do your ears Whydetect doy longitudinal waves while gitudinalyour eyes whiledetect y y transverse waves?dete
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1. What is represented by the letter G in the diagram?
A.
B. Trough
C. Wavelength
D. Amplitude
2. What does the frequency of a sound wave determine?
A. Loudness
B. Pitch
C.
D. Speed
3. What wave characteristics are needed to calculate wave speed?
A. Direction and frequency
B. Frequency and wavelength
C. Wavelength and velocity
D. Direction and wavelength
4. How are both amplitude and frequency related to the energy of a wave?
The amount of energy determines the amplitude of the wave Because each wave carries the energy, the
5. Why is light transmitted through space, but sound is not?
Light waves are electromagnetic waves and do not require particles to transmit energy, so they can travel through space. Sound waves are longitudinal waves and require particles to compress to transmit energy. Space does not have particles that are close enough to be compressed, so energy cannot be transmitted by longitudinal waves.
6. Why is amplitude not required to calculate the speed of a wave?
Speed/velocity is a ratio of distance over time The distance of a wave is the wavelength, and frequency is a measure of waves and time Amplitude is a measure of the energy that is carried by a wave independent of its speed.
Behavior of Waves
How many times per day do you look in a mirror?
Why are you able to see yourself in a mirror?
Waves transmit energy from point to point without transmitting matter. Waves travel through a medium and continue traveling until they encounter an object. When a wave reaches that object, it can behave in different ways depending on the wavelength of the wave and the object it is encountering. Some light waves will hit the object and bounce back in the same direction they traveled from. This is known as
1. What are some other examples of are familiar with?
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waves travel through different media, they eventually run into various objects in the environment. When waves hit different objects, they don’t just stop; they are actually encountering a new medium, and they change their direction of travel depending on the type of wave, the wavelength, and the composition of the new medium. occurs when a wave hits the surface of a new medium and is sent back to the medium it traveled from. In other words, the wave bounces back toward the original direction and medium after it encounters the new object. The ray of light that strikes the surface is known as the incident ray, and the ray
strikes the surface, we can draw a line that is perpendicular to the surface, known as the normal line. This angle, formed between the incident ray and the normal line, is the angle of incidence, and the angle formed between the normal line and surface at the same angle at which the incident rays hit the surface, and the waves travel in the
scattered in all different directions and angles.
Echoes occur because sound waves hit a surface measure the depth of underwater objects using sonar technology by sending out sound waves and
new medium and continue traveling at a different angle and in a different direction. This is known as . Refraction occurs because light travels at different speeds in different media. Light travels the quickest in a gas medium, like air, and the slowest in a solid medium. Sound waves are just the opposite and travel fastest through solid and slowest through gas media. As waves pass through different media, they change their speed of travel, which changes the direction and angle of their travel. The angle at which the wave hits the surface of the new medium is called the angle of incidence. Once the wave passes through the surface of the new medium and changes direction, the angle of change is known as the angle of refraction. Waves with shorter wavelengths are refracted at greater angles than waves with longer wavelengths.
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through a new medium, waves can travel around objects or through gaps and holes. This is known as Diffraction occurs because the wave has encountered an object, gap, or hole that is similar in size to the size of its wavelength. This is why we can hear people around corners or through open doors. Have you ever seen rainbow light shining off a CD? This happens because a CD consists of a grooved track in a spiral pattern, known as diffraction grating. This diffraction grating allows the light waves to diffract, which shows up as a rainbow. Diration
2. Explain the
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Wave occurs when two or more waves interact and combine with each other while traveling along the same medium. There are two types of wave interference that can occur. During , the crests of the two waves are displaced in the same direction. The crests of the two waves meet when they reach the same point and combine. This results in one wave with a large amplitude that is equal to the sum of the amplitudes of the individual waves. Let’s take two waves: Wave A and Wave B. They are both traveling along a medium in opposite directions, with their crests facing the same direction. Wave A has an amplitude of 3, and Wave B has an amplitude of 2; when they meet along the medium, Wave A and Wave B will combine to form one wave with an amplitude of 5. occurs when the crests of the waves are facing opposite directions. When these waves meet, the resulting wave is smaller than the individual waves, and sometimes the wave gets cancelled out completely. Let’s look at Wave A and Wave B again. They are still traveling in opposite directions, but this time their crests are facing opposite directions. Wave A has an amplitude of 2, with its crest facing up, and Wave B has an amplitude of -1, with its crest facing down. When these two waves meet and combine, the resulting wave has an amplitude of 1. If Wave A had an amplitude of 2, and Wave B had an amplitude of -2, the two waves would completely cancel each other out, and no wave would occur at that point along the medium. The process of waves traveling along the same medium and interacting is known as .
3. What is the
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When two or more waves with the sample amplitude and frequency interfere while traveling in the same medium in opposite directions, are formed. Standing waves appear to be vibrating but not moving horizontally. Let’s look at Wave A and Wave B again. They are moving at the exact same frequency in opposite directions. Wave A has a crest with an amplitude of 2 and a trough with an amplitude of -2. Wave B also has a crest with an amplitude of 2 and a trough with an amplitude of -2. When the two waves meet, they will undergo destructive interference at their midpoints. This creates a point of no displacement and forms a node. As the midpoints meet, the crest of Wave A and the trough of Wave B are traveling through the same location. The trough of Wave A and the crest of Wave B also travel through the same location. This creates points of vibration called antinodes. Because the two waves are traveling at the same frequency in opposite directions, this continues to happen, and the wave appears to vibrate in place. A standing wave can easily be seen on a plucked guitar string. As the guitar string is plucked, pulses form and the string appears to vibrate vertically.
important in the formation of
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If you were to take a rope, tie one end to a pole, and stretch it out as far as it could go, you would form a straight line with the rope. If you started to move the rope up and down, you would start to create waves in the rope. If you looked directly at the waves, it would appear that they were traveling toward you in one plane. This is common for many different types of waves, and when light waves travel in one plane, it is known as polarized light. However, light waves do not normally travel in one plane; instead, light vibrates in numerous planes, which is known as unpolarized light. We can transform unpolarized light into polarized light through a process called You may have heard of polarized
moving along the vertical plane while the light moving on the horizontal plane is blocked.
erticall laried tt
rintall laried tt
Little r n tt
ertical ilter
rintal ilter
ertical ilter and hrintal ilter
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Have you ever been riding in a car on the highway when you heard an ambulance approach and speed by? As the ambulance approaches, the siren sounds very high pitched, and as it passes by and travels away, the siren sounds much lower pitched. This change in the frequency of the pitch is due to the . Due to the Doppler effect, there is an apparent shift in the frequency of the wave. As the source of the sound moves closer to the observer, there is an upward shift in frequency. This is because the sound waves enter the observer’s ear at a shorter wavelength and increased frequency, causing the sound to be more high pitched. As the source of the sound moves farther away, there is a downward shift in frequency as the wavelengths increase, which causes a lower-pitched sound to the observer. The Doppler effect is also apparent with light waves. As an object moves away from us, the light is shifted toward the red end of the visible-light spectrum as the wavelength increases. When objects move toward us, light is shifted toward the blue end of the visible-light spectrum as the wavelength decreases. This is known as , and it allows us to determine if objects are moving toward us or away from us.
5. What are some other examples are familiar with?
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Dr. William L. Wilson, PhD, is the executive director of the Center for Nanoscale Systems at Harvard of the behavior of light. He is the chief scientist and founder of InPhase Technologies, which is focused on using holographic storage. Holographic storage allows for millions of bits of storage on a very small disc rather than smaller amounts of storage on a larger disc, like a CD. In holographic storage, rather than using one laser (like with CDs or Blu-ray), there are two intersecting lasers that scan the hologram, allowing for retrieval of data from the storage medium
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As waves move through media, they can behave in different ways as they encounter objects, new original direction and medium from which it was traveling. Refraction occurs when a wave passes through to a new medium and changes the direction and angle of travel because light and sound travel at different rates in different media. Refraction is what causes pencils placed in water to appear broken; light travels faster in air than in water. Diffraction occurs when waves travel through gaps or holes and around objects. Superposition occurs when two or more waves are traveling along the same medium and interact with each other, causing interference. When the two waves combine, there is a resultant wave that is either larger or smaller than the two individual waves. If the resultant wave is larger, constructive interference is occurring, and if the resultant wave is smaller or nonexistent, this is due to destructive interference. Standing waves are waves that appear to be vibrating vertically but not moving horizontally. This is due to destructive interference of two waves that form nodes, which appear to have no displacement, and antinodes, which are areas of maximum amplitude. Light waves vibrate in more plane and become polarized. This process is known as polarization. The Doppler effect occurs as sources of sound or light move closer to or farther from an observer. As a source of sound or light moves closer to an observer, the wavelengths increase in frequency and decrease in wavelength. As the source moves farther away from an observer, the frequency decreases and wavelength increases. This is the reason why a siren sounds high pitched as it approaches you and lower pitched as it is moving away from you.
