#### Answer

(a) $47,300~J$ of work must be done to raise the pile driver.
(b) The work done by gravity on the pile driver is $-47,300~J$
(c) The work done by gravity on the pile driver is $47,300~J$

#### Work Step by Step

(a) We can find the change in gravitational potential energy:
$\Delta PE = mgh$
$\Delta PE = (402~kg)(9.80~m/s^2)(12~m)$
$\Delta PE = 47,300~J$
$47,300~J$ of work must be done to raise the pile driver.
(b) The change in gravitational potential energy is $47,300~J$. Therefore, the work done by gravity on the pile driver is $-47,300~J$
(c) As the pile driver falls, the change in gravitational potential energy is $-47,300~J$. Therefore, the work done by gravity on the pile driver is $47,300~J$