Physics: Momentum, Impulse, and Conservation Worksheet

Question 1

A 1200 kg car travels east at 20 m/s. Calculate the car's momentum, including direction.

Accepted Answer

The car's momentum is 24000 kg m/s east because momentum equals mass times velocity, so p = 1200 kg × 20 m/s.

Question 2

A 0.50 kg soccer ball is kicked with an average force of 150 N for 0.20 s. Find the impulse delivered to the ball and the change in the ball's velocity.

Accepted Answer

The impulse is 30 N s because J = FΔt = 150 N × 0.20 s. The change in velocity is 60 m/s because Δv = J/m = 30 N s ÷ 0.50 kg.

Question 3

A 1000 kg car moving at 15 m/s brakes to a stop in 3.0 s. Find the average braking force on the car.

Accepted Answer

The average braking force is 5000 N opposite the direction of motion. The change in momentum is -15000 kg m/s, and F = Δp/Δt = -15000 kg m/s ÷ 3.0 s = -5000 N.

Question 4

Two ice skaters start at rest and push off from each other. Skater A has a mass of 60 kg and moves left at 1.5 m/s. Skater B has a mass of 45 kg. Find Skater B's velocity.

Accepted Answer

Skater B moves right at 2.0 m/s. The total momentum was initially zero, so Skater B must have +90 kg m/s of momentum to balance Skater A's -90 kg m/s momentum.

Question 5

A 2.0 kg cart moving at 3.0 m/s collides with a 1.0 kg cart at rest. The carts stick together. Find their final velocity.

Accepted Answer

The carts move together at 2.0 m/s in the original direction of the 2.0 kg cart. The total initial momentum is 6.0 kg m/s, and the combined mass is 3.0 kg, so v = 6.0 ÷ 3.0 = 2.0 m/s.

Question 6

A 0.15 kg ball moving at 40 m/s hits a wall and rebounds in the opposite direction at 30 m/s. Take the original direction as positive. Calculate the impulse on the ball.

Accepted Answer

The impulse on the ball is -10.5 N s. The final velocity is -30 m/s, so J = m(vf - vi) = 0.15 kg × (-30 m/s - 40 m/s) = -10.5 N s.

Question 7

A force-time graph for a collision is a triangle with a base of 0.10 s and a maximum force of 800 N. Find the impulse delivered during the collision.

Accepted Answer

The impulse is 40 N s. Impulse equals the area under the force-time graph, and the triangular area is 1/2 × 0.10 s × 800 N = 40 N s.

Question 8

A 0.010 kg bullet leaves a 4.0 kg rifle at 400 m/s forward. If the rifle was initially at rest, find the recoil velocity of the rifle.

Accepted Answer

The rifle recoils at 1.0 m/s backward. The bullet's momentum is 4.0 kg m/s forward, so the rifle must have 4.0 kg m/s backward; v = -4.0 kg m/s ÷ 4.0 kg = -1.0 m/s.

Question 9

A 0.20 kg baseball moves at 35 m/s. A 5.0 kg bowling ball moves at 1.2 m/s. Determine which object has greater momentum and by how much.

Accepted Answer

The baseball has greater momentum by 1.0 kg m/s. The baseball's momentum is 7.0 kg m/s, and the bowling ball's momentum is 6.0 kg m/s.

Question 10

Explain why an airbag reduces the force on a person during a car crash even though the person's change in momentum is the same.

Accepted Answer

An airbag increases the time over which the person's momentum changes. Since average force equals change in momentum divided by time, increasing the stopping time reduces the average force.

Question 11

A 4.0 kg object at rest explodes into two pieces. A 1.5 kg piece moves east at 8.0 m/s. Find the velocity of the other piece.

Accepted Answer

The other piece moves west at 4.8 m/s. The first piece has 12 kg m/s east of momentum, so the 2.5 kg second piece must have 12 kg m/s west of momentum; v = 12 ÷ 2.5 = 4.8 m/s west.

Question 12

A 0.50 kg cart moving right at 2.0 m/s collides elastically with an identical 0.50 kg cart at rest. State the final velocity of each cart after the collision.

Accepted Answer

After the elastic collision, the first cart stops and the second cart moves right at 2.0 m/s. For a one-dimensional elastic collision between identical masses, the carts exchange velocities.

Question 13

A 0.20 kg puck initially moves east at 10 m/s. After a collision, it moves north at 6.0 m/s. Find the impulse vector on the puck.

Accepted Answer

The impulse vector is 2.0 N s west and 1.2 N s north. The initial momentum is 2.0 kg m/s east, and the final momentum is 1.2 kg m/s north, so Δp = (-2.0, 1.2) N s.

Question 14

A 0.40 kg cart moves right at 2.0 m/s and collides with a 0.60 kg cart moving left at 1.0 m/s. The carts stick together. Find their final velocity.

Accepted Answer

The carts move right at 0.20 m/s. The total momentum is 0.40 kg × 2.0 m/s + 0.60 kg × (-1.0 m/s) = 0.20 kg m/s, and the total mass is 1.00 kg, so v = 0.20 m/s right.

Question 15

An 80 kg astronaut at rest in space throws a 5.0 kg tool to the right at 12 m/s. Find the astronaut's velocity after throwing the tool.

Accepted Answer

The astronaut moves left at 0.75 m/s. The tool has 60 kg m/s of momentum to the right, so the astronaut must have 60 kg m/s of momentum to the left; v = -60 kg m/s ÷ 80 kg = -0.75 m/s.

Physics: Momentum, Impulse, and Conservation

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