Why can we see ourselves in the mirror?
from the same direction and medium that they initially came from, those light waves hit the portions of our eyes that allow us to see. We see our image clearly because mirrors are smooth and shiny, and the are a common attraction at carnivals and fairs. If you were to stand in front of a funhouse mirror, you normal height, or your head might be large and wavy. This occurs because the surface of the funhouse mirror is not smooth and shiny like the mirrors at home. Instead, these mirrors often have a concave or
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Summarize It
A light wave is traveling through air when it hits a new medium and changes its angle and direction of travel. This is known as–refraction. diffraction. interference.
Two waves are traveling along the same medium in opposite directions. Wave A has an amplitude of 2, and Wave B has an amplitude of 2. What will the resultant wave look like?
Constructive interference will occur with an amplitude of 4.
Destructive interference will occur with an amplitude of 4.
Constructive interference will occur with an amplitude of 0.
Destructive interference will occur with an amplitude of 0
You are standing in the hallway, and you hear two teachers talking around the corner. This is possible because of the _______________ of sound waves. refraction diffraction interference
What are standing waves, and how do they form?
Standing waves are waves that appear to be vibrating but not moving horizontally. It is when two or more waves with the sample amplitude and frequency interfere while traveling in the same medium in opposite directions. When the two waves meet, they undergo destructive interference at their midpoints, creating a node of no displacement. Their crests and troughs combine to form areas of maximum amplitude called antinodes.
Explain why a racecar driving on a track sounds high pitched as it travels in front of you but low pitched as it drives on the opposite side of the track.
This is due to the Doppler effect As the racecar drives close by, the sound waves from the racecar vibrate in the observer’s ear with a higher frequency, which causes a higher-pitched sound. As the racecar drives on the opposite side of the track, the vibrations reach the observer’s ear at a lower frequency, causing a lower-pitched sound.
What is the process of polarization?
Polarization is the process of turning unpolarized light into polarized light. Unpolarized light waves vibrate in more than one plane of motion while polarized light travels in only one plane of motion.
Image Formation
When you look at yourself in a mirror, you are looking at an image. The image produced by the mirror is a result of the shape of the surface of the mirror and how light waves interact with it.
1. Imagine being a small child seeing a . smallmagchild
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you are not literally inside or behind the mirror. What you are seeing is an image of yourself. But what is an image? How is an image formed? Why does it look like you are behind the mirror?
This picture shows several images of the same toy dog. The images produced are virtual images. How do you think the multiple images were achieved?
An optical image is the apparent reproduction of an object. It is formed when light rays interact with mirrors or lenses. The images in the mirrors are virtual images; they appear to be in the mirror but are not really there. Optical images can also be real images, which, as the name suggests, are really formed.
The type of image produced is determined by the shape of the surface of a mirror or lens. A ray diagram is used to illustrate how light rays interact with a mirror or lens to produce an image and show if the image is virtual or real.
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A plane mirror is the most common type of mirror that people use to look at themselves.
image that is formed. The image appears to be behind the mirror, but if you look behind the mirror, the image is not there. The image does not really exist; it is a virtual image. So how can you see it? A ray diagram will help explain this.
In the diagram of a plane mirror to the right, the lines show two light rays coming from the top
eye, but at slightly different angles. Extensions of these rays through the mirror intersect at the top of the image. These extensions, which are not actual light rays, are shown with dashed lines. Similar rays are drawn from the bottom of the object, and their extensions would intersect at the bottom of the image.
In order for your eye to see an object, light rays must bounce off the object to your eye. If you look directly at an object, the light rays from the object enter directly into your eye.
When you look at a mirror, you are not seeing the light rays directly from the object. The light rays from the object encounter the mirror at an angle, called the angle of incidence The light
angle, called the
. Your brain interprets the as if the light had traveled in a straight line to your eye and creates an image in the mirror. Notice in the diagram that no light rays are actually creating the virtual image. Because no light rays are used to create it, the image is not real.
The virtual image that is produced by the plane mirror is very similar to the object that produced it. The image is upright, the same size, and the same distance from the mirror as the object. But there is a difference; the image is reversed from left to right.
Image Formation by Reflection in a Plane Mirror
•The virtual image is located behind the mirror.
•The image is reversed left to right.
•The image and object are the same distance from the mirror.
•The image is the same size as the object.
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direction in a process called refraction. Exactly how the light rays change direction depends on the shape and thickness of the lens as well as the material from which the lens is made.
A convex lens is thicker in the middle than it is at the edges. As light rays pass through the curved lens, they are refracted at different angles. This causes the light rays to converge into a single point.
Light rays refract through a convex lens and converge to a single point.
When light rays converge, they form a real image. The lens of your eye is a convex lens. It produces a real image on the retina of your eye, enabling you to see. The location of the object in relation to the lens determines whether the light rays from the object will converge once they are refracted by the lens.
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For the light rays from an object to converge and produce a real image on the other side of the lens, the object must be located outside the focal point of the lens, as shown in the ray diagram.
Notice that the light rays from the top of the object are refracted to the bottom of the image that is produced. As a result, the image is inverted. If the object is placed at twice the focal length (2F) of the lens, the image will be the same size and same distance from the lens as the object (as shown). If the object is moved farther from the lens, the image will still be inverted but will be smaller than the object and move closer to the lens, as shown.
Image real iage at the sae sie as the ect ppliation eeiece lens a telesce
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thin lens equation can be used to calculate where the image will appear.
f = focal length
d o = object distance
di = image distance
In the image on the previous page, assume that the focal length is 4.0 cm and the object is located at 10.0 cm from the center of the lens. Calculate the image distance.
The image is 6.7 cm from the lens.
How do you think the image would appear if the object were between F and 2F?
Telescopes use convex lenses to produce real images of distant objects. Cameras use convex lenses to images that can be projected on screens, like the image of the cat at the beginning of this lesson 1 f 1 d o 1 di
For objects that are located between the focal point and the lens, the image that is formed is very different.
Refraction of Object inside F
Image: magnified virtual image on the same side of the lens as the object
When an object is located inside the focal length of the lens, the light rays that are refracted by the lens do not converge, so no real image is formed. However, to an observer looking through the lens, a virtual image is formed. This virtual image is upright and larger than the object and on the same side of the lens. This is how a magnifying glass is able to make an object appear larger. The farther the object is from the lens, the larger the virtual image will appear until the object reaches the focal point of the lens.
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So what happens if an object is located at the focal point of the lens? Does it produce a real image or a virtual image?
The answer is—neither. For an object that is placed at the focal point, the light rays do not converge to form a real image, nor is a virtual image produced.
change the image imag e ig
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convex mirror is a type of spherical mirror where the surface of the mirror curves outward. Since they produce wide-angle, upright images, they are perfect as side-view mirrors on cars, allowing drivers to get a better view of what’s happening around them. A concave mirror is a type of spherical mirror where the surface of the mirror curves inward. Concave mirrors can produce images that are larger or smaller than reality; their images can also be upright or inverted
The mirror formula is the same as the thin lens formula and shows the relationship between the focal length, object distance, and image distance.
f = focal length
d o = object distance
di = image distance
For a convex mirror, the focal length will always be a negative number because the focal point of these mirrors is on the opposite side of the mirror from the object. For a concave mirror, the focal length will always be positive because the focal point is on the same side as the object. The image distance for spherical mirrors can be positive or negative depending on whether the image is real or virtual. A convex mirror always produces virtual images, so the image distance is always negative.
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Alvan Clark (1804–1887) was an accomplished artist who created hundreds of oil portraits and miniatures. Following the appearance of the Great Comet of 1843, Alvan taught himself to grind and polish a glass lens to help his son George (1827–1891) construct a small telescope. In 1846, he and refracting telescopes in the world. They ground the lens for the 91 cm telescope at the Lick Observatory, which is still the third largest refracting telescope, and the 100 cm telescope at Yerkes Observatory, discovered two double stars using refracting telescopes. In 1862, while testing a lens he had made, Alvan Graham (the son) discovered the star Sirius B, the predicted companion star of Sirius. It was the stars.
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Light rays interact with mirrors and lenses in different ways to produce images. If the light rays converge, a real image is produced and can be projected. If the light rays do not converge, a virtual image is created.
How did your parent get in the mirror?
the mirror? Fortunately, children do not seem to be confused about this for long.
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1. What type of image is produced where light rays converge?
A. Virtual image
B. Real image Real
C.
D. Refracted image
2. What type of image is produced by a plane mirror?
A. Upright, virtual image virtual
B. Inverted, real image
C.
