# Problem: A proton with mass 1.67 x 10-27 kg moves in an accelerator with speed of 0.850 c. What is its kinetic energy? (c = 3.00 x 108 m/s).

###### FREE Expert Solution

In this problem, the proton is moving very fast with a speed close to that of light.

In such a case, the moving mass of the proton is expressed as:

$\overline{){\mathbf{M}}{\mathbf{=}}\frac{\mathbf{m}}{\sqrt{\mathbf{1}\mathbf{-}\frac{{\mathbf{v}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}}}}$, where m is the mass of the rest particle, v is the velocity of the particle, and c is the speed of light in a vacuum.

The kinetic energy for a particle with a very high velocity is:

$\overline{){\mathbf{K}}{\mathbf{=}}{\mathbf{\left(}}{\mathbf{M}}{\mathbf{-}}{\mathbf{m}}{\mathbf{\right)}}{{\mathbf{c}}}^{{\mathbf{2}}}}$

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###### Problem Details

A proton with mass 1.67 x 10-27 kg moves in an accelerator with speed of 0.850 c. What is its kinetic energy? (c = 3.00 x 108 m/s).