The force acting on a particle varies as shown in the figure below. (The x axis

Question

The force acting on a particle varies as shown in the figure below. (The x axis in the graph has its tickmarks marked in increments of 20.00 m.) Find the work done by the force on the particle as it moves across the following distances. (a) from x = 0 m to x = 80.00 m (b) from x = 80.00 m to x = 120.00 m (c) from x = 0 m to x = 120.00 m The work done on the particle by the force F as the particle moves from x = x_i to x = x_f is the area under the curve from x_i to x_f. (a) For x = 0 to x = 80.00 m, W_AC = area of triangle ABC = 1/2 AC times altitude The work done by the force from point A to point C is positive.

Explanation / Answer

The area under the force-distance graph represents the work done. So from x = 0 m to x = 80 m, the work done is the area of the triangle, height 6N base 80 m (8 divisions on the x-axis). Ue 'half base x height'

1)

WD = (1/2) x 80 x 6 = 240 J

2)

WD = (1/2) x (120 - 80) x (-3) = -60 J

3)

WD = (1/2) x 120 x (-3) = -180 J

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