A 100 kg mass, initially at rest, is blown apart into two 50.0 kg pieces. After the blast, the two masses are moving apart with a relative velocity of 100 m/s. The total kinetic energy after the explosion is A) 8.42 × 10⁴ J. B) 1.25 × 10⁵ J. C) 3.62 × 10⁵ J. D) 6.50 × 10⁵ J. E) 1.24 × 10⁶ J.

Question

Quizplus · Accepted Answer

The total kinetic energy after the explosion can be calculated using the formula for kinetic energy, $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity of the object. Since the two masses are equal and moving apart with a relative velocity of 100 m/s, each mass is moving at 50 m/s relative to the center of mass. The kinetic energy for each piece is $KE = \frac{1}{2} \times 50 \times (50)^2 = 62500 J$. Since there are two pieces, the total kinetic energy is $2 \times 62500 J = 125000 J$, or $1.25 \times 10^5 J$.

A 100 Kg Mass, Initially at Rest, Is Blown Apart