A 120 kg mass, initially at rest, is blown apart into an 80 kg piece and a 40 kg piece. After the blast, the two masses are moving apart with a relative velocity of 60 m/s. The total kinetic energy after the explosion is
A) 21 kJ.
B) 35 kJ.
C) 48 kJ.
D) 56 kJ.
E) 82 kJ.

Question

Quizplus · Accepted Answer

From conservation of momentum:

$0 = m_1v_1 + m_2v_2$

where $m_1$ = 80 kg, $m_2$ = 40 kg, and $v_2$ = 60 m/s.

Solving for $v_1$, we get:

$v_1 = -\frac{m_2}{m_1}v_2 = -\frac{40}{80}(60) = -30$ m/s

The total initial kinetic energy was zero since the mass was at rest.

The final kinetic energy can be found using:

$K = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2$

Plugging in the values, we get:

$K = \frac{1}{2}(80)(-30)^2 + \frac{1}{2}(40)(60)^2 = 48$ kJ.

Therefore, the answer is choice C.

A 120 Kg Mass, Initially at Rest, Is Blown Apart