First slide

Work done by Diff type of forces

Question

A block B of mass m is kept on the rough surface of a plank p, also of mass m. The plank is placed on a smooth horizontal floor. The block B is projected to the right with velocity V₀ on the plank. Work done by force of friction on B is W_B and that on P is W_P. Then

Moderate

A

W_p is negative and W_B is positive
B

$|W_{P}| > |W_{B}|$
C

$(W_{B} {+W}_{P})$ is negative
D

$(W_{P} {+W}_{B})$ is positive

Solution

Force of friction on B is f_B and that on P is f_P and they are equal in magnitude. f_B is directed to the left and f_P is directed to the right.
When the block is projected, after initial slipping, B and P start moving with same velocity and the force of friction reduces to zero. During the course of slipping displacements of B and P relative to the ground are d_B and d_P respectively and also $d_{B} {>d}_{P}$ .
Now $W_{B} = \vec{f_{B}} . \vec{d_{B}} = - f_{B} d_{B} = - f . d_{B}$ and $W_{P} = \vec{f_{P}} . \vec{d_{P}} = f_{P} d_{P}$ . Since $d_{B} > d_{P}$ we can write $|W_{B}| > |W_{P}|$ and $(W_{B} + W_{P})$ is negative

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