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

Step-by-step 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)=(1)/(2) V_(train)` since we are told the velocity of the train goes to half

Hence:

`p_(f)=2m_(train)(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.