A steel

A steel hammer with a weight of 0.5 kg hits the nail at a speed of 3 m/s. How deep the nail penetrates the wood if the hammer acts on the nail with an average force of 50N.

Correct result:

x =  45 mm

Solution:

$$\begin{gathered} m=0.5\text{ kg } \\ v=3\text{ m/s } \\ F=50\text{ N } \\ {E}_1=1\mathrm{/}2\cdot m\cdot v^2=1\mathrm{/}2\cdot 0.5\cdot 3^2={\displaystyle \frac{9}{4}}=2.25\text{ J } \\ {E}_1=F_x \\ {x}_1=E_1\mathrm{/}F=2.25\mathrm{/}50={\displaystyle \frac{9}{200}}=0.045\text{ m } \\ x=1000\cdot x_1=1000\cdot 0.045=45\text{ mm} \end{gathered}$$

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