### Momentum Questions

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March 2013

4 A bullet of mass 10g, moving at a velocity of 300 m.s-1, strikes a wooden block of mass 1,99 kg resting on a flat horizontal surface as shown in the diagram below. The bullet becomes embedded in the block. Ignore the effects of air friction.

4.1 Write down in words the principle of conservation of linear momentum. (2)
4.1 The total (linear) momentum remains constant (is conserved) in an isolated (a closed) system / the absence of external forces.

4.2 Calculate the speed of the block-bullet system immediately after the collision. (4)
4.2

4.3 Is this collision elastic or inelastic? Give a reason for the answer. (2)
Inelastic
Kinetic energy is not conserved.

OR

Inelastic
Objects stick together

OR

Inelastic
Structural damage to the block.

OR

Inelastic
There is deformation to the block / bullet.

OR

Inelastic
Energy converted to other forms such as sound and heat.

The floor exerts a constant frictional force of 8N on the block-bullet system as it comes to rest.

4.4 Calculate the distance that the block-bullet system moves after the collision. (4)
4.4

OR

March 2012

4 The bounce of a cricket ball is tested before it is used. The standard test is to drop a ball from a certain height onto a hard surface and then measure how high it bounces. During such a test, a cricket ball of mass 0,15 kg is dropped from rest from a certain height and it strikes the floor at a speed of 6,2 m.s-1. The ball bounces straight upwards at a velocity of 3,62 m.s-1 to a height of 0,65 m, as shown in the diagram below. The effects of air friction may be ignored.

4.1 Define the term impulse in words. (2)
4.1 Impulse is the product of the net (average) force and the time during which the force acts.

OR

Impulse is the change in momentum.

4.2 Calculate the magnitude of the impulse of the net force applied to the ball during its collision with the floor. (3)
4.2

4.3 To meet the requirements, a cricket ball must bounce to one third of the height that it is initially dropped from.

Use ENERGY PRINCIPLES to determine whether this ball meets the minimum requirements. (5)
4.3.

Nov 2012

4 The diagram below shows a car of mass m travelling at a velocity of 20 m.s-1 east on a straight level road and a truck of mass 2m travelling at 20 m.s-1 west on the same road. Ignore the effects of friction.

4.1 Calculate the velocity of the car relative to the truck. (2)
4.1   40 m.s-1 east

The vehicles collide head-on and stick together during the collision.

4.2 State the principle of conservation of linear momentum in words. (2)
4.2 The total (linear) momentum remains constant (is conserved) in an isolated (a closed system) (the absence of external forces) if the impulse of external forces is zero.

4.3 Calculate the velocity of the truck-car system immediately after the collision. (6)
4.3

4.4 On impact the car exerts a force of magnitude F on the truck and experiences an acceleration of magnitude a.

4.4.1 Determine, in terms of F, the magnitude of the force that the truck exerts on the car on impact. Give a reason for the answer. (2)
4.4.1   F
Newton's Third Law of motion

4.4.2 Determine, in terms of a, the acceleration that the truck experiences on impact. Give a reason for the answer. (2)
4.4.2

4.4.3 Both drivers are wearing identical seat belts. Which driver is likely to be more severely injured on impact? Explain the answer by referring to acceleration and velocity. (3)
4.3 Car driver
• (Car - driver system) have greater acceleration.
• (Car - driver system) have greater change in velocity /greater Δv.

March 2011

4 Two shopping trolleys, X and Y, are both moving to the right along the same straight line. The mass of trolley Y is 12 kg and its kinetic energy is 37,5J.

4.1 Calculate the speed of trolley Y. (3)
4.1

Trolley X of mass 30kg collides with trolley Y and they stick together on impact. After the collision, the combined speed of the trolleys is 3,2 m.s-1. (Ignore the effects of friction.)

4.2 Write down the principle of conservation of linear momentum in words. (2)
4.2 The total linear momentum remains constant (is conserved) in magnitude and direction in a closed system.

