Momentum

Figure 14 shows a footballer and a ball.

The ball is stationary before it is kicked.

The mass of the ball is 0.43 kg.

The kick exerts a force of 2700 N on the ball.

The velocity of the ball just after it has been kicked is 36 m / s.

Calculate the momentum of the ball just after it has been kicked.

State the unit for momentum.

Calculate the amount of time that the footballer’s kicking foot is in contact with the ball.

Explain how Newton’s third law applies to the interaction between the kicking foot and the football.

Figure 15 shows a system consisting of two toy trolleys, S and T, on a straight, horizontal track.

T is not moving.

S is moving with a velocity of 0.36 m / s towards T.

S collides with T.

The trolleys stick together and move off together.

With reference to the momentum of the system, explain why the velocity of the trolleys after the collision is less than the velocity of S before the collision.

Two people, L and M, have a 100 m race.

L starts running before M.

Figure 4 shows a distance/time graph of the race.

State the distance that L has run when M overtakes.

Calculate the velocity of L when running the 100 m race.

A motorcycle is travelling at a velocity of 6.2 m/s.

The motorcycle accelerates at 2.5 m/s² until its velocity is 10 m/s.

Calculate the time taken for this acceleration.

Use the equation

The motor cycle now decelerates (slows down) from 10 m/s to a stop.

The deceleration is at a constant rate of 4.4 m/s².

Calculate the distance the motorcycle travels as it slows down to a stop.

Use the equation

A car collides with a barrier on a road.

The time of the collision is very short.

Explain one factor, other than the time of the collision, that would affect the force on the car in the collision.

Your explanation should refer to an equation in the Equation Booklet.

Figure 13 shows a ball being rotated in a horizontal circle.

Which arrow in Figure 13 shows the direction of the centripetal force on the ball?

The ball is moving at constant speed. Give one reason why the velocity of the ball is continuously changing.

Figure 14 shows a gymnast landing on a mat and coming to rest.

The gymnast has a mass of 53 kg.

The gymnast lands on the mat with a velocity of 4.0 m/s.

The average force exerted by the mat on the gymnast is 3500 N.

Calculate the time taken for the gymnast to come to rest.

Give your answer to an appropriate number of significant figures.

Use the equation

* (c) Figure 15 shows two trolleys, P and Q, moving at the same speed, v, directly towards each other.

The trolleys have the same mass.

When the trolleys collide, they stick together and stop.

Explain how momentum and energy are both conserved in this collision.

An atom of mass 6.6 × 10^–26kg is moving with a velocity of 480 m / s.

Calculate the momentum of the atom.

momentum =_........ kg m / s

Figure 18 shows a ball before and after it collides with a wall.

The arrows show the direction of movement of the ball.

Before the collision, the momentum of the ball is 0.80 kg m / s.

After the collision, the momentum of the ball is 0.60 kg m / s in the opposite direction.

The ball is in contact with the wall for a time of 70 ms during the collision.

Calculate the force exerted on the ball by the wall.

Use an equation selected from the list of equations at the end of the paper.

*(c) Newton’s second law can be stated as

force = mass × acceleration

A student is provided with a trolley and a runway on a bench, as shown in Figure 19, and access to other equipment.

Describe a procedure the student could use to investigate how the acceleration of the trolley depends on the force applied to the trolley.

You may add to the diagram in Figure 19 to help your answer.

Which of these is a unit of momentum?

Students investigate conservation of momentum using two identical trolleys.

A card is then added to trolley A.

Some of the apparatus is set up as shown in Figure 8.

Describe an investigation the students could carry out to show that momentum is conserved when these two trolleys collide.

You may add to the diagram to help with your answer.

Give a reason for the runway being at a slope.

Figure 9 shows a racket and a tennis ball.

The tennis ball is travelling towards the racket at a velocity of 8.2 m/s.

The ball is hit back in the opposite direction at a velocity of 15 m/s.

The ball has a mass of 0.075 kg.

The ball is in contact with the racket for 12 ms.

Calculate the average force exerted by the ball on the racket.

Use the equation

Describe how Newton’s Third Law of Motion applies to the collision between the racket and the ball.

Figure 10 shows a small steel ball held at a height, h, above the ground.

The ball is released and allowed to fall to the ground.

The height h is 1.4 m.

Calculate the time, t, for the ball to reach the ground.

Use the equation

Two students use the arrangement shown in Figure 10.

They use a stopwatch to time the ball falling through the height of 1.4 m.

The students repeat the measurement many times, but their average value for t is different from the calculated value.

Suggest a reason why the students’ value for t is different from the calculated value.

Suggest one improvement the students could make to their procedure so that their value for t is closer to the calculated value.

Figure 11a shows a box falling towards a hard floor.

The box hits the floor and crumples a little before it comes to rest as shown in Figure 11b.

The momentum of the box just before it hits the floor is 8.7 kg m/s.

The box comes to rest 0.35 s after it first hits the floor.

Calculate the magnitude of the force exerted by the floor on the box.

Use an equation selected from the list of equations at the end of this paper.

State the magnitude and direction of the force exerted by the box on the floor.

Figure 12 shows a ball held in a clamp at R, above the ground.

The ball is released from the clamp and falls.

S is 3.8 m below R.

At S the momentum of the ball is 0.40 kg m/s.

Calculate the mass of the ball.

Acceleration due to gravity, g, = 10 m / s²

mass of the ball_........

Figure 12 is a diagram showing a rocket that is sent into space to try and change the path of a small asteroid.

The rocket has a mass of 5.510⁵kg and is travelling to the right at 14 km / s.

Which of these is a correct calculation of the momentum of the rocket in kg m / s?

Use the equation

The asteroid has a momentum of 7.510¹⁰kg m / s and a mass of 8.0 × 10⁶kg.

Calculate the speed of the asteroid.

speed of the asteroid =_........

*(b) A student investigates the effect of a crumple zone on the force exerted during a collision.

The student has one trolley with a spring at the front and another trolley without a spring.

trolley spring trolley

The student uses the arrangement in Figure 13.

After a trolley is released, it accelerates down a slope and bounces off a rigid wall.

The speed of a trolley can be measured just before a collision with the wall and just after a collision with the wall.

The silver foils are connected to a millisecond timer.

The silver foils make contact with each other during the collision, so the time they are in contact can be read from the millisecond timer.

Explain how the student could investigate the effect of a crumple zone on the average force exerted during the collision.

Your explanation should include:

• how to determine the force (you may wish to refer to an equation from the list of equations at the end of this paper)

• how the effect of crumple zones may be shown in the investigation

• precautions that may be necessary to achieve accurate results.

Newton’s third law, when applied to the collision of the rocket and the asteroid as shown in Figure 12, can be stated as follows:

The force exerted by the rocket on the asteroid is equal and opposite to the force exerted by the asteroid on the rocket.

Explain how this statement links to the conservation of momentum in the collision.

(a) A student investigates the relationship between force and acceleration for a trolley on a runway.

Figure 12 shows some of the apparatus the student uses.

Describe how the student could increase the accelerating force applied to the trolley.

Describe how the mass of the moving system can be kept constant.

Explain how the student could improve the procedure to compensate for the effects of frictional forces acting on the trolley.

*(b) Figure 13 shows two objects, Q and R, before and after they collide.

The arrows show the direction of movement of the objects. The arrows are not to scale.

Explain how momentum is conserved in the collision.

Use Newton’s third law and Newton’s second law in your answer.

Newton’s second law can be written as