(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?

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.

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.