D. Upright, refracted image
3. What determines the type of image that is produced by a thin convex lens?
A. The thickness at the center of the lens
B. The size of the object
C. The amount of light rays being refracted
D. The distance of the object from the lens The distance of the object from the lens
4. Compare and contrast a virtual image that is produced by a plane mirror and one that is produced by a thin convex lens.
Both virtual images are produced by light rays that do not converge and are upright The image that
Both virtual images are produced rays that do not converge and are upright. The image that is produced by the mirror is the same size as the object and is left-right reversed. The image that is is the mirror is the same size as the and is reversed. The image that is produced by the lens is larger than the object and not left-right reversed. the lens is than the and not reversed.
5. Why can a real image be projected, but a virtual image cannot?
A real image is produced by converging light rays, so it exists and can be projected. A virtual image does A real is rays, so it exists and can be A virtual image does not really exist. It only appears to exist. Because it is not made of real light rays, it cannot be projected. not really exist. It only appears to exist. Because it is not made of real light rays, it cannot be projected.
6. How do light rays behave differently when encountering a plane mirror and convex lens?
bending at different angles as they pass through the different thicknesses of the lens.
Electromagnetic Spectrum
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Televisions are very common and are used by many people. You probably have one or more of them in your home. The radio waves that transmit signals to your television are the same type of energy as the deadly gamma rays in radioactive materials. Both are forms of electromagnetic waves.
1. How do you Howelectromagneticthink t waves can be electromagn both harmless and dangerous?
Radio Waves Gamma Rays
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Electromagnetic Waves
are disturbances that transfer energy. Electromagnetic waves are transverse waves. They are characterized by their amplitude (how tall they are) and their wavelength (how long they are).
The amplitude of the wave is determined by the energy of the disturbance that created it. Think about dropping a stone in a pond. The heavier the stone that is dropped, the more energy that disturbs the water and the higher the waves that are created.
The wave’s length is determined by how many of them are created at a time, also known as wave frequency. The frequency of the wave is determined by the frequency of the vibrations that cause the wave.
If a lot of waves are created, the frequency is high, so the waves are closer together. If fewer waves are created, the frequency is low, and the waves are farther apart.
Each wave transfers energy by mass-less particles called photons. The more waves that pass by, the more energy that is transferred. This means that waves of the same amplitude with higher frequency transfer more energy than waves with lower frequency.
2. How are both amplitude and frequency related to wave frequencyenergy? rela
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The range of frequency and wavelength for electromagnetic waves is represented on the electromagnetic (EM) spectrum.
Wavelengths can be kilometers long or shorter than the distance across an atomic nucleus. This wide range of wavelengths means that there is a correspondingly wide range of frequencies. With increasing on their wavelength and frequency. Because it is a continuous spectrum, there is some overlap in radio waves. Radio waves range from about 1 millimeter to 100 kilometers long. Their long wavelength and low frequency mean that they are the lowest-energy electromagnetic waves. Radio waves are emitted in nature by lightning and celestial objects.
Microwaves range from 1 millimeter to about 1 meter long and are sometimes considered part of the radio wave category. They are generated naturally by stars and comprise the cosmic microwave background radiation that is left over from the formation of the universe. They can also be produced by atoms and molecules.
Infrared rays (IRs) are next on the EM spectrum. Their name indicates their location, which is immediately next to the wavelengths of red visible light. Infrared rays range from a few millimeters long to microscopic lengths of about 0.7 micrometers. Infrared waves are emitted by hot objects and are sometimes referred to as heat radiation.
Visible light
Wavelengths of visible light are measured in nanometers. As indicated by the name, these waves have enough energy to stimulate cells in your eyes and allow you to see. The colors of visible light are determined by their wavelengths within this part of the spectrum. In order from longest to shortest, they are red, orange, yellow, green, blue, indigo, and violet. Visible light is emitted naturally by celestial objects and can be emitted by atoms and molecules.
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ultraviolet (UV) waves. UV waves are also measured in nanometers. The energy of ultraviolet waves from the Sun causes skin to tan but can in stimulating skin to produce vitamin D. Ultraviolet waves are emitted naturally by celestial objects. As frequency increases, waves become more harmful. Next to ultraviolet waves are X-rays These highenergy waves are not much longer than an atom, measuring from about 10 to 0.01 nanometers. They are able to penetrate skin and body tissue and cause damage. Long-term exposure can cause many health problems, including radiation sickness and cancer. X-rays are emitted naturally by some celestial objects and some atoms.
The highest-frequency electromagnetic waves are gamma rays. Gamma waves are measured on the subatomic level. Due to their high energy, gamma rays can destroy living cells. This makes them extremely dangerous to living organisms. Gamma rays are emitted naturally by some celestial objects and by radioactive atoms. They can also be formed by atmospheric interaction with cosmic rays.
3. Explain why visible light is y Exp located in the visi middle of the electromagnetic spectrum.
4. Which types of electromagnetic typ waves have you made use of aves havey s and for what applications?
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Electromagnetic waves carry energy, and that energy can be put to use. Because of their unique properties, the different types of electromagnetic waves have different applications
M SM
avelength in eters ie a avelength
reenc aves er secnd nerg ne htn electrn vlts
EM Wave
Radio Waves
Microwaves
Infrared Waves
Applications
Radio telescopes, AM and FM radio signals, TV signals, space communication, remote-controlled toys
Microwave ovens, space telescopes, satellite communication, radar, phone signals, computer data transmission
Space telescopes, blacklights, tanning beds, medical and food sterilization
Space telescopes, medical imaging, industrial imaging, security screening
Space telescopes, medical screening, radiotherapy, medical and industrial sterilization, nuclear power
Observational Tools for Electromagnetic Waves
The tools that scientists have used to observe electromagnetic waves have changed over time. The earliest observations were done with just the human eye. The ancient Greeks did this more than 2,000 years ago. As time progressed, new tools were invented to help people study electromagnetic waves. These include the following:
• Lenses
• Mirrors
• Prisms
Lenses bend light by the process of refraction. Lenses allow scientists to focus light and project images. lens that breaks up visible light into its component colors, allowing each to be studied.
Sir Isaac Newton famously used prisms and lenses to study the various colors of light. Our modern conception of the colors of light, which are well known as “ROY G BIV,” comes from Newton’s studies. But technology does not rest, and progress always continues. Building on what Newton found, in 1814, Joseph von Fraunhofer invented the spectroscope to capture light and disperse it. Light from different sources can be analyzed to determine the chemical compositions of objects that emit light.
Interferometer perpendicular to Earth’s rotation
LInterferometer parallel to Earth’s rotation
to create separate beams of light that have similar characteristics. This was used by Michelson and Morley to measure the speed of light. Ironically, they disproved what they were trying to prove using their modern tools. They were trying to detect the presence of luminiferous aether, which supposedly permeated space and was the carrier of light waves. They expected that light traveling with Earth’s rotation would move faster through the aether than light traveling at a right angle to Earth’s rotation, as shown in the images above. This was shown to not be the case. It was this experiment that helped inspire Albert Einstein to create the theory of special relativity, which showed that light travels at the same speed in a vacuum at all times—the speed of light
More recent tools for observing electromagnetic radiation include various specialized telescopes, such as the Chandra X-ray Observatory, the Fermi Gamma-ray Space Telescope, and the James Webb Space Telescope. These telescopes specialize in X-rays, gamma rays, and infrared, respectively. Our view of the electromagnetic spectrum has broadened immensely!
Dr. Anneila Sargent and Space Telescopes
Dr. Anneila Sargent was born in Scotland. She earned a BSc in physics at the University of Edinburgh in 1963 and a PhD from the California Institute of Technology (Caltech) in 1978. She was a professor of astronomy at Caltech for many years, where she also served as the director of Caltech’s Owens Valley Radio Observatory. There, she led the effort to construct the Combined Array for Research in Millimeter-wave Astronomy (CARMA). She has also been involved with the planning of the international submillimeter wave array (Atacama Large Millimeter/Submillimeter Array, or ALMA) in Chile. She uses millimeter, submillimeter, and infrared observations of space to study how new stars are created in dense clouds of dust and gas and to look for potential sites for the formation of planets
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The electromagnetic spectrum arranges naturally existing electromagnetic waves according to their make them useful for a variety of applications.
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How can a harmless television signal and dangerous radioactive waste be caused by the same type of energy?
Electromagnetic waves are one type of energy, but the amount of energy that is carried by different
5. Why is the amount of energy t y that is carried byg radio waves different y hat is car from the amount of energy that is carried by dangerousnergy gamma rays? ied dang
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1. What determines the wavelength of an electromagnetic wave?
A. Amplitude
B. Frequency
C. Energy
D. Speed
2.
