A hammer

A hammer weighing 500 g hits the nail at a speed of 3 m/s. What is the average force acting on the nail, which penetrates the board to a depth of 5 cm?

Correct result:

F =  45 N

Solution:

$$\begin{gathered} m=500\text{ g}\to \text{ kg}=500\mathrm{/}1000\text{ kg}=0.5\text{ kg } \\ v=3\text{ m/s } \\ s=5\text{ cm}\to \text{ m}=5\mathrm{/}100\text{ m}=0.05\text{ m } \\ E={\displaystyle \frac{1}{2}}\cdot m\cdot v^2={\displaystyle \frac{1}{2}}\cdot 0.5\cdot 3^2={\displaystyle \frac{9}{4}}=2.25\text{ J } \\ E=W=Fs \\ F=E\mathrm{/}s=2.25\mathrm{/}0.05=45\text{ N} \end{gathered}$$

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