A block of mass m is kept on a rough plank which moves with a horizontal acceleration a. If the plank was at rest at `t=0`, and the block does not slide relative to the plank, find the work done by friction on the (a) block, (b) plane, (c) system, (block+plank) during time `t`.

Explanation

a. `W_(f_1)=f_ss` (i)
where `f_s=ma` (ii)
and `s=1/2at^2` (iii)
Using the above equations,


`W_(f_1)=1/2ma^2t^2`
b. `W_(f_2)=-f_ss=-(ma)(1/2at^2)=-1/2ma^2t^2`
c. `W_f=W_(f_1)+W_(f_2)=(f_ss)+(-f_ss)=0`