ESO 2 UNIT 1: Forces and movements
WHAT IS MOVEMENT?
Which of these things move?
Great example of movement and systems of reference
For people on the big wheel, the boat moves but to people on the boat, it will be at rest.
We say that an object is moving when it changes its position with respect to another one that we consider as fixed.
Don't forget that even if you appear to be standing still, the Earth is moving around the Sun, and the Sun is moving around our galaxy.
Everything in the universe moves. Movement can be slight or slow, but it still happens.
MOTION ELEMENTS Trajectory. Position. Distance travelled Time taken Speed Acceleration.
TRAJECTORY Trajectory is the path that a moving object follows through space. It can be rectilinear, circular, elliptical, parabolic, etc.
POSITION Position is where an object is located. If we want to describe the movement of a person who is running, we measure the distance from the person to a point that we have taken as reference. This distance is called position and is represented by the letter â€œsâ€?.
Positions on the left of the reference system are often taken as negative and on the right as positive.
1m
s0
s1

+
s2
s3
R
The positions of the ball would be: s0 =  6 m
s2 = + 3 m
s1 =  4 m
s3 = + 8 m
DISTANCE TRAVELLED The distance travelled is equal to the subtraction between two positions, the final position minus the initial position if there is no change in the sense of the movement. 1m
s0
s1

+ R
s2
s3
Example
1m
s0
s1

+
s2
s3
R The distance travelled by the ball from the initial position to the position 3, would be: distance travelled = s3  s0 = 8 m â€“ (6 m) = 8 m + 6 m = 14 m Imagine that the ball goes from the position 3 to the position 2. The distance travelled would be: s2  s3 = + 3 m â€“ 8 m =  5 m
However, we will say that the distance travelled is 5 m. The position can be either a positive or a negative number but the distance travelled is always a positive number.
SPEED Speed is how fast an object is moving. It is the ratio between the distance travelled and the time elapsed to do it. It is represented by the letter “v”.
The mathematical expression of the speed is:
Speed (v)
Distance
Time
The SI unit of speed is m/s REMEMBER SIDOT Speed Is Distance Over Time
Example
A sheep is running down a farmerâ€™s track. It takes exactly 10 seconds to move between two fence posts, 10 meters apart. Whatâ€™s the sheep`s speed?
Step 1) Write down what you know: Distance: 10m Time: 10 seconds Step2) We want to find speed: Speed (v) = Distance (e) / Time (t) v= 10/10= 1m/s
â€˘ A car is moving on a straight road at an average speed of 72km/h. Calculate the distance covered in one and a half hours. Use SI units. Speed (v)
Distance Time
Distance= Speed*Time e= 72km/h*1,5h=108h
108.000m
An athlete can run long distances at 4 metres per second. How far can she run in? a) 50 seconds 200m b) 3 minutes 720m
c) 1 hour 14400m d) 2 hours and a half 36000m
A dog can run long distances at 3 metres per second. How long can it run in? a) 120 meters  40 s b) 1200 meters400s
c) 2100 meters  700s d) 5400 meters 1800s
An athlete can run long distances at 8 meters per second. How far can he run in?
a) 10 seconds 80m b) 12 minutes5.760m c) 1 hour and a half 43.200m
d) 2 hours 57.600m
Andrew rows at an average speed of 2 meters per second. a)How long does he take him to row: • 70 m35s • 800 m 400s • 1 km and a half 750s
b) How far can Andrew row in: • 12 seconds24m • 3 minutes and a half420m • 4 hours28800m
Use common sense with speed â€˘ Although it is very important use SI unit sometime has no sense use it. For instance: Average speed of the Continental Plates is 2cm per year 6,34*1010 m/s
Average speed of halleyâ€™s comet is 100km/s 10*104m/s
A snail moves 5 m in 2 hours. If it moves at the same speed all the time, calculate:
a) The time it takes to move 20 m 8h or 28000s b) The time it takes to move 1 m  0,4h 贸 24min 贸 1440s c) The distance it would move in 3 hours and a half  8,75m d) The distance it moves in 15 minutes 0,625m
GRAPHS OF THE UNIFORM MOTION (I) Distance versus Time In the uniform motion the speed is always the same. The distancetime graph for constant speed is a straight line.
DO NOT FORGET
• The graph s/t doesn’t say to us anything about the trajectory
GRAPHS OF THE UNIFORM MOTION (III) (example) The steeper the straight line is, the faster the movement is
VB =4m/s
VA =2 m/s
vA
4 m/s
vB
2 m/s
Draw the distancetime graph for 6 m/s and 8 m/s constant speed
.
Draw the distancetime graph for 3 m/s and 10 m/s constant speed
.
GRAPHS OF THE UNIFORM MOTION (II) Speed versus Time In the uniform motion the speed is constant. The velocitytime graph for constant velocity is a horizontal line.
v (m/s)
t (s)
Speed (m/s)
Distance (m)
Time (s)
20m/s
20m
1s
20m/s
40m
2s
20m/s
60m
3s
20m/s
80m
4s
20m/s
100m
5s
ACCELERATION If speed does not change in a movement, it is an uniform motion and if it changes in a movement, it is an accelerated motion The acceleration is defined as the ratio between what the speed has changed and the time elapsed to occur that change. In other words Acceleration is defined as the rate at which an object changes its speed. An object is accelerating if it is changing its speed. It is represented by the letter â€œaâ€?. The mathematical expression of the acceleration is: a
The SI unit of acceleration is m/s2
vfinal  vinitial tfinal  tinitial
Example A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration ? a cyclist
vfinal  vinitial tfinal  tinitial
8 m/s – 0 m/s
2,6 m/s2
3s–0s
A car accelerates from 0 to 30 m/s in 8 seconds. What is its acceleration? a car
vfinal  vinitial tfinal  tinitial
30 m/s – 0 m/s
3,7 m/s2
8s–0s
A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car a = 11.2 m/s2
FORCES
• A FORCE IS ANYTHING THAT CAN DEFORM A BODY OR CHANGE ITS STATE OF MOVEMENT OR REST
FORCES (II) • Forces are nearly always pushes and pulls. •
We need to use a force to get something moving.
• Small forces can be measured with a force meter in units called Newton (N).
• Forces have direction and we use arrows to .show the direction of a force
FORCES (III) • A force can • Change the direction
• Speed something up
• Slow something down
• Change shape
MASS versus WEIGHT MASS It measures the amount of matter.
Mass is measured in kilograms, kg, or grams, g.
The mass of an object doesnâ€™t depend on its location.
We can measure it with balances.
WEIGHT It measures the gravitational force acting on an object. Weight is a force and forces are measured in Newton, N. The weight of an object weight depends on its location, because the gravitational force varies with the location. gEarth: 9,8 m/s2 gMoon: 1,67 m/s2; gMars: 9,8 m/s2;gMercury: 2,6 m/s2
We can measure it with force meter or dynamometers.
Weight and mass are linked to gravity, g, through the equation W=m.g
Exercise â€˘ Complete the following chart: Mass in the Earth
Weight in the Earth
Weight in the Moon
Weight in Mars
Weight in Mercury
gEarth: 9,8 m/s2
gMoon:1,67 m/s2
gMars: 3,71 m/s2
gMercury: 2,6 m/s2
10Kg 19,6N 66,8N 40,81N 52N
ArchimedesÂ´ Principle An immersed body is buoyed up by a force that is equal to the weight of the fluid that it displaces.