Question

the momentum of a body increases by 20%.what is the percent increase in its kitnetic energy?

Answer 1

That depends upon whether it is the mass that is increasing by 20% or its velocity. Recall that momentum \(p=mv\) and kinetic energy \(E=\frac{1}{2}mv^2\).

So a 20% increase in mass produces a 20% increase in momentum and a 20% increase in Kinetic energy.

A 20% increase in velocity, results in a 20% increase in momentum, but a 44% increase in Kinetic energy. this is because of the squared term in velocity for kinetic energy. Look at the numbers, let the mass equal 2 kg, and the velocity equal 10 m/s, so that the kinetic energy equals 100 Joules. increases velocity by 20% and it now equals 12 m/s. hence Kinetic energy is now 144 joules, which is a 44% increase in kinetic energy.

In most physical cases, it is the velocity that increases as opposed to mass, but a change in mass is still possible.