Question

A 2,200 kg railway freight car coasts at 3.6 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

Answer:

$m_2=2554.83\ kg$

Explanation:

Given that,

Mass of the car, $m_1=2200\ kg$

Initial speed of the car, $u=3.6\ m/s$

Final speed of the car, $v=3.1\ m/s$

To find,

The maximum mass of grain that it can accept.

Solution,

We know that according to the law of conservation of momentum, the initial momentum is equal to the final momentum.

$m_1u=m_2v$

$m_2=\dfrac{m_1u}{v}$

$m_2=\dfrac{2200\times 3.6}{3.1}$

$m_2=2554.83\ kg$

Therefore, the maximum mass of grain that it can accept is 2554.83 kg. Hence, this is the required solution.