Answer to Question #330110 in Physics for Jane

Question

An 8.00 kg shell at rest explodes in two fragments, with mass ratio of 3:2. If the lighter fragment

gains 90.0 3 of kinetic energy from the explosion, how much kinetic energy does the heavier fragment gain?

Answer 1

According to the momentum conservation law, the momentum $p$ of each fragment is the same. By definition, the kinetic energies of them is given as follows:

$$K_1 = \dfrac{p^2}{2m_1}\\ K_2 = \dfrac{p^2}{2m_2}$$

where $m_1, m_2$ are the masses of the first and second fragment respectively, and $m_2/m_1 = 3/2$.

Let $K_1 = 90.0J$. The ratio of kinetic energies is:

$$\dfrac{K_2}{K_1} = \dfrac{p^2}{2m_2} /\dfrac{p^2}{2m_1} = \dfrac{m_1}{m_2}\\ K_2 = K_1\dfrac{m_1}{m_2}\\ K_2 = 90.0J\cdot \dfrac{2}{3} = 60.0J$$

Answer. 60.0J.