A. Speed and frequency
B. Amplitude and speed
C. Frequency and wavelength
D. Wavelength and amplitude
3. Which types of electromagnetic waves can be most harmful to humans?
A. Microwaves, infrared rays, X-rays
B. Gamma rays, ultraviolet rays, radio waves
C. X-rays, ultraviolet waves, visible light
D. Ultraviolet waves, gamma rays, X-rays
4. Why are different types of telescopes needed to study space?
Different celestial objects emit different types of electromagnetic waves To effectively study these objects, telescopes that can detect these different types of waves are needed
5. Why do ultraviolet waves from the Sun cause skin damage and cancer when visible light waves from the Sun do not?
Ultraviolet waves have a higher frequency than visible light waves do, so they carry more energy. The increased energy makes them more damaging to human tissues.
6. Why is there overlap in the categories of electromagnetic waves?
Electromagnetic waves are categorized based on their wavelength and frequency, but the spectrum is continuous The waves on a continuous spectrum gradually change in wavelength and frequency, so
Speed of Light
Think about what you hear when you see lightning. Do you hear thunder at the same time as you see lightning? No, you see the lightning before you hear the thunder that goes along with it. This tells you that light travels faster than sound. What is the speed at which light travels, and how do we measure it?
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Scientists have been fascinated with the behavior of light since the 1600s, when Sir Isaac Newton theorized that light was composed of particles. As time went on, scientists discovered that light actually consists of and behaves like waves, which explains how light is able to travel through space and does not need any matter to carry the waves along.
Amplitude, wavelength, and frequency can be observed when graphing the wave cycle of light. Amplitude is the height of a wave from the midline to the crest or trough of the wave. Wavelength is the distance between the crests of waves, measured in meters, or how far apart the tops of the waves are from each other. Frequency is the speed of a wave, or the number of wave cycles in a given amount of time, and is often measured in cycles per second or hertz (Hz). Wavelength and frequency are inversely related, meaning that as the wavelength of light decreases, the frequency increases, and vice versa.
Visible light is one kind of electromagnetic radiation; the different kinds of electromagnetic radiation are described in the diagram of the electromagnetic spectrum below.
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1. How are wavelength and frequencywavelengthrelated? a
Ole Romer observed the amount of time that it took for Jupiter’s moons to eclipse, or project their shadows onto the surface of the planet as they were crossing. He proclaimed that light must travel at a reach our eyes. Based on his data collection and calculations, he found the value of the speed of light
Scottish scientist James Clerk Maxwell further showed that all light waves, no matter the type or wavelength, travel at the same speed in a vacuum. While there are some atoms between the planets in our solar system and stars in the galaxies, they are minimal enough that light still travels at a c and is measured to be approximately speed of light, without additional information, refers to light traveling in a vacuum; however, when light travels through a medium such as air or water, it moves able to make it stop completely—momentarily.
The speed of light is important to all studies of our universe. It is used to describe distance, time, atoms, gravity, electricity, and magnetism. The value of the speed of light is unique in its properties. If we were traveling in space at nearly the speed of light—not quite, but close—we would see light moving toward us or away from us with the same value of c
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Doppler effect, there is a shift in the wavelength of light as it moves toward or away from us. Within the spectrum of visible light, this is apparent in a color change. Christian Doppler not only described the change in pitch of moving objects but also the colors of moving objects.
The image below shows how wavelengths of approaching sources are compressed and those of receding sources are stretched out. The light from approaching sources shifts to the blue end of the spectrum, and light from receding sources shifts to the red end of the spectrum. These shifts are aptly called blueshift and redshift, respectively. We notice this in the light shift from stars in the universe, which allows us to determine whether they are moving toward us or away from us. These shifts are also referred to as Doppler shifts after the scientist who enlightened us. The amount of Doppler shift depends on the speed at which light is approaching or receding.
2. Why do you think light slows y dy down when passing slo through a medium own when passg own when p like air or water?mediu
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Albert Einstein’s famous special theory of relativity impacted the study of energy by relating time, space, and mass to one’s frame of reference. He stated that time passes relative to one’s perspective, similar to how throwing a ball could be described differently from the perspective of the thrower and the catcher. The frame of reference sets the coordinates that describe the motion that is being observed. The study of motion describes how speed and time are relative to an observer. For example, when a car is traveling
The motion is relative to the perspective of the observer’s frame of reference. Einstein’s famous equation for special relativity, E = mc2, explains how small amounts of mass that are traveling at the speed of light can be transformed into large amounts of energy. His initial publication neglected the implications of gravity and focused on astronomical distances and traveling at immense speeds. His revision later included gravity and widened the applications for general relativity. Essentially, he stated that as objects to move them.
Einstein used an example of lightning striking two trees simultaneously with a train car halfway between them. He stated that a bystander on the track would observe the lightning strikes simultaneously, as they occurred. However, a person in the train car would see the bolt ahead of the train before the one behind the train because they were moving forward. Because the simultaneous events could be seen differently by each observer and the speed of light does not change, it must be that time moves differently at rest than it does when an observer is in motion. As the speed of the observer increases, time moves more slowly than it does when the observer is at rest, which is a phenomenon known as time dilation.
3. How would you imagine time passage feels for someone agine passg agin traveling near the speed of light? aveling g near
Newton’s Laws and the Speed of Light
Newton’s laws are a limiting case of Einstein’s special theory of relativity at speeds that are much slower than the speed of light. It is not that Newton’s laws are incorrect and Einstein’s are correct. Both laws mathematically model what happens. Einstein’s laws just happen to cover a wider variety of cases. As both are models, we should assume that not every case necessarily needs to be covered.
• on by an external force. This law works well in special relativity—with one limiting factor. If an object keeps a constant speed that is near the speed of light but no force acts on it, it will keep moving at this constant speed that is near the speed of light. If a force acts on it, the limit is that it cannot go faster than the speed of light
• Newton’s second law states that force is equal to mass multiplied by acceleration. Acceleration depends on time. Time is relative to the observer’s motion. If the frame of reference is inertial, this equation for force acts as usual at lower speeds. However, if someone attempted to push an object from rest to relativistic speeds, the object would appear to become more massive and thus harder to accelerate. Again, the speed of light is still the limiting factor.
• Newton’s third law states that every action has an equal and opposite reaction. This law works until you apply force to something that is already near the speed of light. Energy is added to the system, but it doesn’t move much faster. And the speed of light cannot be exceeded under any circumstance
Einstein’s predictions have been backed up by multiple experiments. It has been thoroughly demonstrated that light moves at the same speed in any reference frame, and nothing goes faster than the speed of light. Implications of this led to higher-level physics concepts, such as the following.
• Time dilation: Time appears to move slower for someone who is going faster.
• Length contraction: Faster objects measure smaller in length than slower objects.
It is not that Newton and Einstein contradict one another. It is more that Newton’s laws are more applicable when a large object is moving slowly (compared to the speed of light). Einstein’s laws, which fast. When an object is moving too fast, Newton’s laws are no longer an accurate prediction of what the object will do. This is not because Newton was wrong but rather because of these limiting factors.
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Max Planck, a German physicist, observed that an object that began as black would appear red, then yellow, and then white as the temperature of the object increased. He determined that the color change was due to a change in energy as the temperature increased. From this, he established Planck’s constant (h), 6.626 X 10 J*s, where J (joule) is the unit of energy.
metal electrodes. The electrodes had a voltage applied across them, and the light changed the voltage of the electrode. This became known as the photoelectric effect. The photoelectric effect occurs when electrons are ejected as light shines on metal, creating an electric current, but not all frequencies of light will cause the effect.
At the turn of the 20th century, scientists were beginning to understand and agree on the nature of light behaving as a wave. Einstein used Planck’s theory to expand upon the photoelectric effect. He determined that light is a quantum of energy that behaves like a stream of particles called photons. Einstein’s theory explains why electrons are not ejected at all frequencies; so if the frequency and energy of a photon are too low, an electron will not be ejected, and the photoelectric effect will not occur. Therefore, different wavelengths of light must possess different amounts of energy.
Einstein’s revelation means that light can behave in one of two ways depending on how we view it—as a wave or as a particle. Tests
act as both waves and particles, which is known as the dual nature of light
The Dual Nature of Light
Property
Reflection
Refraction
Polarization
Diffraction
Interference
Photoelectric effect
Compton effect
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These variables can be calculated using the formulas in the examples below.
Example 1
Energy (E = h v) E = (6.626 x 10 10 Hz)
Example 2
Calculate the frequency of a quantum of radiation with an energy of 2.12 x 10 J.
Energy (E = hv) 2.12 x 10 J = (6.626 x 10 J*s) v 12 Hz
Example 3 cm. Calculate the frequency and energy associated with this wavelength.
*Remember to change centimeters to meters (divide by 100).
Part II: Energy (E = h v) E = (6.626 x 10 Hz)
Luc Thévenaz, Physicist g
university known as École Polytechnique Fédérale de Lausanne. His team of researchers worked together is transmitted leaves an optical memory or afterimage of the information, like an echo of a noise that was heard seconds before, and increasing the speed at which light travels can only be done in portions at this time. The implications of this stand to improve both telecommunication signals, which transmit currently bound by the speed at which equipment can process that information, as current technology is limited by the speed at which sensors can read the signals that are being transmitted.
