Question

An explosion breaks an object into two pieces, one of which has 3.80 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire?

Answer 1

let m1 = m

m2 = 3.8*m

momentum gained by m1 in one direction = momentun gained m2 in the opposite direction.

m1*v1 = m2*v2

v1/v2 = m2/m1

v1/v2 = 3.8

Energy released = KE1 + KE2

7500 = KE1 + KE2 ----------(2)

KE2/KE1 = (1/2)*m2*v2^2/((1/2)*m2*v1^2)

KE2/KE1 = 3.8*(v2/v1)^2

KE2/KE1 = 3.8*(1/3.8)^2

KE2/KE1 = 1/3.8 <<<<<<<<<<------ (2)

on solving the above two equations

KE1 = 5938 J <<<<<<<<------Answer

KE2 = 1563 J <<<<<<<<------Answer