P4 Explaining Motion

Forces always arise from an interaction between two objects
i.e. an interaction pair

Interaction pair

• Forces equal in size
• Forces opposite in direction
• Two forces act on different objects

An example: Deborah is wearing rollerskates. She pushes against a wall, and immediately starts to move backwards. When she pushes the wall, the wall pushes back on her, with an equal force in the opposite direction. This force is what makes her move.  

Rockets: Burning hot gases are pushed out of the base of the rocket, thus the rocket is pushed in the opposite direction. Rockets carry everything they need to make the burning gases they push against, therefore they can work in space as well as air.

Jet engines: Same principle as rockets. Air drawn into engine and pushed out back. Other force of the pair pushes engine forward. Jet engines draw air in, so don't work in space.

Car: On a road, the engine makes the car wheel turn. It pushes back on the road. The wheel can't slip, so minimal wheelspin occurs, and thus exerts a very large force backwards on the road surface. The other force of interaction pair is the same size. It is this large forward force that gets the car moving. 

Walking: When you walk, you push back on the ground with each foot in turn, thus the ground pushes you forward. This is difficult on ice. 

Friction adjusts its size in response to its situation, up to a limit. This limit depends on the objects and surfaces involved. 

When one object slides over another, it must ride up and down over the (sometimes microscopic) bumps and hollows of the other object. This requires a force to overcome the friction involved.

Since all surfaces are quite rough, they only touch at a few points. This means that there are only a few points of contact, therefore the pressure at these points is very large. This pressure is enough to 'cold weld' these points together, meaning that when you slide one object over another, these welds must be broken. This needs a force.

There are two main forces acting on a tennis ball sitting on a table:

1) Force exerted by the Earth on ball (gravity)
2) Force exerted by the table on ball

These two forces are equal. 

However, a table can't always exert an upward force on an ball to balance the downward force on it - there is a limit. This depends on the material that the table is made from. If the force exerted on the table top is bigger than this, it is distorted beyond the point where it can spring back. It breaks. Up to this point, however, it exerts an upward force that exactly matches the downward force exerted on it. therefore the tennis ball is able to sit on the table. 

If there is a force acting on an object, but it is not moving, there must be another force balancing (or cancelling out) the first one.

If the forces acting on an object balance each other, they add to zero.

The sum of all forces acting on an object is called the resultant force.

To find the resultant force, you add the separate forces. You must take account of their directions. 

Average speed = distance travelled / time taken

The speed at a particular moment is called the instantaneous speed. A car speedometer shows this.

Ways to measure a vehicle's speed:

Gatso speed camera - use radar to detect vehicles above speed limit. Two photographs are taken 0.5s apart to provide evidence. Distance markers on the road show how far the car has travelled in this time.

Truvelo speed camera - triggered by detector cables in the road. Pressure sensors in cables detect when a car is passing over. A computer in the camera measures the speed from one cable to the next. If it is going faster than the speed limit, a picture is taken.

Police radar gun - bounces microwaves off approaching cars. Microwaves reflected off an oncoming car have a higher frequency than original waves. This is picked up by the radar gun. Frequency change is used to calculate the car's instantaneous speed. 

Distance-time: Shows how far a moving object is from its starting point at every instant during its journey

Speed-time: Shows the speed of the moving object at every instant during its journey

Tachograph: monitors the distance and speed of a vehicle, drawing a graph of its speed against time. Either a tachograph-trace graph, or a speed/time graph can be drawn with these results.

Velocity-time: Velocity means the speed in a certain direction. A negative velocity indicates traveling in the opposite direction to original motion, a positive velocity means that the direction is the same. 

momentum (kg m/s) = mass (kg) x velocity (m/s)

If an object is moving in one direction, it has a positive momentum. If it moves in the the other direction, its momentum is negative. In any situation, you can choose which direction to call 'positive'. 

Imagine two trolleys, one with a release knob and a spring loaded plunger. When there is no interaction, there is no force on the other trolley. When there is an interaction, both objects move. If the objects have different masses, the heavy one moves more slowly than the light one. 

Momentum change depends on:

• Size of the force
• Time for which the force acts

momentum change (kg m/s) = force (N) x time for which it acts (s)

Example:

(a) A football has a mass of around 1kg. A free kick gives it a speed of 20 m/s. What is its momentum?

momentum = mass x velocity
1kg x 20m/s
20 kg m/s

(b) The amount of time the ball was kicked for was around 0.05s. Estimate the force exerted on the ball during the kick.

momentum change = force x time for which it acts
20 kg m/s = force x 0.05 s
20 kg m/s / 0.05s = force
= 400N 

When two objects interact, the total momentum change of the two objects (taking direction into account) is zero.

Example:

1) Zelda and Jake are skaters. Zelda pushes on Jake's hands, and they both move apart. Jake's mass is 60 kg, and he is moving at 2 m/s. Thus, his momentum is 120 kg m/s. Therefore, Zelda's momentum must also be 120 kg m/s, in the opposite direction. As her mass is 40 kg, at what speed is she moving?

momentum = mass x velocity
velocity = momentum / mass
120 kg m/s / 40 kg = 3 m/s

These sort of interactions we've seen so far are 'explosions', where two objects push apart. Collisions are another type of interaction. Momentum is conserved in any collision.  

