Answer:
Energy added to the system = 3393.75J
Step-by-step 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