Collisions (physics)

Question

A 1905-kg railway freight car coasts at 4.8 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 2.6 m/s, what is the maximum mass of grain that it can accept?

Answer 1

Calculate the momentum (P₁) before the grain is dumped. Since momentum = mass times velocity then:

P1 = (1905)(4.8) = 9144 kg•m/s

Calculate the momentum after the grain is dropped (P₂) by letting the mass of the grain = x::

P₂ = (1905 + x)(2.6) = 4953 + 2.6x kg•m/s

Conservation of momentum says P₁ = P₂ therefore:

9144 = 4953 + 2.6x

2.6x = 4191

x = 1612 kg which should be rounded to 1600 kg