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Relativistic mechanics kinetic energy

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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:

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.