Blog: How far must a 225 kg pile driver fall if it is to do 1.38 x 10^4 J of work?

Work done by gravity (near the surface of the Earth, where gravity is approximately constant) is given by the equation $\displaystyle{W}={m}{g{{h}}}$ , where $\displaystyle{m}$ is the mass of the object, $\displaystyle{g{}}$ is the acceleration of gravity, and $\displaystyle{h}$ is the distance fallen.We know $\displaystyle{g{=}}{9.80}\frac{{m}}{{{s}}^{{2}}}.$ We are given $\displaystyle{m}={225}{k}{g{}}$ and $\displaystyle{W}={1.38}\cdot{{10}}^{{4}}{J}$ . All that remains to do is substitute in and solve...

We know $\displaystyle{g{=}}{9.80}\frac{{m}}{{{s}}^{{2}}}.$ We are given $\displaystyle{m}={225}{k}{g{}}$ and $\displaystyle{W}={1.38}\cdot{{10}}^{{4}}{J}$ . All that remains to do is substitute in and solve for $\displaystyle{h}$ :

$\displaystyle{1.38}\cdot{{10}}^{{4}}{J}={\left({225}{k}{g}\right)}{\left({9.80}\frac{{m}}{{{s}}^{{2}}}\right)}{h}$
$\displaystyle{1.38}\cdot{{10}}^{{4}}{J}={\left({2205}{N}\right)}{h}$
$\displaystyle{6.2585}{m}={h}$

We are given three significant figures, so we should round our answer to three significant figures as well: 6.26 m. The pile driver must fall 6.26 meters in order to do that much work due to gravity.