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?

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

Kinetic energy is that part of full energy which a body has due to its motion. The formula for kinetic energy is `E_k = (m V^2)/2,` where `m` is the mass and `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 `16` times, roughly speaking some other bodies will join our initial body.

In such a case, its kinetic energy becomes `E'_k = ((16 m) V^2)/2 = 16 E_k.` To compensate this change by a speed change, we have to reduce `V^2`  `16` times, which means to reduce `V`  `sqrt(16)=4` times.

This is the answer: body's speed must be reduced 4 times to maintain the same kinetic energy.