Question

If there were a speed limit for this train as
it traveled through a city, but not a weight
limit, what mass must be added to the train
to slow it down to 5 m/s while at the same
time keeping the momentum the same as in
the second part?
Answer in units of kg.

Answer 1

Answer on Question #57063, Physics / Other

If there were a speed limit for this train as it traveled through a city, but not a weight limit, what mass must be added to the train to slow it down to $5\mathrm{m/s}$ while at the same time keeping the momentum the same as in the second part?

Answer in units of kg.

Solution:

Momentum is defined to be the mass of an object multiplied by the velocity of the object.

$$p = m v$$

The conservation of momentum states that, within some problem domain, the amount of momentum remains constant.

Thus,

$$p _ {1} = p _ {2}$$ $$m v _ {1} = (m + m _ {x}) v _ {2}$$ $$m v _ {1} = m v _ {2} + m _ {x} v _ {2}$$ $$m _ {x} v _ {2} = m \left(v _ {1} - v _ {2}\right)$$ $$m _ {x} = \frac {m (v _ {1} - v _ {2})}{v _ {2}}$$

where $v_{2} = 5 \, \text{m/s}$,

$m =$ initial mass of train,

$v_{1} =$ velocity of train from the second part of question.

Answer: $m_{x} = \frac{m(v_{1} - v_{2})}{v_{2}}$.