Question

A 2,300 kg railway freight car coasts at 4.0 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 3.1 m/s, what is the maximum mass of grain (in kg) that it can accept?

Answer 1

To solve this problem we will apply the concepts related to the conservation of momentum. According to the principal of conservation of momentum, the initial momentum of railway freight car is equals to the momentum of the loaded railway freight car, therefore,

$m_tv_t = (m_t+m_g)v$

$m_g = \frac{(m_tv_t-m_tv)}{v}$

Here $m_t$ is the mass of railway freight car, $m_g$ is the mass of the dumped grain.

Replacing our values we have,

$m_g = \frac{(2300kg)(4.0m/s-3.1m/s)}{(3.1m/s)}$

$m_g = 667.74kg$

Therefore the maximum mass of the grain that can be accepted is $667.74kg$