Question

A train is loaded with coal, doubling its weight and causing it to go at half the speed. What happens to the overall momentum? (Consider the formulas p = mv and )

Answer 1

Answer: It remains the same

Explanation:

The Conservation of Momentum principle establishes that the initial momentum $p_{o}$ must be equal to the final momentum $p_{f}$:

$p_{o}=p_{f}$ (1)

In the case of the train, its initial momentum is:

$p_{o}=m_{train}V_{train}$ (2)

Where $m_{train}$ is the mass of the train and $V_{train}$ is the initial velocity of the train

And, its final momentum is:

$p_{f}=(m_{train}+m_{coal})V_{train+coal}$ (3)

Where:

$m_{train}+m_{coal}=2m_{train}$ since we are told the mass of the train is doubled

$V_{train+coal}=\frac{1}{2} V_{train}$ since we are told the velocity of the train goes to half

Hence:

$p_{f}=2m_{train}\frac{1}{2} V_{train}$ (4)

$p_{f}=m_{train}V_{train}$ (5)

$m_{train}V_{train}=m_{train}V_{train}$ (6)

$p_{o}=p_{f}$

This means the momentum of the train remains the same.