Physics
How to use this book Important scientific vocabulary is highlighted. You can check the meanings in the Glossary at the end of the book.
Remember! To cover all the content of the AQA Physics Specification you should study the text and attempt the End of chapter questions.
Physics
Each topic is divided into three sections. The level of challenge gets harder with each section.
Each section has levelappropriate questions, so you can check and apply your knowledge.
Learning objectives: • • •
half-life
explain what is meant by radioactive half-life calculate half-life calculate the decline in activity after a number of half-lives.
1600 1400 1200 1000 800 600 400 200 0
Half-life
0
We cannot predict when the nucleus of one particular atom will decay. It could be next week or not for a million years. Radioactive decay is a random process. If there is a very large number of atoms, some of them will 80 decay each second. We plot a graph of 70 activity against time and draw a curve of best fit. We can then use this curve to find 60 when the activity has halved (Figure 4.11). 50 The half-life of a radioisotope is the average 40 time it takes for half the nuclei present to 30 decay, or the time it takes for the activity to fall to half its initial level. We use half-life 20 because we cannot predict the time it will 10 take for all the atoms to decay. The activity of a radioactive substance gets less and less as time goes on. The graph line in Figure 4.11 gets closer and closer to the time axis but never reaches it because the activity halves each half-life.
0
0
1
2
Explain why you can’t predict when a particular atom will decay.
2
Explain what is meant by ‘half-life’.
3
What will the activity in Figure 4.11 be after: a 2 days? b 4 days? c 6 days? d 8 days?
15
20 25 30 Time (minutes)
35
40
45
50
Time in minutes
a Draw a graph of activity against time. b Draw a best-fit curve through the points.
6
3
4 5 Time (days)
6
7
0
100
0.5
76
The activity of a radioactive sample took 4 hours to decrease from 100 Bq to 25 Bq. Calculate its half-life.
HIGHER TIER ONLY
To calculate the half-life of a radioisotope, plot a graph of count rate detected (which is proportional to the total activity) against time, as shown in Figure 4.12. The background count should be subtracted from each reading before the graph is plotted. Plot the points and then draw a smooth curve of best fit through the points. Then find several values for the half-life from the graph by finding the time for the activity in counts per minute to fall from 80 to 40, 40 to 20, 20 to 10 and so on. You should calculate the average of the values you have found. The time for the activity to halve may not be exactly the same each time. Any differences will be due to the random nature of radioactive decay.
When you draw a curve of best fit on a graph of activity against time for a radioisotope, not all of the points will be on the curve. Some will be above the curve and some will be below the curve because of the random nature of radioactive decay.
Activity in Bq
c Calculate the half-life by looking at time for the activity to halve at three different points on your curve. Calculate the average.
8
KEY INFORMATION
Calculating decline in activity
1.0
51
1.5
40
2.0
26
2.5
18
3.0
12
3.5
10
4.0
8
Each topic has some fascinating additional background information.
For some applications such as a smoke alarm, a radioisotope with a long half-life is most suitable so that the rate of decay does not decrease significantly. Some radioisotopes are used as tracers, using the radiation they emit to trace the path of a substance the radioisope is attached to. Radioisotopes can be used as environmental tracers (such as detecting a leak in a pipe) or medical tracers. For these applications, a short half-life is best. This means that the activity will decrease to a level similar to the background count fairly quickly because the time taken for half the radioactive nuclei to decay is very short. 7
Technetium-99m is widely used in medicine. It has a half-life of 6 hours. How much of it remains after 1 day?
8
What fraction of the original sample remains after 80 minutes in Figure 4.12?
9
Caesium-134 has a half-life of 2 years. If its activity was monitored for 6 years, what fraction of the original activity level would it have dropped to after 6 years?
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75061_P100_121.indd 111
For Foundation tier you do not need to understand the content in the Higher tier only boxes. For Higher tier you should aim to understand the other sections as well as the content in the Higher tier only boxes.
DID YOU KNOW? The half-lives of different radioactive isotopes vary from a fraction of a second to millions of years.
Google search: 'half-life'
AQA GCSE Physics for Combined Science: Trilogy: Student Book
AQA GCSE Physics for Combined Science: Trilogy: Student Book
10
The table shows the activity of a radioactive sample over time.
5
Calculating half-life
75061_P100_121.indd 110
5
Figure 4.12
Figure 4.11 The time it takes for the activity to halve is constant
1
4.5
2000 1800
Radioisotopes are often used to monitor a biological process in the body or in the environment. We need to know the half-lives of different radioisotopes so that we can minimise contamination or irradiation.
