The graph above plots the force exerted on a box against the displacement of the box. What is the work done by the force in moving the box from x = 2 to x = 4?

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Solution

Work done is given by $W = F d cos θ$ ,
where $θ =$ angle between force $F$ and displacement $d$ ,
as given that force is against displacement , therefore $θ = 180^{o}$ ,
now work done $W = F d cos 180 = - F \times d$ ,
the work done (product of $F$ and $d$ ) will be the area of the shaded portion because in a F-d graph work done is given by area under force curve and displacement axis ,
therefore $W =$ area of rectangle + area of triangle (shaded portion has a rectangle and a triangle)
$W = 4 \times 2 + 2 \times 2 / 2 = 10 J$ ,
or $W = 10 J$

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