OR

In a closed system, the total linear momentum before collision is equal to the total linear momentum after collision.

4.3 Calculate the speed of trolley X before the collision. (5)
4.3

During the collision, trolley X exerts a force on trolley Y. The collision time is 0,2 s.

4.4 Calculate the magnitude of the force that trolley X exerts on trolley Y. (4)
4.4

Nov 2011

4 A patrol car is moving on a straight horizontal road at a velocity of 10m.s-1 east. At the same time a thief in a car ahead of him is driving at a velocity of 40m.s-1 in the same direction.

4.1 Write down the velocity of the thief's car relative to the patrol car. (2)
4.1   30m.s-1 east

A person in the patrol car fires a bullet at the thief's car. The bullet leaves the gun with an initial horizontal velocity of 100 m.s-1 relative to the patrol car.
Ignore the effects of friction.

4.2 Write down the initial velocity of the bullet relative to the thief's car. (2)
4.2   70 m.s-1 east

While travelling at 40 m.s-1, the thief's car of mass 1000 kg, collides head-on with a truck of mass 5000 kg moving at 20m.s-1. After the collision, the car and the truck move together. Ignore the effects of friction.

4.3 State the law of conservation of linear momentum in words. (2)
4.3 The total linear momentum remains constant (is conserved / does not change) in an isolated (a closed system) in the absence of external forces.

4.4 Calculate the velocity of the thief's car immediately after the collision. (6)
4.4 To the right as positive

4.5 Research has shown that forces greater than 85 000N during collisions may cause fatal injuries. The collision described above lasts for 0,5 s.

Determine, by means of a calculation, whether the collision above could result in a fatal injury. (5)
4.5

March 2010

4 During an investigation a police officer fires a bullet of mass 15g into a stationary wooden block, of mass 5kg, suspended from a long, strong cord. The bullet remains stuck in the block and the block-bullet system swings to a height of 15 cm above the equilibrium position, as shown below. (Effects of friction and the mass of the cord may be ignored.)

4.1 State the law of conservation of momentum in words. (2)
4.1 The total linear momentum in an isolated system is conserved. 

OR

If no net external force acts on a system of particles, the total linear momentum of the system cannot change.

4.2 Use energy principles to show that the magnitude of the velocity of the block-bullet system is 1,71 m.s-1 immediately after the bullet struck the block. (3)
4.2

4.3 Calculate the magnitude of the velocity of the bullet just before it strikes the block. (4)
4.3

4.4 The police officer is pushed slightly backwards by the butt of the rifle, which he is holding against his shoulder, whilst firing the rifle. Use the relevant law of motion to explain why this happens. (3)
4.4 According to Newton's third law, the gun will exert a force on the bullet and the bullet will exert an equal but opposite force on the gun.
 The force of the gun on the officer pushes him slightly backwards. 

Nov 2010

Go to Energy CatView.
March 2009

Go to Energy CatView.
Nov 2009 Unused

Go to Energy CatView.
Nov 2009

6 A man of mass 87kg on roller skates, moving horizontally at constant speed in a straight line, sees a boy of mass 22kg standing directly in his path. The man grabs the boy and they both continue in a straight line at 2,4 m.s-1.

6.1 Calculate the man's speed just before he grabs the boy. Ignore the effects of friction. (4)
6.1

6.2 Is the collision elastic? Use a calculation to support your answer. (6)
6.2

Collision is inelastic / No

6.3 After grabbing the boy, they both continue at a velocity of 2,4m.s-1 along a straight line until they arrive at a loose gravel surface near the end of the path. They now move at constant acceleration in a straight line through the loose gravel for 2m before coming to rest.

Calculate the magnitude of the force exerted by the gravel surface on the man and the boy. (5)
6.3 Option 1

Option 2

Nov 2008

5 The most common reasons for rear-end collisions are too short a following distance, speeding and failing brakes. The sketch below represents one such collision. Car A of mass 1000kg, stationary at a traffic light, is hit from behind by Car B of mass 1200kg, travelling at 18m.s-1. Immediately after the collision Car A moves forward at 12m.s-1.