110
6
Calculate the half-life of the radioisotope shown in Figure 4.12.
4
KEY WORDS
Count rate (counts/min)
This introduces the topic and puts the science into an interesting context.
Radioactive half-life
Activity (counts per minute)
These tell you what you will be learning about in the lesson and are linked to the AQA specification.
111
Look for the internet search terms at the bottom of the page.
02/11/16 3:49 PM
How to use this book
7
Physics
End of chapter questions
11
Look at the image of the house.
Getting started 1
Sally is choosing a new electric kettle. One is rated at 1.5 kW and the other at 2 kW. What does this show?
1 Mark
a The first one is smaller. b The second one is a newer design. 12
What has to be done for wood to be a renewable resource?
2 Marks
d The second one will transfer energy more quickly.
13
Using the idea of heat capacity, explain why a fairly small hot water bottle can warm a bed.
2 Marks
Write down the equation for efficiency.
1 Mark
3
What is meant by a non-renewable resource?
1 Mark
4
Two steel blocks, one with a mass of 100 g and the other with a mass of 200 g, are placed in boiling water for several minutes. Which of these statements is not true?
More challenging The power of a kettle is 2000 W. Explain what 2000 W means in terms of energy transfer.
1 Mark
15
Write down what each of the symbols stands for in ΔE = mcΔq
1 Mark
16
Night storage heaters charge up during the night time and release energy during the day. Explain why they are made from a material with a high specific heat capacity.
2 Marks
A student was given some rods made from different materials. He was asked to arrange the rods in order of increasing thermal conductivity. Describe a proce dure the student could follow to carry out the task safely by using a fair test.
6 Marks
14 1 Mark
a They are both at the same temperature. b They are made of the same material. c They have the same amount of stored thermal energy.
17
d They remain solid. Order these light bulbs from most to least powerful.
2 Marks
15 W, 0.1 kW, 60 W, 0.08 kW, 150 W 6 7
Most demanding
Describe the difference between elastic potential energy and gravitational potential energy.
2 Marks
Elise has a weight of 400 N and can clear a high jump of 2 m. Calculate how much work she does in raising her body up 2 m.
2 Marks
Going further 8
When energy is being wasted we say it is
1 Mark
a diffusing b propagating d refracting Which of these does not affect the amount of energy needed to heat up a material?
2 Marks
19
Explain why energy is conserved within a closed system.
2 Marks
20 16
A student was investigating how the efficiency of a squash ball changed with temperature. The efficiency of a squash ball can be worked out by using the formula: gravitational potential energy associated with the squash ball when it reaches its maximum height after it bounces / gravitational potential energy associated with the squash ball before it is dropped.
Mass of squash ball = 25 g Gravitational field strength on Earth = 9.8 N/kg Temperature (°C) Bounce height 1 (cm) Bounce height 2 (cm)
b Its mass. c Its specific heat capacity. d The temperature rise. Explain why bubble wrap is an effective insulator.
Explain the difference between stored thermal energy and temperature.
Here are her results: 1 Mark
a Its colour.
10
18
The student placed the ball in a beaker of water and heated the water to the desired temperature. She then removed the ball from the water and dropped it from a height of 1 m onto a hard surface. Once the ball had bounced, the student measured the height that the ball bounced up to by using a metre ruler.
c dissipating 9
2 Marks
c The first one will keep the water hot for longer. 2
5
Use the image to name the part of the building that needs insulating the most. Explain your answer.
2 Marks
20 6 18
30 28 23
40 39 36
50 43 40
60 45 42
The student concluded that the higher the temperature of the squash ball, the more efficient it was. Discuss whether the student came to a valid conclusion and evaluate the limitations of the experiment.
42
AQA GCSE Physics for Combined Science: Trilogy: Student Book
6 Marks Total: 40 Marks
End of chapter questions
43
Physics
Learning objectives • describe how, when substances change state, mass is conserved • describe energy transfer in changes of state • explain changes of state in terms of particles.
boil changes of state conservation of mass evaporate freeze melt sublimate
When a liquid boils, the energy transferred to the liquid gives the molecules enough energy to break away from the surface.
When substances change state, mass is conserved. If you start with 1 kg of ice and melt it, you will have 1 kg of water. Nothing has been added or removed. The process is reversible. If you freeze the 1 kg of water you will end up with 1 kg of ice again.
1
What type of change occurs when a substance changes from liquid to solid?
