Question

You are hitting a nail with a hammer (mass of hammer =1.8lb) the initial velocity of the hammer is 50 mph (73.33 ft/sec). The time of impact is .023 sec. Assuming the nail heads directly in the -j direction, what is the magnitude of the force exerted on the hammer from the nail?

Answer 1

Answer:

The nail exerts a force of 573.88 Pounds on the Hammer in positive j direction.

Explanation:

Since we know that the force is the rate at which the momentum of an object changes.

Mathematically $\overrightarrow{F}=\frac{\Delta \overrightarrow{p}}{\Delta t}$

The momentum of any body is defines as $\overrightarrow{p}=mass\times \overrightarrow{v}$

In the above problem we see that the moumentum of the hammer is reduced to zero in 0.023 seconds thus the force on the hammer is calculated using the above relations as

$\overrightarrow{F}=\frac{m(\overrightarrow{v_{f}}-\overrightarrow{v_{i}})}{\Delta t}$

$\overrightarrow{F}=\frac{m(0-(-73.33)}{0.23}=\frac{1.8\times 73.33}{0.23}=573.88Pounds$