5.1 Assume that linear momentum is conserved during this collision. Calculate the speed of Car B immediately after the collision. (4)
5.1 Consider to the left as positive

5.2 Modern cars are designed to crumple partially on impact. Explain why the assumption made in QUESTION 5.1 may NOT be valid in this case. (2)
5.2 Not an isolated system / external forces present / frictional forces present / driver in front car has his foot on the brake.

5.3 A traffic officer appears at the scene of the accident and mentions the dangers of a head-on collision. He mentions that for cars involved in a head-on collision, the risk of injury for passengers in a heavier car would be less than for passengers in a lighter car.

Use principles of Physics to explain why the statement made by the traffic officer is correct. (3)
5.3 During the collision, both cars experience a force of equal magnitude. This net force on the car with larger mass causes it to experience a smaller acceleration. Therefore the passenger will experience a smaller change in velocity and will be less injured.

Prep Paper 2008

6 A railway truck A of mass 2000kg moves westwards with a velocity of 3m.s-1. It collides with a stationary truck B of mass 1200 kg, loaded with electronic equipment of mass 300kg. The two trucks combined after the collision. Ignore the effects of friction.

6.1 Write down magnitude and direction of the 'reaction force' to the weight of truck A. (2)
6.1   1,96 x 104 N , upward

6.2 Calculate the velocity of truck B after the collision. (5)
6.2

6.3 Calculate the magnitude of the force that truck A exerts on truck B if the collision
lasts for 0,5s. (4)
6.3

6.4 The electronic equipment on the stationary truck is wrapped in bubble plastic (plastic filled with air bubbles).

Use physics principles to explain why bubble plastic is preferred to ordinary plastic. (3)
6.4 The air bubbles will increase the time of impact and thus reduce the Force. This may minimize damage to the equipment.

Exemplar 2008

6 Collisions happen on the roads in our country daily. In one of these collisions, a car of mass 1600 kg, travelling at a speed of 30m.s-1 to the left, collides head-on with a minibus of mass 3000 kg, travelling at 20m.s-1 to the right. The two vehicles move together as a unit in a straight line after the collision.

6.1 Calculate the velocity of the two vehicles after the collision. (6)
6.1 Consider motion to the right as positive:

6.2 Do the necessary calculations to show that the collision was inelastic. (6)
6.2 Before collision

After collision

Ek before collision not equal to Ek after collision, thus the collision is inelastic

6.3 The billboard below advertises a car from a certain manufacturer.

Use your knowledge of momentum and impulse to justify how the safety features mentioned in the advertisement contribute to the safety of passengers. (3)
6.3 During a collision, the crumple zone / airbag increases the time during which momentum changes  and according to the equation :

the force during impact will decrease.

6 New cars have a crumple zone to help minimise injuries during accidents. In addition seat belts, air bags and padded interiors can reduce the chance of death or serious injury.

6.1 Use principles in Physics to explain how air bags can reduce the chance of death or injury. (3)
6.1 When the airbag inflates during a collision, the contact time of a passenger/driver with an air bag is longer than without an airbag and thus the force on the passenger/driver is reduced  according to :

6.2 In a crash test, a car of mass 1,2 x 103 kg collides with a wall and rebounds as illustrated below. The initial and final velocities of the car are 12 m.s-1 to the left and 2m.s-1 to the right respectively. The collision lasts 0,1 s.

Calculate the:

6.2.1 Impulse of the car during the accident (4)
6.2.1 Take to the right as positive

to the right or away from wall

6.2.2 Average force exerted on the car (3)
6.2.2

to the right or away from the wall

6.3 How will the magnitude of the force exerted on the car be affected if the time interval of the collision remains 0,1 s, but the car does not bounce off the wall? Write down only INCREASES, DECREASES or REMAINS THE SAME. Explain your answer. (2)
6.3 Decreases
 The final velocity of the car is zero and thus Δp decreases 

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