Physics > Work Energy and Power > 1.0 Introduction
Work Energy and Power
1.0 Introduction
2.0 Work done by a constant force
3.0 Spring Force
4.0 Conservative & Non-conservative forces
5.0 Kinetic Energy $(K)$
6.0 Potential energy $\left( {\Delta U} \right)$
6.1 Potential energy $\left( {\Delta U} \right)$ is negative of the work done by conservative forces.
6.2 Types of potential energy
6.3 Law of conservation of mechanical energy
7.0 Work energy theorem
8.0 Power
9.0 Types of equilibrium
10.0 Work done by a distributed mass
1.1 Work done by area under force displacement curve
6.2 Types of potential energy
6.3 Law of conservation of mechanical energy
Mathematically work done is,
$$ W = \int\limits_{{x_1}}^{{x_2}} {\overrightarrow F (x).d\overrightarrow x } $$
The above equation calculates the area under force – displacement curve.
Note: Area under force-displacement curve must be added with a proper sign to obtain work done by the force.
Question 1. Find the work done by a constant force $ F $ in displacing an object by $ 3m $ as shown in the figure.
Solution: From the figure, constant force $F=3N$
Displacement $x$ of the object $=3m$
Work done is the area under the curve,
$$W=3\times3$$ $$W=9J$$
Question 2. A force $F$ acting on a particle varies with displacement $s$ as shown in the figure. Find the work done by the force in displacing a body from $-2m$ to $2m$.
Solution: Work done by the force is equal to the area under the curve.
$$Area = \frac{1}{2} \times ( - 2) \times ( - 2) + \frac{1}{2} \times 2 \times 2$$
Total area under the curve from position $-2m$ to $2m=4$ sq units.
$$Work\ done=4J$$