Changing state Changes of state occur when substances change from one state to another. The processes of changing from one state to another are:
Give an example of a change of state. Specify the material involved.
4
We often say ‘it is freezing’ when the temperature is cold outside. Explain why this is not an accurate statement.
When a substance changes state, energy is transferred to change the arrangement of the particles. When a substance melts, such as ice changing to water, energy must be transferred to the ice to change its state from solid to liquid.
When a liquid cools down, the particles decrease their kinetic energy, allowing them to come closer together and form bonds (freezing). Energy is released to the surroundings. Energy is also released when a gas condenses to form a liquid. Did you know? Dry ice is frozen carbon dioxide which turns directly from a solid to a gas at a temperature of –78.5 °C. The fog you see is a mixture of cold carbon dioxide gas and cold, humid air, created as the dry ice sublimates (Figure 3.5).
melting: changing from solid to liquid freezing: changing from liquid to solid boiling: changing from liquid to gas at the boiling point evaporating: changing from liquid to gas when the temperature of the liquid is lower than the boiling point • condensing: changing from gas to liquid • sublimating: changing from solid to gas without going through the liquid state.
3.3
Explaining changes of state
In the solid state, such as ice, the particles are close-packed with strong bonds between them. Energy must be provided to weaken these bonds and allow the particles to move more freely in the liquid state (water). To change into a gas (steam) a lot of energy must be provided to break the bonds between the particles and allow the gas particles to spread out, filling the available space.
Conservation of mass
This is an important idea as it shows that when the state of something is altered, no material has gone away or has been added. There are the same number of particles of the substance there. It is the arrangement that has been changed, not the amount. It also shows that material has the same mass, even though it might have changed state. Boiling 1 kg of water will produce 1 kg of steam.
3
Key words
Evaporation produces cooling (Figure 3.6). As a liquid warms up, the average speed of the molecules in it increases. But not all the molecules in the liquid will be travelling at the same speed (Figure 3.7). It is the faster molecules with more energy which escape from the surface of the liquid, leaving behind the slower molecules with less energy (Figure 3.8). 5
Explain why you hang out washing rather than leaving it in a pile to dry.
6
Explain why evaporation produces cooling.
7
Suggest why being burnt by steam is worse than being burnt by hot water.
8
Explain how sweating can help to reduce body temperature.
Figure 3.6 The sand in this pot is wet. Evaporation transfers thermal energy away from the inner pot and keeps the food cool Relative number of molecules
Changes of state
300 K 1000 K
400
800
1200
Speed (m/s)
Figure 3.7 The molecules in a liquid do not all travel at the same speed
• • • •
Figure 3.8 Evaporation from the surface of a liquid
Changes of state are physical changes. Unlike a chemical change, the change does not produce a new substance. If the change is reversed, the substance recovers its original properties. 2
82
Suggest how you could prove that mass is conserved when ice melts.
AQA GCSE Physics for Combined Science: Trilogy: Student Book
Figure 3.5 Dry ice sublimates
Google search: 'changes of state, conservation of mass'
83
Physics
MATHS SKILLS
MATHS SKILLS
Time (min) Activity (Bq)
Using ratios and proportional reasoning
0
10
20
30
40
50
60
70
80
90
96
78
62
54
40
32
26
21
15
14
Half-life calculations
net decline ratio
Another way of calculating the half-life of a radioactive source is fraction reasoning. After one half-life has passed, the activity decreases by 12 . This is always true no matter when you start to measure the activity of the sample. The decrease in activity over several half-lives can be written as a sequence, as shown in the table.
calculate radioactive half-life from a curve of best fit calculate the net decline in radioactivity.
Example: A radioactive source has an initial activity of 1200 counts per minute. If the count rate has fallen to 147 after 6 hours, calculate the half-life.
When you draw a graph of activity for a radioisotope against time, the points do not fit a straight line – the line of best fit is a curve.
Starting with 1200 counts per minute at time 0: • after 1 half-life, the activity should be 600 counts per minute; • after 2 half-lives, the activity should be 300 counts per minute; • after 3 half-lives, the activity should be 150 counts per minute. (The actual count rate is 147, showing that radioactivity is a random process.) After 6 hours, 3 half-lives have passed, so the half-life is 2 hours.
Measuring half-life from a graph
Look for numbers on the vertical scale that are easy to halve. For example, you can halve 40 easily to get 20. From the 40 on the vertical axis, draw a line across to the graph. Then draw a line down to the time axis. So the activity at 2 days is 40 counts/minute. Now repeat this for 20 counts/minute. The time is 4 days.
