draw diagrams showing a situation where a bigger train, moving at velocity, vi,

Question

draw diagrams showing a situation where a bigger train, moving at velocity, vi, collides with a smaller train that is not moving. Assume that after the collision the trains strick together. Show separate diagrams for the situation just before the collision and just after the collision. Assume the trains have different masses mbig and msmall. Make sure you identify your isolated system. Write down the moemntum conservation eqation for the scenario in question. Solve for the fianl velocity of the two trains, vf, in terms of vi,mbig and msmall.

Explanation / Answer

Draw a big box to show the system. Keep one small rectangle with wheels inside it and label it m. Draw a big rectangle with wheels and label it M. On this bigger rectangle with wheen also show an arrow moving towards the small rectange and write "u" on top of it. State on the diagram somewhere that M>m. No draw another big box just below this one. and now show two rectangles with wheels sticking to each other.Now draw a smaller arrow on the top but keep the direction same as old one. write "v" on top of it. That's your second situation after the collision.

Now as momentum has to be conserved:

(m*0)+(M*u) = (m+M)*v
v=(M*u)/(M+m)

where M=mbig and m=msmall and u=vi and v=vf

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