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?

Respuesta :

Answer:

[tex]m_2=2554.83\ kg[/tex]

Explanation:

Given that,

Mass of the car, [tex]m_1=2200\ kg[/tex]

Initial speed of the car, [tex]u=3.6\ m/s[/tex]

Final speed of the car, [tex]v=3.1\ m/s[/tex]

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.

[tex]m_1u=m_2v[/tex]

[tex]m_2=\dfrac{m_1u}{v}[/tex]

[tex]m_2=\dfrac{2200\times 3.6}{3.1}[/tex]

[tex]m_2=2554.83\ kg[/tex]

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