Question

projectiles that strike objects are good examples of inelastic collisions. a 0.1 kg nail driven by a gas powered nail driver collides in an inelastic collision with a 10 kg block of wood at rest. the total momentum of the system after the collision is 4.8 kg·m/s. round your answers to two significant digits. the velocity of the nail and block after the collision is calculated to be m/s. the expected velocity of the nail prior to the collision is m/s.

Explanation:

Step1: Calculate velocity after collision

Use formula $p = mv$, where $p$ is momentum, $m$ is mass and $v$ is velocity. Total mass after collision $m_{total}=0.1 + 10=10.1$ kg and $p = 4.8$ kg - m/s. So $v=\frac{p}{m_{total}}$.
$v=\frac{4.8}{10.1}\approx0.48$ m/s

Step2: Calculate velocity of nail before collision

Before collision, momentum of wood is 0 as it is at rest. Let velocity of nail before collision be $v_1$. Using conservation of momentum $p_{before}=p_{after}$. So $m_{nail}v_1=p_{after}$. Given $m_{nail}=0.1$ kg and $p_{after} = 4.8$ kg - m/s. Then $v_1=\frac{p_{after}}{m_{nail}}$.
$v_1=\frac{4.8}{0.1}=48$ m/s

Answer:

The velocity of the nail and block after the collision is 0.48 m/s.
The expected velocity of the nail prior to the collision is 48 m/s.