Question

An explosion breaks an object initially at rest into two pieces, one of which has 1.8 times the mass of the other. If 7200 J of kinetic energy were released in the explosion, how much kinetic energy did the heavier piece acquire?

Answer 1

Since the object is ate rest initially and after explosion it is broken into two parts of masses m₁ and m₂ ,

we have, by momentum conservation,   m₁ v₁ = - m₂ v_{2 ...................(1)}

where v₁ is velocity after explosion of mass m₁ and v₂ is velocity after explosion of mass m₂ .

let m₁ > m₂   i.e.,   m₁ = 1.8 m₂ .................(2)

from eqn.(1) and eqn.(2), we get v₂ = - m₁ v₁ / m₂ = -1.8v_{1   .................(3)}

If energy released in the explosion becomes kinetic energy of fragments,

then we have, (1/2)m₁ v₁² + (1/2) m₂ v₂² = 7200

Using eqn.(2) and (3), we get, (1/2) m₁v₁² + (1/2) ( m₁ /1.8 ) ( 1.8 v₁ )² = 7200

[ (1/2) m₁ v₁² ] ( 1 + 1.8 ) = 7200

(1/2) m₁ v₁² = 7200/2.8 2571 J