Activity (counts per minute)
Working out the half-life of a radioisotope usually involves drawing a graph and using the graph to calculate the half-life. Figure 4.19 shows the activity in counts per minute against time for a certain radioactive isotope. You can use the graph to work out the half-life of the isotope.
a Calculate the half-life for the source shown in Figure 4.20. b Work out three values for the half-life. c Calculate the average of the values.
116
60 50 40
3
A radioactive isotope has an activity of 160 Bq and a half-life of 2 hours. What is the activity after 6 hours?
4
The activity of a radioactive source used to sterilise equipment in a hospital is 200 kBq. The activity is measured again in 21 years and is found to be 12.5 kBq. What is the half-life?
5
1 The activity of a sample decreases to 16 th of its original value over 24 hours.
30 20 10 0
1
2
3 4 5 Time (days)
6
7
0
1 1
1
1 2
2 3 4
1 4 1 8 1 16
5
1 32
6
1 64
HIGHER TIER ONLY
Net decline
200
In the example above, after 6 hours (3 half-lives) the activity will have reduced to 18 th of the original. This can also be expressed as a ratio of the final value to the initial value, 1:8. This ratio is called the net decline.
175
Activity (Bq)
Number of Fraction of activity half-lives remaining passed
Calculate the half-life of the sample.
8
225
So the half-life is 2 days.
1
70
Figure 4.19: Working out the half-life of a radioisotope
It takes 4 – 2 = 2 days for the activity to reduce by half from 40 to 20 counts/minute. You should always repeat for a second pair of values, just to check. Choose another value that can be halved easily, e.g. 20. Repeating the process for halving the count rate from 20 to 10 gives the same answer, 2 days.
80
0
4.8
b Calculate the half-life.
KEY WORDS
Learning objectives: • •
a From the data in the table plot a graph of activity against time.
2
150 125
6
100
Sodium-24 has a half-life of 15 hours. A sample of sodium-24 has an activity of 640 Bq.
75
a Calculate the activity after 60 hours.
50
b Calculate the net decline.
25
7
0 0
40
a Calculate the count rate after 32 days.
80 120 160 200 240 280 320 360 400 440 480 520
Time (seconds)
Figure 4.20: A line of best fit can be drawn from the data plotted
AQA GCSE Physics for Combined Science: Trilogy: Student Book
Iodine-131 has a half-life of 8 days. A sample of iodine-131 has an activity of 1800 counts per second.
b Calculate the net decline in the activity of the sample. 8
A sample of pure polonium-210 decays into lead-206 with a half-life of 138 days. Calculate how long it would take for the sample to contain three times as much lead as polonium.
Google search: 'half-life decay curves'
117
Physics
KEY CONCEPT
KEY CONCEPT Forces and acceleration Learning objectives: • • •
recognise examples of balanced and unbalanced forces apply ideas about speed and acceleration to explain sensations of movement apply ideas about inertia and circular motion to explain braking and cornering.
5.16 KEY WORDS acceleration balanced force inertia speed velocity
The reason why scientists study forces is that they tell us about how things move. If you know all the forces acting on something, you can predict very accurately if and how it will move. Newton’s laws of motion are very simple but the situations you can apply them to can be complex. The laws were first suggested by Isaac Newton and published in 1686. NASA used these simple laws to get men safely to the Moon and back, and theme parks use them to thrill us on their rides.
2
Looping the loop Curves and loops on the ride (Figure 5.41) cause the direction you are travelling in to change, so your velocity changes. Remember that a change in velocity is acceleration even if the speed remains constant. To change direction, there needs to be a force towards the centre of the circle that the curve is part of. This is an example of Newton’s second law. 3
You feel the seat pushing you as you go round the loop. Suggest what would happen if there was no seat.
4
Why do we say that a train going round a loop is accelerating, even when its speed is constant?
5
Use your answer to question 4 to explain the difference between speed and velocity.
6
Newton said that unless there is an unbalanced force, an object will continue in a straight line at a steady speed. Describe how this force is applied to the riders in the roller coaster.
Balanced and unbalanced forces People who design rides for theme parks understand what will make a ride exciting. It’s not just speed. Stealth, at Thorpe Park, is the UK’s fastest roller coaster and reaches 128 km/h, which is not much faster than a car on a motorway, but is much more exciting. You need high acceleration for a good ride and that requires force, or, to be precise, unbalanced force.