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speed of light impacts how scientists study the universe. The way we understand distance, time, atoms, gravity, and more all centers on our understanding of the behavior of light. If we were able to travel at the speed of light through space, we would see light slow down due to the limitations of time and our frame of reference. Colors are determined through perceived wavelengths and frequencies of light, as demonstrated by the electromagnetic spectrum. However, that perception can be altered as objects move toward or away from our frame of reference. The speed of light impacts how the world around us is perceived, which alters our decisions in response to that perceived reality.
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How is time affected by speed?
The observations that occur on Earth move at only a fraction of the speed of light. While there can be different frames of reference for events, special relativity assumes that light is traveling at a constant speed in all scenarios. Therefore, distance and time are the only factors that can change. Clocks that are traveling on a jet airplane move slower than those that are stationary on the ground, but because neither the plane nor Earth is moving anywhere near the speed of light, this difference in time is negligible.
5. If a jet were we its headlights on, how fast would you headligh perceive the speed y of light coming from perceive the spe p the lightheadlights? coming
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1. Which of the following travels the fastest?
A. Ultraviolet light
B. Visible light
C. Radio waves
D. They all travel at the same speed.
2. What causes a shift in the appearance of a wave due to the motion of an observer?
A. Doppler effect
B. Photoelectric effect
C. Duality of light
D. Frame of reference
3. What happens to the energy of a wave when the distance is increased?
A. Energy increases.
B. Energy decreases.
C. Energy remains unchanged.
D. Energy is relative to the frame of reference.
4. If two observers were moving at different speeds in a vacuum, how would they view light?
5. 10 Hz.
6. Determine the energy that is produced from radiation with a wavelength of 2.6 x 10 m.
Patterns of Matter in the Universe
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When you look up at the night sky, thousands of objects sparkle into view. If you gazed through a telescope, you would see many more of these objects. You are observing stars, which give off energy in the form of visible light.
However, the stars that you can see are only a very small portion of the universe. What objects in space, other than stars, make up the universe? What kinds of energy, other than light, do these objects give off? And how do scientists answer these and other questions about objects that are so far away?
1. What objects in space, other than stars, make up the stars,universe? p p
The Universe
The universe contains everything that exists, from particles of matter that are smaller than an atom to the largest stars. The universe also includes all forms of energy, from the light that streams from stars to invisible radio waves and X-rays. Even time is part of the universe. Scientists think of time as beginning when the universe began.
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been observed from Earth. The different colors are masses of matter as they were a short time after the universe was born. These masses of matter later became stars and galaxies.
All of the matter and energy in the universe is contained in a volume of space that scientists have discovered is constantly expanding. The expanding universe is similar to a balloon that is constantly
that the universe started very small and has grown in all directions ever since.
The most distant objects that have been detected are about 13.7 billion light-years away from Earth. A light-year is a unit of distance. It is equal to the distance traveled by light in one year, which is approximately 9.5 trillion kilometers. So, light from the most distant objects that scientists have observed began its journey to Earth 13.7 billion years ago. If these objects are actually the most distant objects in space, they are also the farthest back in time. For these reasons, scientists estimate that the universe is about 13.7 billion years old.
To learn about the properties of objects in space, scientists study the energy that comes from these objects. The energy may be in the form of visible light or other components of the electromagnetic spectrum, such as radio waves and X-rays. The electromagnetic spectrum is an arrangement of forms of energy that travel through space in waves. Objects in space emit these forms of energy in different patterns. Scientists use special telescopes to detect these patterns and learn about the objects that emit them.
From its birth to the present, the universe has changed tremendously. Huge pockets of gas have been pulled together by gravity to form stars. In turn, these stars have been drawn together by gravity to form families of billions of stars. Stars that were born long ago developed, aged, and died. This process goes on today, and it will continue to go on in the future.
gases, like all forms of matter, are composed of particles in motion. These particles are tiny, but they have mass, so they are affected by gravity. As the density of a gas increases, gas particles collide more frequently and with greater force, causing the gas’s temperature to increase as well. Eventually, gases can become so hot that they ignite, becoming huge, burning spheres—stars.
2. Why does distance equal time do in astronomical observations?
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Stars
Stars are large objects in space that generate their own energy. Almost everything that you can see in the night sky with your unaided eyes is a star. (Exceptions include a few planets of our solar system, Earth’s Moon, and an occasional comet.) A star is a huge ball of gas that produces its own energy, mostly through nuclear reactions in its core. Light is the most obvious form of energy that is produced by a star. However, stars produce many other forms of energy, such as infrared radiation (or heat) and ultraviolet radiation. Gravity holds together the particles that make up the body of a star. In other words, a star is so massive that it is held together by its own gravity.
9.5 trillion kilometers; therefore, Proxima Centauri is about 40 trillion kilometers from Earth. Light from this star takes 4.22 years to reach Earth. So, when we see Proxima Centauri through a telescope, we see the star as it existed 4.22 years ago.
Scientists don’t know for certain how stars form. The most commonly accepted hypothesis is that stars form from vast clouds of dust and gas called nebulae (singular: nebula). The force of gravity is strong between the countless particles of dust and gas. Gravity causes the cloud to condense and eventually collapse on itself. As the center of the cloud becomes denser, it starts to spin and heat up. Gravity pulls more gas and dust particles into the hot, spinning mass—a process that continues for millions of years. Finally, the matter becomes so hot that it ignites. Nuclear reactions begin, and the nebula forms a star.
3. What effect does gravity have on matter in es gravity vy the universe?
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The stars in the universe are not all the same. Some are very large whereas others are relatively small. Some are extremely hot; others are cooler. Some emit great amounts of energy; others emit less energy. Stars may be young, middle aged, old, or dying. They may be composed primarily of hydrogen, or they may contain mostly helium and heavier elements. Some are very bright; others are dimmer. Their colors range from blue and white to yellow and red.
developed a way to classify stars according to their luminosity, temperature, and color. (Luminosity is the brightness of a star relative to the brightness of other stars. Luminosity is also called absolute shown below.
measured in units called kelvins (K). (To convert a measurement in kelvins to degrees Celsius, subtract 273 from the Kelvin measurement.) Hotter stars are plotted on the left side of the diagram, and cooler stars are plotted on the right side.
Stars are plotted along the y axis by increasing luminosity. Brighter stars are plotted at the top of the diagram. Less-bright stars are plotted at the bottom of the diagram. The diagram shows a star’s luminosity relative to Earth’s Sun. So, stars alongside the 102 (100) tick mark are 100 times brighter than the Sun, and stars alongside the 10–2 (0.01) tick mark are 100 times dimmer than the Sun
Stars are plotted along the x axis by color. Blue and white stars are plotted on the left side of the diagram. Yellow stars are plotted at the side of the diagram.
in the main sequence make up the vast majority of stars in the universe. In general, the hotter a star is on the main sequence, the brighter and bluer it is. As stars age, they fall outside the main sequence and become giants or supergiants depending on their mass. As less-massive stars die, they become relatively tiny white dwarfs. More-massive stars die by exploding into powerful supernovas. (Even smaller stars live for billions of years. The Sun, which is an average-sized star in the main sequence, is about midway through its 10 billion–year life cycle.)
4.
What are the four groups of stars on an ur group H-R
diagram?
Habitable Zone
Named after the developer of the planetary laws, the Kepler Space Telescope hunts for planets that may be able to contain life. These planets are located within the habitable zones around stars. The habitable zone is a zone that is in the range of distance from a star where liquid water might pool on and temperature.
Water and Potential for Life: There are several chemical properties of water that make it a crucial component for life. Water is capable of dissolving almost anything. Water can exist in solid, liquid, and gaseous forms in a relatively narrow range of temperatures; this is a rare property.
Life as we know it on Earth uses a membrane to separate an organism from its environment. Staying alive requires taking in important materials for energy creation while at the same time keeping out toxic
Water molecules are made of two hydrogen atoms bonded to an oxygen atom. The way they bond makes water a universal solvent; in other words, almost every substance can dissolve in water. Water molecules have polarity, with hydrogen atoms grouping together on one side of the molecule. This creates a positive region while oxygen holds the negative end of the charge. The positive hydrogen end attracts negative ions while the negative region attracts positive ions. With these properties, water makes the perfect medium for transmitting substances into and out of a cell. In particular, elements that are essential for life, such as phosphates or calcium ions, can be transmitted.
Phases of Water: Water can act as a solid, liquid, or gas in temperatures such as those on Earth. Other molecules that meet the criteria to support life tend to be found in liquid form at temperatures or pressures that are not considered hospitable to known life-forms. Finding water in all three phases in
Evolution of Life: have been the catalyst for carrying life to Earth. One of the theories about the origin of life, called panspermia, contends that icy comets crashed into Earth, carrying tiny organic molecules that formed as would destroy such delicate molecules. In solid form, water provided a shield from the radiation.
