An object, with mass 30 kg and speed 15 m/s relative to an observer, explodes into two pieces, one 4 times as massive as the other; the explosion takes place in deep space. The less massive piece stops relative to the observer. How much kinetic energy is added to the system during the explosion, as measured in the observer's reference frame?

Energy added to the system = 3393.75J

Explanation:

Since one is 4 times larger than the other, thus,

Mass of larger piece = 4/5 x 30 = 24kg

Mass of smaller piece = 1/5 x 30 = 6kg

Now, we know that;

momentum = mass x velocity

Thus,

Initial momentum of system

= 30 kg × 19 m/s = 570 kg.m/s

And,

Momentum of system just after explosion = 24v

This is because only the larger piece is moving.

From conservation of momentum,

Initial momentum = final momentum

Thus,

570 kg.m/s = 24v

v = 570/24 = 23.75 m/s

Thus, initial kinetic energy of system; KE_i = (1/2)mv² = (1/2) x 30 x 15² = 3375J

Final kinetic energy of system; KE_f = (1/2)mv² = (1/2) x 24 x 23.75² = 6768.75J

Thus,Energy added to the system is;

ΔKE = KE_f − KE_i

ΔKE = 6768.75J - 3375J = 3393.75J