1. 4th form: Motion & Forces

2. Scalars and Vectors
Measurable quantities can be divided into scalars and vectors.
Scalar quantities have a magnitude (size) only
Examples?
Mass, distance, speed, time...
Vector quantities have both a magnitude and a direction associated with them
Force, displacement, velocity...

3. Adding scalars and vectors
Adding scalar quantities is easy, just add the magnitudes
eg if it takes 15 minutes to eat lunch and you have a further 45 minutes before lessons, how long was the break?
Adding vectors, we have to take the direction of the quantities into account
eg pushing a car against friction

4. Adding vectors

5. Adding vectors (more generally)
The resultant R is found by combining all the component vectors together
It is the single vector which is equivalent to the action of all the component vectors
This is A-level
stuff...

6. Speed: a reminder
Speed is a measure of how quickly something is moving
Actually, the above formula really tells you the average speed during the time interval
As the time interval gets smaller, you get closer to calculating the instantaneous speed.

7. Displacement-time graphs
Try to describe the motion shown in the graph
What does the slope of the line represent?
What does the slope of the dotted line tell you?

8. Displacement-time graphs
Constant speed backwards
Constant speed forward
Slope=average speed of return journey
stationary
Slope = speed
Speed=5/0.42=11.9 km/h
After 160 minutes, we are back where we started

9. Calculating speed
The slope of the graph gives the speed (strictly the velocity)
The steeper the line, the higher the speed
(a)
Slope = 60/10 = 6.0 m/s
(b)
(b)
Slope = 0/5 = 0.0 m/s
(a)
(c)
(c)
Slope = -100/25 = -4.0 m/s
(d)
(d)
Slope = 40/15 = 2.7 m/s

10. Displacement-time graphs
How would you represent something getting slower? t x
Note: distance can also become negative, if object travels in the opposite direction

11. Speed and Velocity
The velocity of an object gives its instantaneous speed and direction
(This is called a VECTOR)
As with displacement, the sign of the velocity indicates the direction
a negative velocity means speed in the opposite direction

12. Speed and Velocity Going from A to B: + velocity
Going from C to F: - velocity

13. Velocity-time graphs Try to describe the motion shown in the graph
What does the slope of the line represent?
Where is the object not moving?

14. Velocity-time graphs Constant speed forwards Constant acceleration
Gradual slowing
More rapid slowing
stationary
Reversing direction and speeding up
Slowing to a stop
Constant speed backwards

15. Acceleration Acceleration is the rate of change of velocity
If you are speeding up, acceleration is +
If you are slowing down, acceleration is -
m/s s
m/s2

16. Acceleration is the slope of the velocity graph
Acceleration = (v-u)/t
So for this region:
a= 8/4 = 2 m/s2
and for this region:
a= 0/6 = 0 m/s2 (constant v)

17. What about the displacement?
Displacement = velocity × time
i.e. the area under the
graph
So in the first 4s:
In the next 6 seconds

18. Tachographs
A tachograph is an instrument which records the velocity-time graph of a vehicle.
It is used to check that EU regulations limiting the time lorry and bus drivers can spend at the wheel are obeyed
9 hours/day
45 minute break every 4.5 hrs.

19. Forces: a reminder A force is a “push” or a “pull”. Unit: newton (N)
Forces arise due to the interaction of two (or more) objects.
Not all forces require contact, some can act at a distance
e.g. gravity, magnetism
Forces are vectors,
Direction matters

20. Weight: a reminder
“Mass” is a measure of how much “stuff” an object contains
measured in kg
“Weight” is the force that object exerts due to the effect of gravity
measured in newtons (N)
So an astronaut has the same mass on Earth or the Moon, but his weight will be different
On Earth,
g ≈10 N/kg
gravitational field strength
weight
mass

21. Representing forces
Forces can be represented with arrows, whose length indicates the size of the force.

22. Force diagrams
A free body diagram can be very useful to analyse the forces acting on an object
We draw it isolated from its surroundings and show all the forces acting

23. What forces are acting here?
Draw on as many as you can think of…
Tension in the rope
Push and friction
(for each person)
Weight and reaction
(for each person)

24. Combining forces
If several forces act on an object, we can work out the equivalent single resultant force by adding them up, taking direction into account.
What is the resultant?
4 newtons downwards
How about these?
7 N
6 N
3 N
4 N
1 N
5 N
4 N
4 N
4 N
0 N

25. Newton’s 1st law
Balanced forces
It is possible to have all forces balanced, so the resultant = 0.
In this case, no resultant force acts and the object continues to move at constant velocity (or remain stationary if it wasn’t moving).
For a plane flying at constant speed and height:
Thrust = drag
Lift = weight

26. Newton’s 1st Law
A body will remain at rest or, if moving, continue to move at a constant velocity, unless acted on by a force.