Other Possibilities: While water is essential to life on our planet, is it possible that there are life-forms out there that don’t follow the same criteria? Scientists have looked at other liquids that may play roles that are similar to water’s. They have searched for something that mimics our universal solvent and transport medium. Ammonia and methane are top choices. Ammonia is a polar molecule (as is water) in the solar system. Methane is not polar, but it can dissolve many substances. However, methane becomes liquid only at very cold temperatures (–296°F, or –182°C). Large lakes of liquid methane exist on Titan, which is a moon of Saturn. This is a possible spot for future exploration.
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Every star in our night sky is part of a galaxy called the Milky Way. This is our home galaxy. However, the Milky Way is only one of billions of galaxies in the universe, and each one contains hundreds of billions of stars, planets, gases, and dust that are held together by the force of gravity. Most galaxies are invisible to the unaided eye. However, if you have keen vision, you might spot one on a clear night. It would look like a faint, fuzzy patch of light. Viewed through powerful telescopes, galaxies appear in various shapes
Spiral: Spiral galaxies are shaped like disks with arms spiraling out from a central hub. Most of the galaxies that are known to scientists—including the Milky Way—are spiral galaxies. The stars and other objects in a spiral galaxy rotate in the same direction around the galaxy’s center, like an incredibly fast-spinning pinwheel.
Lenticular: Lenticular galaxies form a subgroup of spiral galaxies. Lenticular r spiral galaxies, lenticular galaxies have a central hub, but they lack arms. They are sometimes referred
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Elliptical galaxies look a bit like footballs. (An ellipse is an oval.) The stars and matter in an elliptical galaxy rotate around the galaxy’s center in a variety of directions. The largest galaxies in the universe are elliptical. They may be millions of light-years across and hold trillions of stars.
Irregular: needles. Others are shaped like rings or clouds. Astronomers think that the gravities of nearby galaxies may be pulling irregular galaxies into their disorganized shapes.
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The universe includes everything that exists—all matter, energy, space, and time. But how did the universe and its components come from? Scientists have found solid evidence that the universe had a beginning.
The big bang theory is the most widely accepted theory to explain the origin of the universe. According to this theory, the universe began as a single, tiny point—smaller than an atom—called a singularity. This in the universe. The Big Bang was the moment when all of this matter and energy suddenly expanded out from this singularity. The universe has been expanding ever since. The laws of physics, including matter to come together to form the particles from which all of the components in the universe are made: protons, neutrons, and electrons.
During these seconds, the universe was too hot for these particles to form atoms. Also, the clouds of subatomic particles—these protons, neutrons, and electrons—were so dense that no light could shine through them. About three seconds after the Big Bang, the universe had cooled enough for protons and neutrons to come together to form simple nuclei
After about 300,000 years, electrons joined with these nuclei to form the atoms of the simplest which contains two protons per atom, formed next. To this day, hydrogen and helium remain the most common elements in the universe. As atoms continued to form, the dense cloud of subatomic particles
Prior to the discovery of the Big Bang, many scientists thought that the universe had always existed and would always exist—in an unchanging state. This was called the steady state theory. The steady state theory was disproved in the 1920s by a scientist named Edwin Hubble. By analyzing light from distant stars, Hubble discovered that the universe is actually expanding. This discovery led to the big bang theory. Scientists reasoned that if the universe is expanding, it must once have been compressed into a much smaller, denser space. Later discoveries have continued to support the big bang theory.
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The fact that the universe is expanding was one of the most important early pieces of evidence for the big bang theory. To understand how scientists know that the universe is expanding, you need to know a bit about light waves. When stars give off light, the light travels in waves through space. Some waves are longer; longer waves are seen as red light. Some waves are shorter; shorter waves are seen as blue light.
As a star moves away from Earth, light waves from the star that reach Earth seem to have stretched. As a result, the star appears redder. This is called redshift. In contrast, as a star moves toward Earth, light waves from the star that reach Earth seem to compress. As a result, the star appears bluer. This is called blueshift.
BLUESHIFT REDSHIFT
The stars and galaxies that Edwin Hubble observed experienced redshift. In other words, they were moving away from Earth. If galaxies are moving away from Earth (and each other), the universe cannot exist in a steady state. Hubble ultimately concluded that the universe must be expanding. He also discovered that galaxies that are farther from Earth experience greater redshift. In other words, the farther a galaxy is from Earth, the faster it is moving away from Earth. Hubble concluded that not only is the universe expanding, but it must be expanding more quickly all the time!
Scientists can now measure the intensity of a galaxy’s redshift and use this value to calculate the galaxy’s distance from Earth and the speed at which it is moving. Scientists still have not developed a way to measure the current size of the universe.
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Visible light is a form of electromagnetic radiation; energy that travels through space in wave-like patterns at high speeds. In fact, this energy is the fastest thing in the universe. Electromagnetic radiation travels at a constant rate of about 300,000 km/s. (We call this the speed of light.) Because the universe is so vast and light moves so quickly, light gives scientists a useful tool for measuring distances in space. As you will discover, scientists can also use light to measure the universe’s age.
A light-year is the distance that light travels in one year, which is about 9.5 trillion kilometers. If a star is four light-years from Earth, light from that star takes four years to reach Earth. If a star is 4 million light-years from Earth, light from that star takes 4 million years to reach Earth. This means that scientists are looking into the past when they observe electromagnetic radiation in space. Scientists can estimate the age of the universe by observing the universe’s oldest stars and the intensity of their redshift. Scientists can use these observations to calculate the rate of the expansion of the universe and work backward to determine when the expansion began. Using this method, scientists have estimated that the universe is about 13.7 billion years old. In other words, the Big Bang occurred 13.7 billion years ago.
The speed of light in a vacuum is a universal physical constant that equals exactly 299,792,458 m/s
speed at which all massless particles (including electromagnetic radiation such as light) and gravitational waves travel in a vacuum. These particles and waves travel at the speed of light regardless of the motion of the source or the inertial frame of reference of the observer. Nothing travels faster than the speed of light in a vacuum, which is the same for all observers, no matter how fast they or the light source are moving. In other words, regardless of the speed of an observer or a source, in a vacuum, the speed of light is always c (3 x 108 m/s).
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1.The principle of relativity: All the laws of physics are valid in any inertial reference frame.
2. c, relative to any inertial reference frame independent of the motion of the light source.
The theory of relativity describes the relationship between mass, energy, and the speed of light as E = mc2. The speed at which light propagates through transparent materials, such as glass or air, is less than c. The ratio between c and the speed, v, at which light travels in a material is called the refractive index, n, of the material: n = c/v.
In many cases, light and other electromagnetic waves are assumed to propagate instantaneously, but for long distances and very sensitive measurements, the exact speed of light is important to calculate very distant objects in the universe, such as planets and stars. The light that we observe from stars took many years to travel to us, and from these properties, scientists discover the history of the universe.
must be sent within the computer from chip to chip. After centuries of increasingly precise measurements, in 1975, the speed of light was found to be 299,792,458 m/s with a measurement
International System of Units (SI) as the distance that is traveled by light in a vacuum in 1/299,792,458 of a second. As a result, the numerical value of c
Frame of Reference
The energy, E, and the momentum, p, depend on the frame of reference in which they are measured (e.g., Lorentz contraction). Kinetic energy is the energy of motion and consequently is a function of velocity. This means that an object’s energy and its momentum depend on the object and the observer’s frame of reference. Energy and momentum are frame dependent. According to Einstein, the measures for length, time, and mass depend on an observer’s motion relative to a chosen frame of reference. In special relativity, a stationary observer who is watching a fast-moving object will see that (A) the length of a fast-moving object is shorter than if the object were at rest (Lorentz contraction) and (B) time passes more slowly on the fast-moving object than when it is at rest. From an observer with a different frame of reference, such as one inside the fast-moving object, everything inside looks like a normal length, and time passes normally. For those outside this frame of reference, lengths are foreshortened, and clocks are slow.
Edwin Hubble, Astronomer g
many of the things that we view today as separate galaxies were viewed as nebulae that were part of the Milky Way galaxy. Hubble proved that stars in these nebulae were so distant that they were millions of light-years away, beyond the Milky Way itself. Hubble
(spiral, elliptical, and irregular) and showed that all galaxies except local ones are moving away from us. It was his research that showed that the universe is expanding. The Hubble Space Telescope was named in his honor.
