Answer
(a) The block will come to rest after sliding for 20 meters along the rough patch.
(b) The work done by friction is -78.4 J.
Work Step by Step
(a) The work done by friction will be equal in magnitude to the initial potential energy of the block.
$F_f~d = mgh$
$mg~\mu_k~d = mgh$
$d = \frac{h}{\mu_k} = \frac{4.0~m}{0.20}$
$d = 20~m$
The block will come to rest after sliding for 20 meters along the rough patch.
(b) $W_f = -mg~\mu_k~d$
$W_f = -(2.0~kg)(9.80~m/s^2)(0.20)(20~m)$
$W_f = -78.4~J$
The work done by friction is -78.4 J.
