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# Newton's laws of motion: Collision

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An object at rest on a frictionless surface is struck by another object. Is it possible for both objects to be at rest after the collision? Explain using the principle of conservation of momentum.

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An object at rest on a frictionless surface is struck by another object. Is it possible for both objects to be at rest after the collision? Explain using the principle of conservation of momentum.

Law of conservation of linear momentum states that if there is no external force acting on a system its linear momentum remains conserved.

Now in our problem the surface is frictionless and hence the force acting on the objects are their weights and the normal reactions (normal force) of the surface. Both are vertical, equal and balancing such that net force on the system in vertical direction is zero.

There is no tangential external force on the system of the two objects and hence according to the law of conservation of momentum the momentum of the system will remain unchanged.

As one object is at rest its momentum is zero and the other is moving and have some momentum. The resultant momentum of the system can not be zero. If both objects after collision comes to rest, the momentum of the system will become zero which violets the law of conservation of momentum and hence not possible.

Actually the object at rest not allows the moving object through it and applies a force to stop it. This force decreases the velocity of the moving object and it may come to rest. But a reaction force will be applied on the second object by the first and it will get accelerated and hence can not remain at rest.

The force acting on the two objects are action and reaction forces and are internal forces of the system.

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