# Worksheet: Applying Newton's Third Law of Motion to Collisions

In this worksheet, we will practice applying momentum conservation to find the forces acting on colliding objects and showing that these forces obey Newton's third law of motion.

Q1:

A bowling ball with a mass of 12.5 kg and a momentum of 25 kg⋅m/s collides for 0.25 s with a stationary bowling pin of mass 7.5 kg. After the collision, the pin moves at 2.5 m/s in the same direction that the ball moved before the collision. The ball slows to a speed of 0.5 m/s.

What is the change of the momentum of the pin?

What is the change of the momentum of the ball?

What is the force applied to the pin?

What is the force applied to the ball?

Q2:

During a house removal, a wheeled chair with a mass of 43.2 kg and a wheeled desk with a mass of 108 kg collide with each other. Each object applies to the other a force of 180 N and the collision lasts for 0.15 seconds.

What is the magnitude of the momentum change of the chair?

What is the magnitude of the momentum change of the desk?

What is the magnitude of the velocity change of the chair?

What is the magnitude of the velocity change of the desk?

Q3:

A ball with a mass of 200 g collides with a wall. The impact of the ball on the wall exerts an average force of 7.5 N on the wall for a time of 0.025 s. The ball rebounds from the wall at a horizontal speed of 0.15 m/s. What was the speed of the ball when it hit the wall?

Q4:

A person tries to catch a falling box that tumbles from a shelf above their head. The person claps their hands together to try and grab the box as it drops past them but misses. Each hand exerts a force of 3.5 N on the other hand, and the clap lasts for 0.025 s. What was the sum of the magnitudes of the momentum of each of the person’s hands before they clapped?

Q5:

Two objects A and B are thrown into the air and collide with each other, as shown in the diagram. Object A has a weight of 12 N and object B has a weight of 20 N. In the collision, object A exerts a force of 24 N on object B.

What force is applied to object A by object B during the collision?

Which object is given a greater acceleration due to the collision?

• AObject A
• BBoth objects are equally accelerated.
• CObject B

Q6:

Two soccer players, player A and player B, run toward each other head-on. Player A has a mass of 75 kg and player B has a mass of 50 kg. Player A has a constant speed of 2 m/s and player B has a constant speed of 3 m/s. The players collide, which takes 0.1 s. After the collision, both players are not moving. Consider the direction that player A runs before the collision to be positive.

What is the acceleration of player A during the collision?

What is the acceleration of player B during the collision?

What force is exerted on player A in the collision?

What force is exerted on player B in the collision?

Q7:

Two objects, object 1 and object 2, collide. In the diagram, the top row graphs all show the same change in force with time, which is the force that object 1 exerts on object 2 during the collision. Which of the graphs in the bottom row correctly shows how the force exerted on object 1 by object 2 changes during the collision?

• A(c)
• B(b)
• C(a)
• D(d)

Q8:

A bullet with a mass of 10 g is traveling at 450 m/s and hits a stationary toy car of mass 400 g. The bullet comes to rest 0.01 s after hitting the car.

What force is required to bring the bullet to rest in 0.01 s?

What is the acceleration of the car due to the impact from the bullet?

Q9:

Two bullets that both have masses of 50 g are fired horizontally from guns, each bullet moving at a constant speed of 400 m/s. The two guns are held by people aiming at each other and, by extraordinary chance, the bullets collide with each other head-on, as shown in the diagram. 0.0015 s after the bullets collide, they both have zero horizontal speed. Consider the bullet moving to the left to be moving in the positive direction.

What is the change of momentum of the bullet moving to the right due to the collision?

What is the change of momentum of the bullet moving to the left due to the collision?

What is the change in total momentum of the bullets before and after the collision?

What is the force applied to the bullet moving to the right in the collision, to the nearest newton?

What is the force applied to the bullet moving to the left in the collision to the nearest newton?

Q10:

A steel ball has a mass of 45 g. The ball rolls at 1.5 m/s and collides with a fixed spring, compressing the spring and coming instantaneously to rest when the spring is at its greatest compression, as shown in the diagram. The spring constant of the spring is 150 N/m. How much time is taken for the ball to compress the spring?