An internal explosion breaks an object initially at rest into two pieces, one of which has 1.6 times the mass of the other. If 5900J is released in the explosion, how much kinetic energy does each piece acquire?

The pieces will fly off in opposite directions to conserve momentum so:

m₁v₁ = m₂v₂

m₁v₁ = 1.6m₁v₂

v₂ = v₁/1.6

Ratios of K. E = m₁ (v₁) ²/m₂ (v₂) ²

= m₁ (v₁) ² / 1.6m₁ (v₁/1.6) ²

= 1.6

K. E₁ = 1.6K. E₂

5900 = K. E₁ + K. E₂

5900 = 1.6K. E₂ + K. E₂

K. E₂ = 2270 J for larger piece

K. E₁ = 3200 J for smaller piece