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 `W = m g h` , where `m` is the mass of the object, `g` is the acceleration of gravity, and `h` is the distance fallen.We know `g = 9.80 m/s^2.` We are given `m = 225 kg` and `W = 1.38*10^4 J` . All that remains to do is substitute in and solve...

Work done by gravity (near the surface of the Earth, where gravity is approximately constant) is given by the equation `W = m g h` , where `m` is the mass of the object, `g` is the acceleration of gravity, and `h` is the distance fallen.

We know `g = 9.80 m/s^2.` We are given `m = 225 kg` and `W = 1.38*10^4 J` . All that remains to do is substitute in and solve for` h` :

`1.38*10^4 J = (225 kg)(9.80 m/s^2) h`
`1.38*10^4 J = (2205 N) h`
`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.