A 15-g bullet is shot vertically into an 2-kg block. The block lifts upward 8.0 mm (see the figure). The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. Assume the force on the bullet is constant during penetration and that air resistance is negligible. The initial kinetic energy of the bullet is closest to
A) 21 J
B) 14 J
C) 10 J
D) 0.0012 J
E) 0.16 J

Question

A 15-g bullet is shot vertically into an 2-kg block. The block lifts upward 8.0 mm (see the figure). The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. Assume the force on the bullet is constant during penetration and that air resistance is negligible. The initial kinetic energy of the bullet is closest to 
A) 21 J 
B) 14 J 
C) 10 J 
D) 0.0012 J 
E) 0.16 J

Quizplus · Accepted Answer

The work done on the block by the bullet is given by:
$$W = F\Delta h$$
where $F$ is the force exerted by the bullet on the block and $\Delta h$ is the displacement of the block.

By Newton's third law, the force exerted by the block on the bullet is equal in magnitude and opposite in direction to the force exerted by the bullet on the block. Also, since the bullet comes to rest in the block, the impulse it receives from the force is equal to its initial momentum. Thus, we have:
$$F\Delta t = mv_0$$
where $\Delta t$ is the time interval over which the force is exerted, $m$ is the mass of the bullet, and $v_0$ is the initial velocity of the bullet.

Solving for $F$, we get:
$$F = \frac{mv_0}{\Delta t}$$

Substituting this expression for $F$ into the first equation, we get:
$$W = \frac{mv_0^2}{\Delta t}\Delta h$$

The initial kinetic energy of the bullet is given by:
$$K = \frac{1}{2}mv_0^2$$

Substituting the expression for $W$ from above and the given values, we get:
$$K = \frac{W}{2} = \frac{F\Delta h}{2} = \frac{mv_0^2\Delta h}{2(\Delta t)} = \frac{(0.015\;kg)(600^2\;m^2/s^2)(8.0	imes 10^{-3}\;m)}{2(0.0010\;s)} \approx 21\;J$$

Therefore, the answer is choice A) 21 J.

A 15-G Bullet Is Shot Vertically into an 2-Kg Block