# Relativistic mechanics kinetic energy

1. State the conservation of momentum and kinetic energy in collisions in classical mechanics and relativistic mechanics

2. derive the relativistic kinetic energy.

3. Derive the total relativistic force as a function of momentum.

please show the solutions in detail, stepwise.

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• In Newtonian mechanics momentum is always conserved, while total energy is conserved if and only if the all forces (internal and external) in the system are conservative.

• In relativistic mechanics both momentum and total energy are always conserved.

In the stationary (lab) frame we have a particle that moves with velocity

We start with the basic postulate of special relativity that the four-line element is invariant at any system:

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#### Solution Summary

The expert states the conservation of momentum and kinetic energy in collision in classical mechanics and relativistic mechanics. The relativistic kinetic energy is derived.