Physics
The graph given below shows a force-displacement graph. What is the total work done by force on the body in displacement from x = 0 to x = 6 m ?
- 20 J
- 40 J
- 60 J
- 80 J
Work, Energy & Power
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Answer
40 J
Reason — The work done by a force can be determined from the area under the force–displacement graph.
From x = 0 m to x = 2 m, the graph forms a triangle rising from 0 to 10 N and its area is given by,
Area = Work done = × 2 × 10 = 10 J.From x = 2 m to x = 4 m, the force is constant at 10 N, forming a rectangle whose area is given by,
Area = Work done = 2 × 10 = 20 J.From x = 4 m to x = 6 m, the graph again forms a triangle decreasing from 10 N to 0 N and its area is given by,
Area = Work done = × 2 × 10 = 10 J.
Adding these areas, the total work done is calculated :
Total work done = 10 + 20 + 10 = 40 J
Hence, 40 J is the total work done by the force on the body in displacement from x = 0 m to x = 6 m.
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