Collisions in Two Dimensions
The result of a collision between two objects in a plane cannot be predicted from just the momentum and kinetic energy of the objects before the collision. However, the outcome is constrained to obey conservation of momentum, which is a vector relation. This means that if x and y coordinates are used in the plane, the x and y components of momentum as well as its total magnitude must be the same before and after the collision. The kinetic energy would be the same before and after the collision if the collision were perfectly elastic, but ordinary macroscopic collisions usually have significantly less kinetic energy after the collision because of transfer of energy into other forms. The only way you could have more kinetic energy after the collision would be in the case of some release of energy in the collision, e.g., in a chemical explosion.In the example calculation, the masses, velocities, and angles before the collision are specified. If one of the velocities (magnitude and direction) is specified after the collision, then conservation of momentum determines the other exactly. Examination of the kinetic energy after the collision helps to determine whether or not it is a reasonable outcome.
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