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Momentum and impulse questions
Momentum is the quantity that collisions exchange, and in a closed system the total is conserved whatever else happens. Impulse is the same law written over time, which is why crumple zones, airbags and bending your knees on landing all reduce the force.
19 original questions · 58 marks · the momentum and impulse notes · Mechanics
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Calculate the momentum of a 2.0 kg trolley moving at 8.0 m s−1, and state its unit.
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p = mv = 2.0 × 8.0 (1)
p = 16 kg m s−1 (or N s) (1)State the principle of conservation of linear momentum, including the condition under which it applies.
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In a collision or explosion, the total momentum before equals the total momentum after (1), provided no external resultant force acts on the system (1).Define the impulse of a force and state how it is related to momentum.
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Impulse = force × time for which it acts, FΔt (1). It equals the change in momentum of the object, Δ(mv) (1).A car travels round a bend at constant speed. Explain why its momentum changes.
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Momentum is a vector, directed along the velocity (1). On the bend the direction of the velocity changes, so the momentum changes even though its magnitude is constant. (1)State the quantity represented by the area under a force-time graph.
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The impulse of the force, equal to the change in momentum it produces. (1)State the difference between an elastic collision and an inelastic collision, and name the quantity that is conserved in both.
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In an elastic collision kinetic energy is conserved; in an inelastic collision some kinetic energy is transferred to other forms (1). Momentum is conserved in both. (1)A constant force of 20 N acts for 3.0 s on a 4.0 kg object initially at rest. Calculate (a) the impulse delivered and (b) the final velocity of the object.
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(a) Impulse = FΔt = 20 × 3.0 (1)
Impulse = 60 N s (1)
(b) Impulse = Δ(mv) = mv, so v = 60/4.0 (1)
v = 15 m s−1 (1)A 2.0 kg trolley moving at 3.0 m s−1 collides with a stationary 1.0 kg trolley and they move off together. Calculate their common velocity.
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Momentum is conserved: 2.0 × 3.0 = (2.0 + 1.0)v (1)
v = 6.0/3.0 (1)
v = 2.0 m s−1 (1)For the collision in the previous question, show that kinetic energy is not conserved by calculating the kinetic energy before and after, and state the type of collision.
A 4.0 kg gun fires a 0.040 kg bullet at 200 m s−1. Assuming the gun is free to move, calculate its recoil velocity.
A squash ball of mass 60 g hits a wall at 15 m s−1, at right angles to it, and rebounds along the same line at 9.0 m s−1. The contact time is 7.5 ms. Calculate (a) the change in momentum of the ball and (b) the average force the wall exerts on it.
During a collision, the force on a trolley rises linearly from zero to a peak of 3.0 kN in 20 ms and then falls linearly back to zero in a further 20 ms. Determine the impulse given to the trolley.
A fire hose directs a horizontal jet of water at a vertical wall. Water of total mass 4.2 kg strikes the wall each second, travelling at 15 m s−1, and does not rebound. Calculate the force the water exerts on the wall.
A 3.0 kg trolley moving right at 4.0 m s−1 collides head-on with a 1.0 kg trolley moving left at 2.0 m s−1, and they stick together. Calculate the velocity of the combined trolleys, stating its direction.
A 1000 kg car travelling at 20 m s−1 is brought to rest in a collision. Calculate the average force on the car if it stops in (a) 0.10 s and (b) 0.50 s, and comment on the role of a crumple zone.
Explain, in terms of impulse and momentum, how a seatbelt and an airbag reduce the risk of injury in a crash.
A 1400 kg car ran into the back of a 2100 kg van. The two vehicles locked together, and skid marks show that they moved off at 8.0 m s−1 immediately after the impact. The van driver states that the van was stationary when it was hit. The speed limit on the road is 13.5 m s−1. Assuming the van driver's statement is correct, deduce whether the car was exceeding the speed limit.
Two trolleys, of mass 1.2 kg and 0.80 kg, are held at rest on a smooth track with a compressed spring between them. When the spring is released, the 0.80 kg trolley moves off at 0.90 m s−1. Calculate (a) the velocity of the 1.2 kg trolley and (b) the total kinetic energy after the release, and state where this energy came from.
A rocket in deep space, far from any planet, fires its engine and accelerates. A student claims this is impossible because there is no air for the exhaust gases to push against. Explain, in terms of momentum, why the rocket does accelerate.
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