A plank of mass M and length L is placed at rest on a smooth horizontal surface. A small block of mass m is projected with a velocity `v_0` from the left end of it as shown in figure. The coefficient of friction between the block and the plank is m, and its value is such that the block becomes stationary with respect to the plank before it reaches the other end.

a. Find the time and common velocity when relative sliding between the block and the plank stops.
b. Find the work done by the friction force on the block during the period it slides on the plank. Is the work positive or negative?
c. Calculate the work done on the plank during the same period. Is the work positive or negative?
d. Also, determine the net work done by friction, Is it positive or negative?

Explanation

Displacement of block in `1s`
`s=1/2xx10xx1^2=5m`

The work done by the applied force in the first second,
`W_F=vecF*vecs=F*scostheta=20xx5=100J`
The work done by the weight of th block in the first