Impacts and Collisions

Impacts and collisions between two bodies are considered in this Section. 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. (Some more advanced problems deal with bodies which coalesce after impact or where a loss in kinetic energy due to impact must be considered).

Sample Problem: Direct impact: Two spheres moving in opposite directions

Two smooth spheres of masses m and 4m collide directly when moving in opposite directions with speeds u and v respectively. (See Fig. 1). The sphere of mass 4m 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:

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