Work, Energy and Power
Class 11 Physics · Physics Part I · Chapter 5
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Summary
This chapter gives precise physical meanings to work, energy and power, beginning with the scalar (dot) product of vectors, \(\mathbf{A}\cdot\mathbf{B}=AB\cos\theta\). Work done by a constant force is the scalar product of force and displacement, \(W=\mathbf{F}\cdot\mathbf{d}=Fd\cos\theta\), so it can be positive, negative or zero. Kinetic energy is the energy of motion, \(K=\tfrac12 mv^{2}\), and the work-energy theorem states that the net work done on a body equals the change in its kinetic energy. For a variable force, work is the area under the force-displacement graph, found by integration. Potential energy is the energy stored by virtue of position or configuration; gravitational potential energy is \(mgh\) and spring potential energy is \(\tfrac12 kx^{2}\). For conservative forces, the work done is path-independent and total mechanical energy \(K+U\) is conserved. The law of conservation of energy states that energy can be transformed but neither created nor destroyed. Power is the rate of doing work, \(P=\mathrm{d}W/\mathrm{d}t=\mathbf{F}\cdot\mathbf{v}\), with the watt as its SI unit. Collisions are classified as elastic, in which kinetic energy is conserved, and inelastic, in which it is not, while momentum is conserved in both.
The scalar productNotions of work and kinetic energyWork done by a variable forceThe work-energy theoremPotential energy and conservative forcesConservation of mechanical energyPowerCollisions: elastic and inelastic
Key terms
Work
The product of the component of force along the displacement and the magnitude of displacement, \(W=Fd\cos\theta\).
Kinetic energy
The energy possessed by a body due to its motion, \(K=\tfrac12 mv^{2}\).
Work-energy theorem
The principle that the net work done on a body equals the change in its kinetic energy.
Potential energy
Energy stored in a body by virtue of its position or configuration, such as \(mgh\) or \(\tfrac12 kx^{2}\).
Conservative force
A force for which the work done is independent of the path and depends only on the end points, e.g. gravity.
Power
The time rate of doing work, \(P=\mathrm{d}W/\mathrm{d}t=\mathbf{F}\cdot\mathbf{v}\); SI unit watt.
Extra questions & answers
Try one from this chapter
The work done by a constant force is given by: