Answer to Question #131537 in Mechanics | Relativity for Rethabile

Question

The kinetic energy of an object of mass, m, moving with a speed “v” is 25J. By what factor will its kinetic energy change if its mass is tripled while the velocity is decreased by one third?

Answer 1

Kinetic energy of an object is described by a formula $T=\frac{mv^2}{2}.$ Initial energy of the given object with mass $m_1$ and velocity $v_1$: $T_1=\frac{m_1v_1^2}{2}=25J.$ After we changed the mass and the velocity, we have:$m_2=3m_1, v_2=\frac{v_1}{3}$. Thus, $T_2=\frac{m_2v_2^2}{2}=\frac{3m_1}{2}(\frac{v_1}{3})^2=\frac{m_1v_1^2}{6}=\frac{T_1}{3}.$ Hence, the kinetic energy will decrase by $\frac{1}{3}.$