Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block $$1$$ and block $$3$$ have mass m each and block $$2$$ has mass M (M$$ $$m). Block $$2$$ and block $$3$$ are initially stationary, while block $$1$$ is initially moving towards block $$2$$ with speed v as shown. Assume that all collisions are head on and perfectly elastic. What value of $$M/m$$ ensures that block $$1$$ and block $$3$$ have the same final speed?

Question

Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block $$1$$ and block $$3$$ have mass m each and block $$2$$ has mass M (M$$ > $$m). Block $$2$$ and block $$3$$ are initially stationary, while block $$1$$ is initially moving towards block $$2$$ with speed v as shown. Assume that all collisions are head on and perfectly elastic. What value of $$M/m$$ ensures that block $$1$$ and block $$3$$ have the same final speed?

Infinity Learn · Accepted Answer

Let $$v1$$, $$v2$$ and $$v3$$ be velocities of blocks $$1$$, $$2$$ and $$3$$ after suffering collision each. $$mv=mv1+Mv2$$ and $$v1$$−$$v2=$$−vSolving, we get $$v1=m$$−$$Mm+M$$<$$0$$∴ m

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