Question

A freight car moves along a frictionless level railroad track at constant speed. The car is open on top. A large load of coal is suddenly dumped into the car. What happens to the velocity of the car?

Answer 1

Answer:

Velocity of the car decreases.

Explanation:

We can understand the situation if we apply the conservation of energy principle to the situation

Let the initial mass of the freight be $m_{f}$

Initial velocity of the freight be $v_{fi}$

Thus the initial Kinetic energy of the freight will be $K.E=\frac{1}{2}m_{f}v_{if}^{2}$

When a Coal Block of mass M falls into the freight it's energy will become

$K.E=\frac{1}{2}(m_{f}+M)v_{ff}^{2}$

Equating both the energies we get final velocity as$v_{ff}$

$\frac{1}{2}m_{f}v_{if}^{2}=\frac{1}{2}(M+m_{f})v_{ff}^{2}\\\\v_{ff}=\sqrt{\frac{m_f}{(M+m_{ff})}}\cdot v_{if}$

As we see that $\sqrt{\frac{m_f}{(M+m_{ff})}}$ is less than 1 we can infer that velocity decreases.