There are the 3 spheres in a line, of masses m , m and M. The 2 spheres on the right are slightly seperated and initially at rest, the left sphere is incident with speed Vo. Assuming head on elastic collisions:(adsbygoogle = window.adsbygoogle || []).push({});

a) if M =< m , show that there are two collisions and find all the final velocities

b) if M > m, show that there are three collisions and find all find velocities

if M =< m , there will be two collisions because m will hit m which will hit M and all will continue in the +x direction

if M > m, there will be 3 collisions, as m will hit m which will hit M and bounce back hitting the first m again.

mv1i + mv2i = mv1f + mv2f

mVo + 0 = mv1f + mv2f

Vo = v1f + v2f

v1f = Vo - v2f

v2f = Vo - v1f

and then

mv2i + Mv3i = mv2f + Mv3f

m(Vo - v1f) + 0 = mv2f + Mv3f

I'm getting sortof lost here, is there an easier was to work this into 2 equations

Thanks

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# Homework Help: Show that there are three collisions and find all find velocities

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