What change should be expected in the velocity of a body to maintain the same kinetic energy, if its mass is increased sixteen times? How?

Tuesday, February 12, 2013

What change should be expected in the velocity of a body to maintain the same kinetic energy, if its mass is increased sixteen times? How?

Hello!

Kinetic energy is that part of full energy which a body has due to its motion. The formula for kinetic energy is $\displaystyle{E}_{{k}}=\frac{{{m}{{V}}^{{2}}}}{{2}},$ where $\displaystyle{m}$ is the mass and $\displaystyle{V}$ is the speed (regardless of direction).

Usually a body remains the same during its motion, and the mass of the body also remains the same. In our problem, the mass of the body is supposed to increase $\displaystyle{16}$ times, roughly speaking some other bodies will join our initial body.

In such a case, its kinetic energy becomes $\displaystyle{E}'_{{k}}=\frac{{{\left({16}{m}\right)}{{V}}^{{2}}}}{{2}}={16}{E}_{{k}}.$ To compensate this change by a speed change, we have to reduce $\displaystyle{{V}}^{{2}}$ $\displaystyle{16}$ times, which means to reduce $\displaystyle{V}$ $\displaystyle\sqrt{{{16}}}={4}$ times.