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Physics momentum/energy question?
A body of mass M explodes into two pieces. One piece has twice the mass of the other. What is the ratio of the kinetic energy of the small piece to that of the larger one? Please explain the answer.
1 Answer
- ?Lv 76 years ago
The body of mass M is supposed to be at rest before it explodes. Then its momentum was zero. Therefore, given that only internal forces are at work, the total momentum must be conserved. If the two pieces have mass M/3 and 2M/3 as the exercise states, then for total momentum to be zero after the explosion we must have for the velocities v and u of he two pieces:
M/3 v + 2M/3 u = 0
This means that
u = -(M/3 v) / (2M/3) = -v/2
The ratio of kinetic energies is
1/2 (M/3) v^2 / ( 1/2 (2M/3) u^2)
= (1/6 Mv^2)/(1/3 M (-v/2)^2)
= (1/6) / ( 1/12)
= 2
