Physics Practice Test: Momentum and Collisions
- Momentum and Collisions
- 10 questions
- 15 minutes
These 10 questions practice impulse and conservation of momentum in one and two dimensions. Momentum is a vector: choose a positive direction first, and give velocities in the opposite direction a negative sign.
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Question 1
A 0.40 kg ball hits a wall at 10 m/s and bounces straight back at 8.0 m/s. What is the magnitude of the change in its momentum?
Correct answer: B
Taking the original direction as positive, Δp = 0.40(−8.0) − 0.40(10) = −7.2 kg·m/s. 0.80 kg·m/s comes from subtracting the speeds and forgetting that the direction reversed.
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Question 2
The ball in the previous question is in contact with the wall for 0.012 s. What is the average force the wall exerts on it?
Correct answer: A
F = Δp/Δt = 7.2/0.012 = 600 N. 67 N uses the wrong momentum change of 0.80 kg·m/s.
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Question 3
Why does an airbag reduce injuries in a crash, compared with hitting the steering wheel?
Correct answer: D
The driver's change in momentum is the same either way, but F = Δp/Δt, so spreading the stop over a longer time lowers the average force. The momentum change itself is fixed by the car's speed.
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Question 4
A billiard ball moving at 2.0 m/s hits an identical ball at rest head-on. The collision is perfectly elastic. What happens right after the collision?
Correct answer: C
For equal masses in a head-on elastic collision, the balls exchange velocities, which conserves both momentum and kinetic energy. Moving together at 1.0 m/s conserves momentum but loses kinetic energy, so it describes a perfectly inelastic collision.
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Question 5
Two ice skaters, 60 kg and 40 kg, stand at rest and push off each other. The 60 kg skater moves away at 2.0 m/s. How fast does the 40 kg skater move?
Correct answer: C
Total momentum stays zero, so 60 × 2.0 = 40v and v = 3.0 m/s in the opposite direction. 1.3 m/s inverts the mass ratio.
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Question 6
A 0.010 kg bullet moving at 300 m/s embeds itself in a 2.0 kg wooden block at rest on frictionless ice. What is the speed of the block with the bullet inside?
Correct answer: A
Momentum is conserved: 0.010 × 300 = 2.01v, so v ≈ 1.5 m/s. The other choices are off by a factor of 2 or 10 from errors with the masses.
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Question 7
A 3.0 kg puck moving east at 4.0 m/s collides with a 2.0 kg puck moving north at 3.0 m/s, and they stick together. What is their speed after the collision?
Correct answer: B
The momentum components are 12 kg·m/s east and 6.0 kg·m/s north, so |p| = √(12² + 6.0²) ≈ 13.4 kg·m/s and v = 13.4/5.0 ≈ 2.7 m/s. 3.6 m/s adds the two momenta as if they pointed the same way.
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Question 8
A 1.0 kg cart and a 4.0 kg cart have the same momentum. How does the kinetic energy of the 1.0 kg cart compare with that of the 4.0 kg cart?
Correct answer: D
KE = p²/(2m), so with equal p the kinetic energy is inversely proportional to mass. The lighter cart moves 4 times as fast, which gives it 4 times the kinetic energy.
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Question 9
A firework moving upward explodes into many pieces in midair. Just after the explosion, how does the total momentum of all the pieces compare with the momentum of the firework just before?
Correct answer: D
The explosion forces are internal and act for a very short time, so the total momentum is conserved. Kinetic energy increases a lot, but momentum does not change.
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Question 10
A 2.0 kg cart moving at 5.0 m/s to the right collides head-on with a 3.0 kg cart moving at 2.0 m/s to the left. They stick together. What is their velocity after the collision?
Correct answer: B
Taking right as positive: (2.0)(5.0) + (3.0)(−2.0) = 4.0 kg·m/s, so v = 4.0/5.0 = 0.80 m/s to the right. 3.2 m/s forgets the minus sign for the cart moving left.
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