A body, initial at rest, explodes into two fragments of masses M and 3M having total kinetic energy E. The kinetic energy of the fragment of mass M after the explosion is........

Question

A body, initial at rest, explodes into two fragments of masses M and 3M having total kinetic energy E. The kinetic energy of the fragment of mass M after the explosion is........ ​

resitaana95 · Accepted Answer

The explosion from rest is categorised as inelastic collision. Kinetic energyof the fragment of mass M after the explosion is3E.

Penjelasan dan langkah-langkah:

Assumption:

Assume m₁ and m₂ move in opposite direction after the explosion so that v₁ is positive and v₂ is negative. Initial velocity is zero (at rest), final velocity m₁ is v₁ and final velocity of m₂ is -v₂.

Use inelastic collision formula
Inelastic collision formula:
(m₁+m₂)V = m₁v₁ + m₂(-v₂)
(3M+M)(0) = 3Mv₁ + M(-v₂)
3Mv₁ = Mv₂
v₂ = 3v₁ ...................(1)

Kinetic energy m₁ from the question
Kinetic energy m₁:
$KE = \frac{1}{2}m_{1} v_{1}^{2}$
$E = \frac{1}{2}(3M)v_{1}^{2}$
$E = \frac{3}{2}Mv_{1}^{2}$ ..................(2)