The relationship between force and position is shown in the...

The relationship between force and position is shown in the figure given (in one dimensional case) calculate the work done by the force in displacing a body from $x=0 \mathrm{~cm}$ to $\mathrm{x}=5 \mathrm{~cm}$
(A) 30 ergs
(B) 70 ergs
(C) 20 ergs
(D) 60 ergs

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Key Concepts

Work

Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force. In physics, work is defined as the product of the force applied and the displacement in the direction of the force. When the force varies with position, work is calculated by integrating the force over the path of displacement.

Integration to Calculate Work

When a force is not constant over the distance an object moves, the work done by the force is given by the integral of the force with respect to displacement. This integral represents the area under the force versus displacement graph, allowing one to capture the cumulative effect of the varying forces over the given distance.

Force-Displacement Graph

A force-displacement graph plots the magnitude of force as a function of position. The area under this curve between two points of displacement represents the work done by the force over that interval. Understanding this graphical representation is fundamental for solving problems where the force varies with position.

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