The momentum of a car depends on:

• its mass
• its velocity

momentum change = force x time for which it acts

The bigger the time, the smaller the force (for the same momentum change). This is why cars have front and rear crumple zones, with a rigid box in the middle. They crumple gradually in a collision, which increases the duration of the collision. Therefore the force exerted on the car is less.

The passengers within the car also experience a sudden momentum change. A force exerted on their bodies (by whatever they come into contact with) causes this change. The longer it takes to change the speed of the passengers to zero, the smaller the force they experience. 

Seat belts: During a crash, the seat belt stretches. They work on the same principle as crumple zones. They make the momentum change take longer, so the force that causes the change is less. 

Air bags: Seat belts do not stop the top half of your body moving forward, so you may hit yourself against parts of the car. Air bags cushion the impact, reducing your momentum more slowly, so that the force experienced is less.

Why we need them:

When travelling at 30 mph (14 m/s), you would hit the windscreen and steering wheel 0.07s after impact. This is the same for front and back seat passengers. Human reaction time is about 0.14s, so this would happen too fast for you to react. Even if it were possible to react that quickly, the force required to change your speed from 14 m/s to zero in 0.1s is more than your arms and legs would be able to exert. This is why seat belts and air bags are essential.

Law 1: If the resultant fcancel each other out.orce acting on an object is zero, the momentum of the object does not change.

• A stationary object, since its momentum is not changing. It is zero all the time. The resultant force acting on it is also zero. The forces acting on the object are balanced. They
• An object traveling with a constant velocity. Its driving force balances the opposing force of friction. Thus the resultant force is zero. 

Law 2: If there is a resultant force acting on an object, the momentum of the object will change. The change of momentum is given by momentum change = resultant force x time for which it acts and is in the same direction as the resultant force. 

When you press on the pedals of a bike, the chain makes the back wheel turn. The tyre pushes back on the ground. The other force in this interaction pair is the force exerted by the ground on the tyre. This pushes the bike forward. This is the driving force. As you move, air resistance and friction at the axles cause a counter-force, in the opposite direction to your motion.

1) When you start moving, the counter-force is very small. Your driving force is bigger. So you move forward, and your speed increases.

2) As you go faster, the air resistance force on you gets bigger. So the counter-force increases. You are still getting faster, but not as quickly as before. 

3) Eventually you reach a speed where the counter-force exactly balances your driving force*. Now your speed stops increasing. You carry on traveling, at a steady speed. 

*like terminal velocity

The amount of work done depends on:

• force you have to exert.
• the distance moved in the direction of the force.

work done by a force (J) = force x distance moved in the direction of force (m) 

Example:

Calculate how much work is needed to push a 600N car 50m along a road:

work done = force x distance moved in direction of force
                 = 600N x 50m
                 = 30,000 J

The amount of work that you do is equal to the amount of energy you transfer:

amount of work done = amount of energy transferred.

Work, like energy, is measured in Joules.  

If you do work by lifting, you are increasing the gravitational potential energy (GPE) of the object. The increase is equal to the amount of work you have done.

Example:

You have a suitcase that weight 300N. To lift it up, you have to exert an upward force of 300N. if you lift it 1 metre into the boot of the car, then how much work has been done? 

work done = force x distance moved in the direction the force 
                 = 300 N x 1 m
                 = 300 J

To calculate the change in an object's gravitational potential energy:

gravitational potential energy (J) = weight (N) x vertical height difference (m) 

Example: 

(1) Calculate the change in kinetic energy of a trolley pushed with a force of 6 N overall distance of 5 m (assume there are not frictional forces acting).

change in kinetic energy of trolley = work done by pushing force
                                                      = force x distance
                                                      = 6 N x 5 m
                                                      = 30 J

The equation for calculating the kinetic energy of a moving object is:

kinetic energy (J) = 1/2 x mass (kg) x (velocity) squared (m/s squared)

When a roller coaster runs down a slope, it:

• loses gravitational potential energy.
• gains kinetic energy

If friction is small enough to ignore, on complicated roller coaster shapes, we can use the principle of conservation of energy:

amount of gravitational potential energy lost = amount of kinetic energy gained

1) Calculate the speed of a rollercoaster 20m in height, where it is stationary at the top and in motion at the bottom, assuming there are no friction forces. Each roller coaster carriage has a total mass of 1,000 kg (10,000 N).

(a) loss of gravitational potential energy = weight x vertical height change
                                                               =  10,000 N x 20 m
                                                               = 200,000 J
(b) loss of gravitational potential energy = gain in kinetic energy
                             gain in kinetic energy =  200,000 J
(c) gain in kinetic energy = 1/2 x mass x velocity squared
                         mass x velocity squared = 400,000 J 
                                     velocity squared = 400,000 J / 1,000 kg 
                                                                = 400 (m/s) squared
                                                    velocity = 20 m/s