Figure 5.39 Isaac Newton
1
Figure 5.40 A roller coaster
What happens to the acceleration of the roller coaster if the force propelling it forwards increases? Figure 5.41 Going around a loop
154
AQA GCSE Physics for Combined Science: Trilogy: Student Book
Drop towers
Figure 5.42 A drop tower
Zumanjaro: Drop of Doom in America is the world’s tallest drop tower at 125 m. After a brief pause at the top, you are released and fall under the pull of gravity. You are in freefall for over 10 s, reaching speeds of over 140 km/h. The force is unbalanced and causes acceleration; the same thing happens (but much more gently) when you descend in a lift.
Newton explained that if all the forces on an object balance out, its speed will be constant and its direction will not change, or it will not move if it is at rest. If the forces are not balanced, the object’s speed or direction will change. It is the acceleration that makes roller coasters (Figure 5.40) such fun. Newton’s first law of motion states that a moving object tends to stay moving. This resistance to change is called inertia. When the roller coaster speeds up, the back of the seat pushes you forward, accelerating you. When the roller coaster slows down, your body tries to keep going at its original speed. The harness in front of you pushes your body backwards. These pushes and pulls on your body give you the thrills you enjoy.
Explain what would happen if the roller coaster had a negative acceleration and the passengers weren’t wearing restraints.
To slow the ride down and stop it, another unbalanced force is needed. This is provided by giant permanent magnets which provide an upward force. 7
If a free-fall ride accelerates at 10 m/s2 and the loaded car has a mass of 2500 kg, what force is acting?
8
If the braking force at the end of the ride was half the size of the force of gravitational attraction, what acceleration would the riders experience?
9
A passenger on Zumanjaro was holding an open bottle of water. As the ride accelerated downwards he decided to tip the bottle upside down to make the water fall out. Explain what happened to the water.
DID YOU KNOW? g-force is a way of comparing forces by measuring the acceleration they produce. A force of 1g causes acceleration the same as that of gravity (around 9.8 m/s2). Humans can tolerate greater g-forces horizontally than vertically; accelerating downwards rapidly forces blood into the brain and eyes; any more than 2g is dangerous.
Google search: 'Newton’s laws of motion'
155
Physics
ELECTROMAGNETISM
7
IDEAS YOU HAVE MET BEFORE:
IN THIS CHAPTER YOU WILL FIND OUT ABOUT:
PERMANENT MAGNETS • Permanent magnets are made from nickel, cobalt and most steels. • Iron is a magnetic material but loses its magnetism when the magnetising force is removed. • Like poles repel and unlike poles attract.
S
N
N
S
• Permanent magnets can be used to test for a magnet. • The difference between permanent and induced magnets is that the latter has a field that can be turned off by switching the current flow off.
EARTH’S MAGNETISM
HOW DOES A MAGNETIC FIELD VARY?
• The Earth’s magnetic field is very similar to the magnetic field due to a bar magnet. • A compass uses the Earth’s magnetic field to indicate magnetic north. • The Earth behaves as if there is a gigantic bar magnet inside it.
• The strength and direction of a magnetic field varies according to distance and direction of current flowing in the coils of an electromagnet. • The behaviour of a magnetic compass is indicates that the core of the Earth is magnetic.
MAGNETIC EFFECT OF A CURRENT
WHAT ARE THE EFFECTS OF CURRENT AND MAGNETISM?
• The wires carrying an electric current produce a magnetic field. • The magnetic field made by the current in a wire is a circular shape around the wire. • The magnetic field is increased if more turns are wound on the coil and/or the current in the wire is increased.
• The direction of the magnetic field can be worked out from the direction of the current. • The force on a current-carrying wire in a magnetic field can be calculated. • Fleming’s left-hand rule can be used to work out the direction of force or motion on a current-carrying wire in a magnetic field.
ELECTROMAGNETS • A coil of wire with an iron rod in it makes an electromagnet. • The iron rod becomes magnetised when a current flows in the coil. • The iron rod loses its magnetism as soon as the current is switched off.
196
WHAT ARE PERMANENT AND INDUCED MAGNETS?
AQA GCSE Physics for Combined Science: Trilogy: Student Book
direction of current
circular magnetic field around wire
Spin axis Magnetic field lines
S N
battery + force
switch
rotation produced
WHAT IS A MOTOR AND HOW DOES IT WORK? • Describe some uses of motors. • Explain how a motor works. • Explain how a commutator is used.
coil
N
magnetic field
S
electric current carbon brushes
split-ring commutator
force (motion)
Electromagnetism
197