Momentum 5 th form IGCSE Unit 15 1

1.19 describe the factors affecting vehicle stopping distance including speed, mass, road condition and reaction time 1.20 know and use the relationship between momentum, mass and velocity: momentum = mass × velocity (p = m × v) 1.21 use the idea of momentum to explain safety features 1.22 use the conservation of momentum to calculate the mass, velocity or momentum of objects 1.23 use the relationship between force, change in momentum and time taken: force=change in momentum/time taken 1.24 demonstrate an understanding of Newton’s third law 2

Changing motion What do you need to do to change the motion of an object? –Apply a force What determines how big a force you need to apply? Think about catching a ball... –How quickly do you want to stop it? –How fast is it travelling? –What is its mass? 3

Changing motion So it is relatively harder to change the motion of an object if: –It has a larger mass –It is travelling faster We can define a measure of how hard it is to change the motion of an object: Unit: kgms -1 momentummassvelocity Is momentum a scalar or vector? Momentum is a vector 4

Momentum Momentum is very useful for analysing the motion of objects and how they interact. Practice questions: 1.What is the momentum of a 58g tennis ball travelling at 40 ms -1 ? 2.What is the momentum of a 2000 kg car travelling at 25 ms -1 ? 3.What is the mass of a car travelling at 20 ms -1 with a momentum of kgms -1 ? 4.What is the velocity of a car of mass 1500 kg and momentum of kgms -1 ? 5

Stopping Distances What factors determine how far a vehicle travels between the driver deciding it needs to stop and it actually stopping? –Driver reaction time –velocity of vehicle –Mass of vehicle –Condition of vehicle –Condition of road 6

Stopping distances Made of two parts: thinking distance –How far you travel between realising you need to stop and pressing the brake –Proportional to velocity braking distance –How far you travel while the brakes reduce your velocity to zero –Proportional to velocity 2 (Can you think why?) 7

Stopping distances...according to the Highway Code 8.9 ms ms ms ms ms ms -1 8

Stopping Distances What factors will increase thinking distance? –Speed, tiredness, distraction, alcohol, drugs What factors will increase braking distance? –Speed, mass, road conditions (rain, ice, gravel etc), tyre wear, brake efficiency 9

Back to momentum To change momentum, we must apply a force. Newton found that the rate of change of momentum is proportional to the force applied. 10

Force and momentum change So: Warning: We have assumed constant mass, this is a simplification 11

Example A 500 kg car travelling at 10 m/s takes 8 seconds to stop. What force was exerted by the brakes? Change in momentum = m x v = 500 x 10 = 5000 kg.m/s Change in momentum = F x t 5000 = F x 8, so F=625 N 12

Example A golf ball of mass 0.05 kg is hit off a tee at a speed of 40 m/s. What is its momentum? –Mom = mv=0.05 x 40 = 2 kg.m/s The club was in contact with the ball for 0.5 ms. What force did it exert on the ball? –Change in mom = force x time, so 2 = F –So F=4000 N 13

Reducing the force Accidents often involve sudden changes of momentum, so this means large forces exerted on fragile people – ouch. How can we reduce the force and improve vehicle safety? –Increase the time it takes for the momentum of passengers to change 14

Why does this playground have a rubbery surface on the ground? 15

Passenger safety All the devices shown below are designed to increase the time of the momentum change during an accident. How? 17

Passenger safety Airbags inflate to lower the deceleration of the head and spread pressure over a wider area Seatbelts are designed to stretch, lowering the deceleration of the body Crumple zones in vehicles increase the deceleration time Padding inside crash helmet increases deceleration time 18

2 cars, both travelling at 10 m/s and driven by drivers of mass 70 kg, crash into a solid wall. – Car A has a crumple zone and takes 0.5s to stop. –Car B does not have a crumple zone and takes 0.05s to stop. What is the momentum of both drivers before the collision? What force does driver A experience during the crash? What force does driver B experience during the crash? Momentum = m x v = 70 x 10 = 700 kg.m/s Change in momentum = Force x time 700 = F x 0.5, so F = 1400 N on driver A (equivalent to a mass of 140 kg!) Driver B takes 1/10 of the time to stop, so the force on him is 10 times larger = N (equivalent to mass of 1.4 tons) 19

Momentum is conserved Just like energy, the total momentum of a system of objects is always the same, provided no external force acts In the collision shown above, the yellow ball loses the momentum that the green ball gains Total momentum before collision=total momentum after collision 20

A exerts a force on B, B exerts an equal and opposite force on A (Newton’s 3 rd law) The time of the collision is the same for A and B Change of momentum = force x time for both A and B So total momentum of the is conserved –Although A and B have different momentums before and after the collision 21

Using momentum conservation 1.A skater of mass 60kg moving at 6ms -1 collides with and holds on to another stationary skater of mass 30kg. Find the velocity of the pair after the collision. 2.A lorry of mass 3000kg is travelling at 30ms -1. It collides with a car of mass 1000kg. They move off together with a velocity of 25 ms -1. a.What is the momentum of the vehicles after the collision? b.What was the momentum of the vehicles just before the collision? c.What was the speed of the car before the collision? 22

Explosions Momentum is still conserved in explosions What is the total momentum just before the explosion? What is the total final momentum? 23

Recoil example Trolley example Momentum calcs sheet 24

Force pairs Forces always come in pairs which are –Equal in size –Opposite in direction –Same type of force –Acting on the two objects So when something exerts a force, it always experiences a force in return Newton’s 3 rd law 25

Examples of action-reaction pairs Action and reaction are always equal and opposite 26

What are the Newton pairs here? The weight is still there even if the table disappears –It’s pair is the upward pull on the Earth (gravity) The push of the book on the table is the pair with the reaction push of the table on the book –Both contact forces, if one goes so does the other Remember: A pair have to be the same type of force If one disappears, so must the other… 27

If the force on the carriage is equal and opposite to the force on the horse how can the horse pull the carriage? Is the answer: (a)The horse cannot pull the carriage because the carriage pulls as hard on the horse as the horse pulls on the carriage. (b)The carriage moves because the horse pulls slightly harder on the carriage (c)The horse pulls the carriage before it has time to react. (d)The horse can pull the carriage only if the horse is heavier than the carriage. (e)Another explanation. What might it be? 28

Jets and rockets Jet and rocket engines burn fuel which produces high pressure exhaust gases. These escape through the back, exerting a force. The reaction force of the exhaust gases on the vehicle pushes the vehicle forward. 29

1.19 describe the factors affecting vehicle stopping distance including speed, mass, road condition and reaction time 1.20 know and use the relationship between momentum, mass and velocity: momentum = mass × velocity (p = m × v) 1.21 use the idea of momentum to explain safety features 1.22 use the conservation of momentum to calculate the mass, velocity or momentum of objects 1.23 use the relationship between force, change in momentum and time taken: force=change in momentum/time taken 1.24 demonstrate an understanding of Newton’s third law 30