Question

A train with mass 1000kg is moving at 15 m/s south. A second train engine with a mass of 500 kg is sitting at rest on the tracks ahead. What is the magnitude of the total momentum of the entire system? Assume that after the trains crash the first train comes to a stop at the point of the crash. How fast does the second train slide? Assume that after the crash the trains stick together and slide as one. How fast to they slide? Assume that after the crash the second train is sliding at 20 m/s south. What is the velocity of the first train?

Answer 1

So first we have to solve for the total momentum of the entire system. We can do this by solving momentum for the first train. The equation for momentum is p=mv, where "p" is momentum.

Total momentum is


`p=(1000kg)*(15m/s) = 15000(kg*m/s)`

When the first train comes to a complete stop, it is an elastic collision. We can use conservation of momentum to solve for the velocity of the second train.


`15000(kg*m/s)=500v v=30m/s`

If they stick completely, then it is an inelastic collision. Here we have to combine the mass of the two trains and solve for the velocity.


`15000(kg*m/s) = (1000+500)v v= 10m/s`

Finally, if the train is 20m/s then what is the velocity of the first train. Just like before, we can solve using conservation of momentum.


`15000=(500kg)(20m/s)+1000v v=5m/s`