Question

An object initially at rest breaks into two pieces as the result of an explosion. One piece has twice the energy of the other piece. What is the ratio of the masses of the two pieces? Which piece has the larger mass?

Answer 1

Given:
E1=E; E2=2E
Solution:
This is inelastic collision. That means mechanical energy is not conserved, thus
start with conservation of momentum:
(initial)0=(after explosion)P1+P2; thus P1=-P2, this means objects moves in opposite directions, with equal momentum (say P).
we need to relate momentum, kinetic energy and masses.
\[p=mv\];
\[E=mv^2/2\] thus \[E=P^2/2m\] thus \[m=P^2/2E\]
thus
for first object:
\[m_1=P^2/2E\]
for second:
\[m_2=P^2/4E\];
\[m_1/m_2=2\]
piece with E has larger mass