Chapter 7, Problem 16P

(a)

To determine

The impulse given to the nail.

Answer to Problem 16P

  $J=-102\text{ kg}\text{.m/s}$

Explanation of Solution

Given:

Mass of the hammer is $m=12\text{ kg}$

The velocity with which the hammer strikes the nail is $u=8.5\text{ m/s}$

Final velocity of the hammer is $v=0\text{ m/s}$

Formula used:

The impulse $\left(J\right)$ given to a body is the change in its momentum. That is,

  $J=p_f-p_i=mv-mu=m\left(v-u\right)$  $\left(1\right)$

Where, $p_i$ and $p_f$ are initial and final momentum of the hammer.

Calculation:

Substituting the numerical values in equation $\left(1\right)$ ,

  $J=12\text{ kg}\left(0\text{ m/s - }8.5\text{ m/s }\right)=-102\text{ kg}\text{.m/s}$

Negative sign indicates that the impulse acting on the nail is in the direction opposite to the direction of motion of the hammer.

Conclusion:

The impulse given to the nail is $-102\text{ kg}\text{.m/s}$ .

(b)

To determine

The average force acting on the nail.

Answer to Problem 16P

  $F=12750\text{ N}$

Explanation of Solution

Given:

The time interval at which the hammer comes to rest is $t=8.0\text{ ms = 0}\text{.008 s}$

Formula used:

The average force $\left(F\right)$ acting on the nail can be calculated using the equation,

  $F=\frac{J}{t}$$\left(2\right)$

Where, $J$ is the magnitude of impulse given to the nail, $J=102\text{ kg}\text{.m/s}$

Calculation:

Substituting the numerical values in equation $\left(2\right)$ ,

  $F=\frac{102\text{ kg}\text{.m/s}}{\text{0}\text{.008 s}}=12750{\text{ kgm/s}}^2=12750\text{ N}$

Conclusion:

The average force acting on the nail is $12750\text{ N}$ .