Chapter 6, Problem 2P

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?

To determine

Work done on the nail by the hammer.

Answer to Problem 2P

Solution: 5.88 J

Explanation of Solution

The work it can do on the nail is the same as what work was done to lift the hammer.

People push on the hammer to give it more energy.  Since energy is the ability to do work, so more the kinetic energy provided to the hammer, it strikes the nail withmore force and the more work can be done by the hammer.

Given:

Mass of the hammer, $m=1.2\text{ kg}$

Height, $h=0.50\text{ m}$

Formula used:$\begin{array}{l}F=ma\\ W=Fd\end{array}$

Where F is the Force required to lift the hammer

m is the mass of the hammer

a is the acceleration or gravity force $\left(9.8{\text{ m/s}}^{\text{2}}\right)$

Wis the work done on the hammer

dis the height.

Calculation:

Force required lifting the hammer

  $\begin{array}{l}F=ma\\ F=1.2\times 9.8\\ F=11.76\text{ N}\text{---(1)}\end{array}$

Work done by the hammer

  $W=Fd\text{----(2)}$

By using equation (1) and (2)

  $\begin{array}{l}W=11.76\times 0.5\\ W=5.88\text{ J}\end{array}$

People add force because by doing so, the kinetic energy of the hammer head can be increased, and with more kinetic energy, the hammerhead can do more work.

Conclusion:Work done by hammer on the nail is 5.88 J.