The
Big Picture
The light from distant stars helps us understand the universe. Because distance is time, we are able to peer into the past, seeing the universe as it was by looking ever farther away. When we gaze deep into the cosmos, we can note several things. The universe is full of stars and galaxies. Those galaxies are far apart from each other. It is the attractive force of gravity that tries to bring random clouds of dust and gas together to form stars and galaxies. It is the expansion of the universe that tries to tear those clouds of dust and gas apart, spreading them thinner and thinner. And it is the interplay between these two forces that allows the universe to exist as we see it today and allows us to predict its future.
Connect It
How is matter in the universe distributed?
Matter in the universe is distributed in clusters and clumps. It is not evenly distributed; rather, it forms galaxies, clusters, stars, and planets. There are two forces that drive this distribution: the expansion of the universe and the force of gravity. Gravity pulls matter together while the expansion of the universe spreads it out. The combination of these two forces is what makes the structure of the universe possible.
5. How are gravity and expansion How are g w arg combining to produceexpans the structure of mbining prod the universe?
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1. Which of the following is a component of the universe?
A. Matter
B. Light
C. Gravity
D. All of the above
2. Which of the following is evidence of the big bang theory?
A.
B. Presence of galaxies
C. Dust quantities
D. Frame of reference
3. What effect does gravity have on matter as it is distributed across the universe?
A. It spreads matter out.
B. It pulls matter together.
C. Matter remains unchanged.
D. It is impossible to predict the effect.
4. Describe how matter is distributed in the universe.
5. What evidence exists for the Big Bang?
6. How does distance equal time in astronomy?
GLOSSARY OF TERMS
acceleration atomic theory
acceleration: the rate of change in velocity; speeding up, slowing down, or
changing direction
acceleration due to gravity: the constant acceleration on an object because of gravitational force; on Earth it is 9.81 m/s2.
action-reaction pair: a pair of forces that obeys the statement “for every action force, there is an equal and opposite reaction force”
air resistance: the frictional force that air exerts against a moving object
alpha particle: a positively charged particle identical to the helium atom nucleus, with two protons and two neutrons, that is emitted from radioactive decay of a nucleus
amplitude: the height of a wave from the origin to the crest or trough
atom: the smallest unit of an element that has all of the properties of that element; contains a nucleus within a surrounding electron cloud
atomic model: a model that lists the three subatomic particles that make up atoms; gives the mass and charge of each subatomic particle
atomic nucleus: the tiny, ver y dense, positively charged region in the center of an atom; made up of protons and neutrons
atomic orbital: a model that describes the likelihood, or probability, of finding an electron at a specific location and position around the nucleus
atomic theory: a scientific theor y of the nature of matter, which states that matter is composed of discrete units called atoms
GLOSSARY OF TERMS
big bang theory conductor
big bang theory: a theor y that says the universe began as a small point that expanded rapidly about 13.7 billion years ago
centripetal force: the force pulling on an object traveling in a circular path toward the center of the path
chemical change: a change that occurs when a new substance is created with different properties; observable as a color change, the production of gas or a precipitate, or the release of heat or light
chemical energy: energ y stored in chemical bonds; can be released in a chemical reaction
chemical property: characteristic that can only be observed or measured through a chemical reaction circuit: a closed loop of conductors through which an electric current can flow
closed system: a system that does not exchange matter but does exchange energ y with its surrounding environment
compound: a substance composed of multiple elements combined in fixed proportions
compression: a force that tries to collapse an object; an increase in density caused by external pressure
concave mirror: a mirror with a surface that curves inward
conduction: the transfer of energ y from one medium to another through direct contact
conductive: having the ability to transfer energ y from one medium to another through direct contact
conductor: a material that allows electrons to flow freely from particle to particle
GLOSSARY OF TERMS
constructive interference displacement
constructive interference: when the crest of one wave meets the crest of another wave at the same point, increasing the wave’s amplitude
convection: the transfer of thermal energ y through currents in fluids
convection current: a circular movement of fluids that is caused by the rising of hotter, less dense fluid and the falling of cooler, denser fluid
convex lens: a lens with a surface that curves outward
convex mirror: a mirror with a surface that curves outward
coulomb: the SI unit of electric charge; equal to the quantity of electricity conveyed in 1 second by a current of 1 ampere
Coulomb’s law: a law describing the electrostatic force of interaction between charged particles based on the strength of the charges and the distance between the particles crest: the highest part of a wave
current: the flow of an electric charge through an object or medium
destructive interference: when the crest of one wave meets the trough of another wave at the same point, decreasing the wave’s amplitude
diffraction: the behavior of a wave as it bends around a sharp edge; occurs when a wave passes through a single narrow slit or multiple narrow slits
displacement: the vector quantity that gives the straight-line distance from a starting position to an ending position
GLOSSARY OF TERMS
distance electromagnetic force
distance: a measure of how far apart two objects are
Doppler effect: an apparent shift in the frequency of a wave due to the motion of the observer or the source of the wave
elastic collisions: an encounter between objects in which the total kinetic energy of the objects before and after the collision is equal
electric field: a region around a charged particle or object within which a force would be exerted on other charged particles or objects
electric potential: an expression of the voltage of a circuit or the pressure for pushing current through a circuit
electric potential energy: the potential energ y per unit of charge that an object would have at a point in space as the result of the object’s charge and the charges of other objects at other points in space
electrical energy: energ y produced as a result of moving electric charges
electrical force: the interaction between a charged particle and an electromagnetic field or between two charged particles
electricity: a physical phenomenon associated with the presence and movement of electric charge
electromagentic radiation: energ y in the form of oscillating electric and magnetic fields that is released in electromagnetic processes; characterized based on the frequency and wavelength of the oscillations as radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays
electromagnetic force: the interaction between a charged particle and an electromagnetic field or between two charged particles
GLOSSARY OF TERMS
electromagnetic spectrum focal length
electromagnetic spectrum: a continuum of all electromagnetic waves arranged according to frequency and wavelength
electromagnetic waves: oscillations of electromagnetic fields that carry energ y through a medium or vacuum
electron: a negatively charged subatomic particle of the electron cloud; involved in the formation of chemical bonds
element: one of the primar y substances that make up matter and cannot be chemically broken down or converted into other substances
electron cloud: all of the area inside an atom surrounding the nucleus where electrons are found
electron orbital: the specific regions around the nucleus of an atom in which electrons travel
electrostatic attraction: an attraction related to the relative charge of an object
electrostatic force: a force that is created by the interaction of stationary electric charges
energy: the ability of a system to do work or produce heat
energy transformation: the change of energ y from one type to another (kinetic to potential or potential to kinetic)
equilibrium: a condition in which all competing influences are balanced
fission: a nuclear reaction in which a heavy nucleus breaks into two lighter nuclei, releasing energy
focal length: the distance between the surface of a mirror or the center of a lens and the point at which light rays that were initially parallel intersect after being redirected by the mirror or lens
GLOSSARY OF TERMS
focal point gravitational potential energy
focal point: the point at which light rays that were initially parallel intersect after being redirected by the mirror or lens
force: an interaction between an object and another object or a field that acts to change the motion of the object
frame of reference: a set of space-time coordinates that describes motion of a body relative to something else
free-body diagram: a diagram showing an object and the directions and magnitudes of all the forces that are acting on the object
frequency: the number of wave cycles that pass a given point per unit of time
friction: a force that resists the relative motion of two objects or substances sliding against one another
fusion: a nuclear reaction in which two lighter nuclei combine to form a single heavier nucleus and some of the original mass is converted to energy
galaxy: a large grouping of stars, planets, gas, and dust in space held together by gravity
gamma rays: electromagnetic waves with the highest energ y; produced by supernovas, the destruction of atoms, or the decay of radioactive material
gas: a state of matter where the shape and volume are variable and dependent on the shape of the closed container, and where the particles are completely independent of each other
gravitational force: a force of attraction between two masses
gravitational potential energy: the energ y that is stored in an object due to its position
GLOSSARY OF TERMS
gravity isolated system
gravity: a mutually attractive, physical force of nature that causes two bodies to attract each other
impulse: f o r ce e x e r ted o v e r a t im e i nterval that causes a chan g e in an o b ject’s momentu m
heat: energ y transferred between two objects of different temperatures, moving continually in a predictable pattern from a warmer site to a cooler site until all sites have reached the same temperature
heat transfer: the exchange of thermal energ y from one physical system to another
homeostasis: the tendency for a system, such as a cell, to maintain relatively constant internal conditions
inelastic collisions: an encounter between objects in which some of the kinetic energ y is converted into other forms of energ y
inertia: an object’s tendency to resist changes in its motion
infrared waves: electromagnetic waves with wavelengths that are longer than visible light but shorter than radio waves
insulator: a substance that does not allow electrical or thermal energy to pass through it
hydrogen bond: an attraction between a hydrogen atom that is covalently bonded to a highly electronegative atom (e.g., oxygen or nitrogen) and another highly electronegative atom to which the hydrogen is not covalently bonded
interference: the combination of two or more of the same type of wave
isolated system: a system that does not exchange matter or energ y with its surrounding environment
GLOSSARY OF TERMS
joule longitudinal wave
joule: the SI unit of energ y equal to 1 newton of force applied over 1 meter of distance
Kepler’s law of ellipses (1st): the law that states that all planets move in an elliptical orbit around the Sun
Kepler’s law of equal areas (2nd): the law that describes the speed of planets that orbit the Sun
law of conservation of momentum: a law stating that for collisions in a closed system, the total momentum remains the same law of inertia: a law stating that an object at rest will remain at rest and an object in motion will stay in motion at a constant velocity unless it is acted upon by an unbalanced force
Kepler’s law of harmonies (3rd): the law that describes the size of a planet’s orbit
Kepler’s laws: three laws that describe the motion of planets around the Sun
kinetic energy: the energ y of motion
law of conservation of energy: a law stating that energ y cannot be created or destroyed—it can only change forms
light energy: energy that is carried by an electromagnetic wave as it travels through space
liquid: a state of matter where the shape is variable and dependent on the bottom of the container, where the volume is constant, and where the particles move independently within the liquid
longitudinal wave: a wave that is propagated in the same direction as the displacement of the transmitting field or medium
GLOSSARY OF TERMS
magnetic force net force
magnetic force: a force of attraction or repulsion that arises between electrically charged particles because of their motion
mass: a measure of how much matter is present in a substance
mass defect: the difference between the mass of an atomic nucleus and the sum of the masses of the subatomic particles within the atomic nucleus
microwaves: electromagnetic waves that are between radio waves and infrared waves on the electromagnetic spectrum
molecule: a g roup o f two or more atoms bonded to gether by chemical forces, representin g the smallest possible unit o f a chemical compound that can part i c i pate i n a react i o n
mass-energy equivalence: the principle that mass is concentrated energ y; the amount of energ y in a given amount of mass can be calculated with the formula.
