Question

A block of weight $100N$ is slowly side up on a smooth incline of inclination ${37}^{\circ }$ by a person. Calculate the work done by the person in moving the block through a distance of $2.0m$, if the driving force is (a) parallel to the incline and (b) in the horizontal direction.

Answer 1

Work energy theorem states that -

Work done by all forces is equal to change in kinetic energy

In case 1

work done by force $F$ + work done by $gravity=$ change in kinetic energy

Here it should be noted that change in kinetic energy$=0$ (as block is moved slowly)

$⟹$ work done by force $F$ + work done by $gravity=0$

$⟹$ work done by force $F=-$ work done by $gravity$

Now work done by $gravity=-100\sin 37\times 2=-120J$

($Note:$ work done by $gravity$ is negative because displacement is opposite to direction of gravitational force )

$⟹$ work done by$F=-(-120J)=120J$

In case 2

Work done by force $F+$ work done by $gravity=$ change in kinetic energy$=0$

$⟹$ work done by force $F=-$ work done by gravity

Work done by $gravity=-100\sin 37\times 2=-120J$

$⟹$ work done by force $F=-(-120J)=120J$

In both cases woke done will be $120J$