27. Unbalanced forces
If the resultant force is not zero, a net force is acting on the body and its motion will change.
It will accelerate in the direction of the force.
thrust > drag and lift > weight, so aeroplane accelerates and takes off

28. Force causes acceleration
Newton’s 2nd law
Force causes acceleration
When a force acts on a body, it changes its velocity
If no resultant force acts, there is no acceleration (Newton’s 1st law)
Remember, acceleration can mean a change of speed or direction
1 N is the force which accelerates 1 kg at 1 m/s2
force
mass
acceleration

29. F=ma
So:
For a given mass, a bigger force produces a bigger acceleration
For a given force, a smaller mass experiences a bigger acceleration

30. Force, mass and acceleration
A force of 1000 N is applied to push a mass of 500 kg. How quickly does it accelerate?
A force of 3000N acts on a car to make it accelerate by 1.5 m/s2. How heavy is the car?
A car accelerates at a rate of 5 m/s2. If it weighs 500 kg how much driving force is the engine applying?
A force of 10 N is applied by a boy while lifting a 20 kg mass. How much does it accelerate by?

31. Remember Weight?
We had
where W was the weight – the force due to gravity
Now we know
gravitational field strength
Acceleration due to gravity
On Earth: g ≈10 N/kg, a ≈10 m/s2

32. Investigating F, m and a We can measure acceleration with light gates
What happens as you vary:
The mass on the hanger?
The mass of the trolley?
Why do we need a ramp?
How do we set the right angle?

33. What do we find? acceleration is proportional to force
acceleration is inversely proportional to force
a a F
a a 1/m

34. Horizontal motion Driving force < counter force: vehicle slows down
Driving force – provided by rider/engine
Counter force – air resistance and friction
Driving force < counter force: vehicle slows down
Driving force = counter force: vehicle moves at constant velocity
Driving force > counter force: vehicle speeds up

35. Falling Objects
An object falls because of its weight (force due to gravity)
When object falls freely – no other forces act on it so resultant force is just its weight.
Remember F = ma?
Acceleration of 10m/s2 is constant for all objects.

36. Classic experiment
So if we dropped a hammer and a feather at the same time, which would hit the ground first? Why?
Hammer & Feather

37. Drag Objects moving in a fluid have drag force.
For objects travelling through the air we call this drag force air resistance.
Air resistance increases with speed.
So as a falling object speeds up, the resultant force decreases. This means the acceleration decreases.

38. Reaching a constant velocity
Object reaches a constant velocity when the drag force/air resistance is equal & opposite to its weight.
Resultant force = zero
Acceleration = zero
Velocity = terminal velocity

39. Why does a car have a top speed?
The AR 8C has a 4.7 litre 450 bhp (340 kW) engine to provide driving force.
Force means acceleration, so why can’t the car accelerate forever?

40. What determines terminal velocity?
Frontal area
Shape
Mass
Surface

41. Balanced Forces = Constant Velocity

42. Stages of a parachute jump

43. Just after letting go... Velocity =0 Drag = 0 Force = weight
Acceleration = g

44. Falling quite fast now... Velocity is high Drag is large
Force < weight
Acceleration < g

45. Falling at a constant speed...
Velocity constant
Drag = weight
Force = 0
Acceleration = 0

46. Pull the ripcord... Velocity still high Drag > weight Force upwards
Acceleration upwards (so speed of fall decreases)

47. Drift downward... Velocity constant (slower) Drag = weight Force = 0
Acceleration = 0

49. Terminal Velocity

50. Label the graph

51. Urban Myth?
So, would a penny dropped from a skyscraper kill someone it hit at the bottom?
See here for the answer
(also here if you wonder
about bullets coming down)

52. Springs: a reminder We have seen that springs obey Hooke’s Law:
The extension is proportional to the force applied (up to some limit)

53. Other “stretchy” things
Hooke’s Law also applies to other objects...
Metal bars, wires, bones, even glass!
...up to a point
If you go beyond that point you may get failure (snap) or permanent deformation (doesn’t return to original shape)
Hooke’s Law limit

54. Rubber bands
Rubber bands are elastic, can be stretched and return to their original length, BUT they do not obey Hooke’s Law
How can you tell?
Describe how it stretches...