matter: anything that has volume and mass
mechanical energy: the sum of the potential energy and kinetic energy of an object; changes when work is done on the object
medium: the material through which the wave travels
momentum: a property of a moving object; determined by the product of its mass and velocity
motion: the change in an object’s position with respect to time and in comparison to the positions of other objects used as reference points
net force: the overall force acting on a system or object after opposing or balanced forces cancel each other out
GLOSSARY OF TERMS
neutron orbit
neutron: a subatomic particle of the nucleus of an atom that is without charge and contributes to the mass of an atom
Newton’s third law of motion: the law stating that for every action force, there is an equal, opposite reaction force
newton: the SI unit of force
Newton’s first law of motion: the law stating that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless it is acted upon by an unbalanced force
Newton’s law of universal gravitation: the law stating that every piece of matter is attracted to ever y other piece of matter; the force is directly proportional to their masses but inversely proportional to the square of the distance between them
normal force: the force that is generated by a surface in opposition to an object that is pressed upon it
nucleon: a particle that is part of the nucleus; a proton or neutron
nucleus: the tiny, ver y dense, positively charged region in the center of an atom that is made of protons and neutrons
object: the source of light that forms the image
Ohm’s law: the relationship between potential difference, current, and resistance
Newton’s second law of motion: the law stating the relationship between the force applied to an object and the object’s mass and acceleration
open system: a system that exchanges matter and energy with its surrounding environment
orbit: a curved path followed by a satellite as it revolves around an object in space
GLOSSARY OF TERMS
parallel circuit plasma
parallel circuit: a circuit with components that are connected so that there are multiple current paths, each component has the same voltage across its ends, and the total current in the circuit is the sum of the currents in the components
period: the time that something takes to happen; the time required for the completion of one wave cycle or one revolution
photoelectric effect: the observation that when certain wavelengths of light strike a piece of metal, electrons are emitted, potentially creating an electric current photon: an elementar y particle that is the smallest possible amount of light and all other forms of electromagnetic radiation that can interact with anything
physical change: any alteration to a substance that does not change its chemical identity; examples include changing phase, dissolving into a solution, or breaking up into smaller pieces.
physical property: property that describes matter, including color, feel, smell, boiling point, melting point, and density
Planck’s constant: the constant that gives the unvarying ratio of the energ y of a quantum of radiation to its frequency; as an approximate value of 6.626 x 10 34 joule-seconds; represented by the symbol h
plane mirror: a mirror with a flat surface
plasma: a physical state of matter that exists at extremely high temperatures in which all molecules are dissociated and most atoms are ionized
GLOSSARY OF TERMS
polarization: the restriction of the vibrations of light (electromagnetic radiation) to a single plane or direction
potential energy: the energ y that an object has because of its position relative to a force field or because of the relative positions of its components
power: the rate of work or energ y transfer per unit of time
proton: a positively charged subatomic particle of the nucleus of an atom that contributes to the mass of the atom
radiant energy: electroma g netic waves g iven o ff by a source into the surroundin g environmen t
radiation: the emission or transmission of energ y as particles or waves
radio waves: electromagnetic waves with long wavelengths and low frequencies
rarefaction: the less dense, more spreadout regions of longitudinal waves
ray diagram: a diagram that is used to show how an image is formed using a mirror or lens
real image: the point at which multiple waves converge to produce an image
redshift and blueshift: the change in wavelength that allows us to determine if an object is moving toward us or away from us
reflection: a change in the direction of a wave at an interface between two media that sends the wave back into the medium from which it came
refraction: a change in the direction of a wave as the wave moves from one medium into another
GLOSSARY OF TERMS
repulsion space-time
repulsion: t h e f o r ce t h at te n ds to separate bodies o f like electric char g e o r
ma g netic po l arit y
repulsive force: the force that acts between bodies of like electric charge or magnetic polarity, tending to separate them
resistance: the ability of a material to oppose the flow of an electric current through it
resting position: an object’s default position outside of external forces
scalar quantity: a quantity that is fully described by magnitude and does not have a direction
semiconductor: a material with electric conductivity between that of a conductor and an insulator
series circuit: a circuit with components that are connected end to end so that there is only one path for the current to flow along and each component has the same current; has a total voltage across the circuit that is equal to the sum of the voltages across the components
simple machine: device that reduces the amount of force needed to move an object
solid: a state of matter where the shape is constant and rigid, where the volume is constant, and where the particles vibrate in a fixed position
sound energy: a form of energ y that is made by vibrations traveling as waves and requires a medium (air, water, or solids) in order to travel
space-time: the four-dimensional view of physical reality that makes up the universe
GLOSSARY OF TERMS
speed thermal energy
speed: the measurement of the rate of change of position with respect to time
speed of light: the maximum speed at which all matter and information in the universe can travel, or the measurement of the rate of light’s movement through a given substance over a specific unit of time
standing waves: the vibration of a system in which some particular points remain fixed while others between them vibrate with the maximum amplitude
star: a self-luminous celestial body consisting of a mass of gas held together by its own gravity and emitting energ y that is generated by nuclear reactions in its interior
static electricity: the accumulation of electric charge on the surface of an object
static friction: the friction between two surfaces when there is no relative motion between them
strong nuclear force: the force that binds the protons and neutrons together in the nucleus subatomic particles: particles that are smaller than the atom
superposition: when two (or more) waves travel through a medium at the same time
system: a group of interacting, interrelated, or interdependent elements forming a complex whole
temperature: the hotness or coldness of matter related to the average kinetic energ y of the molecules of that substance
tension: a force that tries to stretch an object or is provided by strings, ropes, or chains
thermal energy: the internal energ y of a system, including the kinetic and potential energ y of its particles
GLOSSARY OF TERMS
thin lens equation wave
thin lens equation: an equation relating object distance, image distance, and focal length time: measurements, such as minutes and hours, used to quantify intervals, durations, and sequences
transverse waves: a wave that is propagated in a direction that is perpendicular to the displacement of the transmitting field or medium
trough: the lowest part of a wave
ultraviolet waves: electromagnetic waves with wavelengths that are longer than X-rays but shorter than visible light
unbalanced force: a situation in which the net force on a system is not zero
universe: all space and the matter space contains
vector quantity: a quantity with both a magnitude and a direction
velocity: the rate of change of the position of an object that is moving in a specific direction
virtual image: an optical image that is produced from the apparent divergence of light rays
visible light: electromagnetic waves with wavelengths that are longer than ultraviolet light but shorter than infrared waves
voltage: the difference in electric potential between two points
watt: SI unit for power
wave: a disturbance in particles or a field that transfers energ y progressively from point to point without the field or particles having any net movement themselves
GLOSSARY OF TERMS
wavelength X-rays
wavelength: the distance between two adjacent crests or troughs of a wave
weak nuclear force: a weaker, noncontact force that governs the radioactive decay of subatomic particles
work: the measure of energ y transfer that occurs when an object is moved over a distance by an external force
X-rays: electromagnetic waves that are the second highest in energ y and are used in medical and astronomical applications
