CBSE Class 11 — Notes, Chapters & Practice Quizzes

Chapter 5: Work, Energy and Power

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.

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