Worksheet: Conservation of Momentum

In this worksheet, we will practice calculating the momentum changes of objects that exchange momentum with each other by applying the principle of momentum conservation.

Q1:

A firework is tied to a toy car to make a toy rocket car. The firework ejects exhaust from its base. The exhaust has a mass of 15 g and moves away from the firework at a constant speed of 55 m/s. The rocket car has a mass of 75 g. What constant speed does the rocket car move at?

Q2:

A boy’s yo-yo has a mass of 20 g. The yo-yo runs down its string at a constant speed of 50 mm/s until it reaches the end of the string. When the yo-yo is at the end of the string, the boy jerks the string upward and this motion increases the upward momentum of the yo-yo by 0.0015 kg⋅m/s. At what instantaneous speed, in millimeters per second, does the yo-yo move up its string after the momentum change occurs?

  • A25 mm/s
  • B50 mm/s
  • C22 mm/s
  • D38 mm/s
  • E125 mm/s

Q3:

A conveyer belt consists of a surface that is a sheet of material wrapped around continually turning wheels that move the surface at an average speed of 6.25 cm/s, as shown in the diagram. When a bag containing 150 g of shopping is placed on the moving surface, the surface and the shopping both have an average speed of 5 cm/s. What is the mass of the surface in grams?

Q4:

The momentum changes over time of two objects 𝐴 and 𝐵 that collide with each other are shown in the graph. Object 𝐴 has an initial velocity of 6 m/s and a mass of 2.5 kg. Object 𝐴 is shown by the blue line.

At what time value do the objects first contact with each other?

At what time value do the objects lose contact with each other?

What is the initial velocity of object 𝐵?

What is the mass of the object 𝐵?

What is the total momentum of the objects?

Q5:

A ping-pong ball of mass 45 g that was moving at a constant speed of 3 m/s collides with a bowling ball of mass 7 kg that was not moving. The ping-pong ball bounces off the bowling ball in the opposite direction to the direction it was moving in before the collision, at a constant speed of 1.6 m/s. How many centimeters per second is the bowling ball moving after the collision to the nearest centimeter per second?

Q6:

During a game of pool, a cue ball that has a mass of 170 g was moving along a pool table at a constant speed of 30 cm/s. The cue ball hit another ball, which has a mass of 160 g and was moving along the table in the opposite direction to the cue ball, at a constant speed of 30 cm/s, as shown in the diagram. After the collision, the cue ball moved along the table in the opposite direction to the direction that it was moving in before the collision and at the same speed that it was moving before the collision.

What was the speed of the 160 g ball after the collision? Round your answer to the nearest centimeter per second.

After the collision, did the 160 g ball move in the same direction as the cue ball or the opposite direction to the cue ball?

  • AIn the opposite direction
  • BIn the same direction

Q7:

During a game of pool, a cue ball that has a mass of 170 g moves along a pool table at a constant speed of 80 cm/s. The cue ball hits another ball, which has a mass of 160 g and is not moving, as shown in the diagram. After the collision, the cue ball does not move. What constant speed, in centimeters per second, does the 160 g mass ball move at after the collision?

Q8:

A balloon consists of a skin with a mass of 5.4 g. It contains air that has a mass of 2.8 g. The balloon is initially stationary. Its end is untied so that air can escape from it, and the escaping air leaves it at an average speed of 1.5 m/s. What is the speed of the balloon when 1.2 g of air has escaped from it? Assume that any air left in the balloon moves at the same speed as the balloon. Give your answer to 2 decimal places.

Q9:

Two balls of equal mass collide with each other, as shown in the “before” part of the diagram. Which of the four ways that the two balls could be moving, as shown in the “after” part, does not conserve the balls’ total momentum?

  • AAll the shown examples conserve momentum.
  • B(B)
  • C(D)
  • D(A)
  • E(C)

Q10:

Two balls of equal mass collide with each other, as shown in the “before” part of the diagram. Which of the four ways that the two balls could be moving, as shown in the “after” part, does not conserve the balls’ total momentum?

  • AAll the shown examples conserve momentum.
  • BD
  • CB
  • DA
  • EC

Q11:

Two balls of equal masses collide with each other, as shown in the Before part of the diagram. Which of the four ways that the two balls could be moving as shown in the After part of the diagram does not conserve the balls’ total momentum?

  • A(D)
  • B(A)
  • C(B)
  • D(C)
  • EAll the shown examples conserve momentum.

Q12:

During a game of pool, a cue ball that has a mass of 170 g moves along a pool table at a constant speed of 60 cm/s. The cue ball hits another ball, which has a mass of 160 g and is also moving along the table and in the same direction as the cue ball but at a constant speed of only 15 cm/s, as shown in the diagram. After the collision, the balls move together at the same constant speed. What is the speed of the balls after the collision? Round your answer to the nearest centimeter per second.

Q13:

During a game of pool, a cue ball that has a mass of 170 g moves along a pool table at a constant speed of 51 cm/s. The cue ball hits another ball, which has a mass of 160 g and is not moving, as shown in the diagram. After the collision, the balls move together at the same constant speed. What is the speed, in centimeters per second, of the balls after the collision? Round your answer to one decimal place.

Q14:

Two balls with equal masses collide with each other, as shown in the “before” part of the diagram. Which of the four ways that the two balls could be moving, as shown in the “after” part of the diagram, does not conserve the balls’ total momentum?

  • AAll of the shown examples conserve momentum.
  • B(D)
  • C(B)
  • D(C)
  • E(A)

Q15:

A boatman pushes a raft along a river, as shown in the diagram. The raft’s pole pushes against a stone on the riverbed and this accelerates the raft to an instantaneous velocity of 0.25 m/s. What is the instantaneous velocity of the stone when the raft has accelerated? Ignore any motion of water or friction from the riverbed.

Q16:

A meteor with a mass of 7,000 g flies through the air, straight toward the ground, at a constant speed of 1,500 m/s. In midair, the meteor explodes into two pieces. The larger piece has a mass of 5,000 g and the smaller piece has a mass of 2,000 g. After the explosion, the smaller piece has an instantaneous downward velocity of 1,200 m/s, as shown in the diagram. What is the instantaneous downward velocity of the larger piece?

Q17:

Two balls of equal masses collide with each other, as shown in the Before part of the diagram. Which of the four ways that the two balls could be moving as shown in the After part of the diagram does not conserve the balls’ total momentum?

  • A(D)
  • B(B)
  • CAll of the shown examples conserve momentum.
  • D(C)
  • E(A)

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