**The momentum of a moving object is its mass multiplied by its velocity. The most convenient way to analyse the impact is to use the Principle of Conservation of Linear Momentum: the total momentum of both objects after the collision is equal to the total momentum before collision.**

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Two smooth spheres of masses

*m*and 4*m*collide directly when moving in opposite directions with speeds*u*and*v*respectively. (See Fig. 1). The sphere of mass 4*m*is brought to rest by the impact. Prove that where*e*is the coefficient of restitution. (Note: masses are in kg, speeds are in m/s)

The next step is to identify the motion of the particles before and after the collision and express this in mathematical equations:

We have:

From the Principle of Conservation of Linear Momentum: