Question

(I) The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.50 m. What is the maximum amount of work it could do on the nail? Why do people not just “let it fall” but add their own force to the hammer as it falls?

Short answer

The maximum amount of work obtained is 5.88 J, and people add their own force to impart additional impact energy to get the required output.

Step-by-step solution

Determine the maximum amount of work the hammer did on the nail

In this problem, the maximum work is done by gravity. The directions of force and displacement are downward as the hammer falls on the nail. So, the angle between force and displacement vectors is zero.

Given data:

The mass of the head of the hammer is\(m = 1.2\;{\rm{kg}}\).

The height is\(h = 0.5\;{\rm{m}}\).

The relation of work done is given by:

\(\begin{aligned}W &= F \cdot h\cos \theta \\W &= mgh\end{aligned}\)

Here, g is the gravitational acceleration and h is the distance traveled by the hammer.

Determine the force exerted by the person on the hammer

On plugging the values in the above relation, you get:

\(\begin{aligned}W &= \left( {1.2\;{\rm{kg}}} \right)\left( {9.8\;{\rm{m/}}{{\rm{s}}^2}} \right)\left( {0.5\;{\rm{m}}} \right)\\W &= 5.88\;{\rm{J}}\end{aligned}\)

The obtained amount of work is small, that is,\(W = 5.88\;{\rm{J}}\). When a person adds a greater amount of force to the hammer during the drop, the hammer will have higher impact energy to transfer to the nail and get the required job done.

Thus, \(W = 5.88\;{\rm{J}}\) is the required work done.