ICA8 - This problem has three parts. I will state the questions for each of the three parts, along with any additional info in "Description" below.

Question

Modern cars have airbags to reduce the injury rate in accidents. Consider a crash in which the car is decelerated from 20 m/s to 0 m/s.

Part a) If your mass is 75 kg, what is your change in momentum during the crash?

Part b) If the crash takes place over a time of 0.1 seconds, what is the average net force on you over this time interval?

Part c) The airbag allows you to decelerate more slowly in the accident, meaning that your body slows over a longer time of 1 second. What is the net force on your body in this case?

Answer 1

This problem just requires one to remember the relationship between force and change in momentum.

Part a) Remember that momentum is mv (m = mass, v = velocity), so the change in momentum would be Δp =Δmv_f - mv_i, where v_f is the final velocity and v_i is the initial velocity. Try plugging in the values and see what you get!

Part b) Remember that F = dp/dt, because F = ma, and a = dv/dt, so F = ma = m dv/dt = d(mv)/dt = dp/dt. In this case, because we may assume the change happens linearly, we can say F = Δp/Δt. Now again, try plugging in the values.

Part c) It is the same as part b), but this time Δt is different.