An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.6 times the mass of the other.

Question

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 6300 JJ were released in the explosion, how much kinetic energy did each piece acquire?

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Answer 1

Let

m₁, v₁ be the mass and speed of one piece,

m₂, v₂ be the mass and speed of the other piece,

E = 6300 J be the total energy,

E₁ = m₁v₁²/2 be the energy of the first piece,

E₂ = m₂v₂²/2 be the energy of the other piece,

r = m₁/m₂ = 1.6 be the ration between the masses.

Then

m₂ = m₁/r

By conservation of momentum

m₁v₁ = m₂v₂

Therefore we can write

v₂ = m₁v₁/m₂ = rv₁

Therefore

E₂ = (m₁/r)(rv₁)²/2 = rm₁v₁²/2 = rE₁

By conservation of energy

E = E₁ + E₂ = E₁ + rE₁ = E₁(1+r)

Therefore

E₁ = E/(1+r)

Plugging in actual numbers

E₁ = 6300/2.6 = 2423 J

E₂ = E - E₁ = 6300 - 2423 = 3877 J