Final answer:
The kinetic energy of the 8 kg piece after the explosion is 288 J, which is calculated by conserving momentum and applying the kinetic energy formula. Option D is correct.
Step-by-step explanation:
To calculate the kinetic energy of the 8 kg piece of the bomb after the explosion, we will use the principles of conservation of momentum and the kinetic energy formula. Since the bomb explodes into two pieces and momentum is conserved, the total momentum before and after the explosion must be equal. There is no initial momentum as the bomb is stationary before exploding, so the momentum of the two pieces after explosion must cancel each other out.
The momentum of the 4 kg piece is:
p4kg = m4kg × v4kg = 4 kg × 24 m/s = 96 kg·m/s
To counter this, the momentum of the 8 kg piece must be:
p8kg = -96 kg·m/s
Therefore, the velocity of the 8 kg piece (v8kg) is:
v8kg = p8kg / m8kg = -96 kg·m/s / 8 kg = -12 m/s
The negative sign indicates that the 8 kg piece moves in the opposite direction to the 4 kg piece. Now, using the kinetic energy formula, K = 0.5 × m × v2:
K8kg = 0.5 × 8 kg × (-12 m/s)2 = 0.5 × 8 kg × 144 m2/s2 = 288 J
Therefore, the kinetic energy of the 8 kg piece is 288 J.