Answer to Question #330110 in Physics for Jane

Question #330110

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?

1
Expert's answer
2022-04-18T17:31:33-0400

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


K1=p22m1K2=p22m2K_1 = \dfrac{p^2}{2m_1}\\ K_2 = \dfrac{p^2}{2m_2}

where m1,m2m_1, m_2 are the masses of the first and second fragment respectively, and m2/m1=3/2m_2/m_1 = 3/2.

Let K1=90.0JK_1 = 90.0J. The ratio of kinetic energies is:


K2K1=p22m2/p22m1=m1m2K2=K1m1m2K2=90.0J23=60.0J\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.


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