5.23 Changes in momentum and car safety
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A car of mass 800 kg travelling at 25 m/s is brought to rest in 5.0 s by its brakes. Calculate the average braking force.
Mark scheme
change in momentum = 800 × 25 = 20 000 kg m/s (1); F = Δp ÷ t = 20 000 ÷ 5.0 (1); 4000 N (1)
Model answer
Change in momentum = 800 × 25 = 20 000 kg m/s. F = 20 000 / 5.0 = 4000 N.
A 60 kg person in a car travelling at 20 m/s is stopped by a seat belt in 0.40 s. Calculate the average force on the person.
Mark scheme
change in momentum = 60 × 20 = 1200 kg m/s (1); F = 1200 ÷ 0.40 (1); 3000 N (1)
Model answer
Change in momentum = 60 × 20 = 1200 kg m/s. F = 1200 / 0.40 = 3000 N.
State the equation that links force, change in momentum and time.
Mark scheme
force = change in momentum ÷ time
Model answer
Force = change in momentum / time taken.
Explain how a crumple zone reduces the force on the passengers in a head-on collision.
Mark scheme
the crumple zone collapses so the collision lasts for a longer time (1); the change in momentum is the same (1); so the force (change in momentum ÷ time) is smaller (1)
Model answer
The crumple zone collapses and makes the collision last longer. The change in momentum is the same, so the force, which is the change in momentum divided by the time, is smaller.
Explain why a cricketer moves their hands backwards as they catch a fast ball.
Mark scheme
this increases the time it takes the ball to stop (1); the change in momentum is the same (1); so the force on the hands is smaller (1)
Model answer
Moving their hands backwards makes the ball take longer to stop. The change in momentum is the same, so the force on the hands is smaller.
Use the graph in this lesson to explain why a long impact is safer than a short impact for the same change in momentum.
Mark scheme
the long impact has a smaller peak force (1); the area under both graphs (the change in momentum) is the same (1)
Model answer
The long impact has a much smaller peak force (5 kN compared with 20 kN), although the area under the graphs (the change in momentum) is the same.
Explain two ways in which an airbag reduces the risk of injury to a driver.
Mark scheme
it increases the time taken for the driver to stop (1); so reduces the force (1); it spreads the force over a larger area (1); so reduces the pressure on the body (1)
Model answer
It makes the driver take longer to stop, which reduces the force. It also spreads the force over a larger area, which reduces the pressure on the driver's body.
A cyclist's helmet has a layer of foam that crushes in a collision. Explain how it protects the cyclist's head.
Mark scheme
the foam crushes so the head takes longer to stop (1); the change in momentum is the same, so the force on the head is smaller (1); this reduces the risk of injury / brain damage (1)
Model answer
The foam crushes, so the head stops over a longer time. The change in momentum is the same, so the force on the head is smaller, which lowers the risk of injury.
A driver of mass 80 kg is travelling at 18 m/s. Compare the average force on the driver when a crash stops the car in 0.10 s with when a crumple zone makes it take 0.40 s. State what you conclude.
Mark scheme
change in momentum = 80 × 18 = 1440 kg m/s (1); F = 1440 ÷ 0.10 = 14 400 N (1); F = 1440 ÷ 0.40 (1); 3600 N (1); a four times longer time gives a four times smaller force (1)
Model answer
Change in momentum = 80 × 18 = 1440 kg m/s. In 0.10 s, F = 1440 / 0.10 = 14 400 N. In 0.40 s, F = 1440 / 0.40 = 3600 N. Increasing the time by four times reduces the force by four times.
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