What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

Define the scalar product of two vectors.

It is \(\mathbf{A}\cdot\mathbf{B}=AB\cos\theta\), a scalar equal to the product of magnitudes and the cosine of the angle between them.

When is the work done by a force zero?

When the force is perpendicular to the displacement (\(\theta=90^{\circ}\)), or when the displacement is zero.

State the work-energy theorem.

The net work done by all forces acting on a body equals the change in its kinetic energy, \(W_{net}=\Delta K\).

How is work done by a variable force calculated?

It is the area under the force-displacement graph, evaluated as the integral \(W=\int F\,\mathrm{d}x\).

Write the gravitational and spring potential energies.

Gravitational PE near the surface is \(mgh\); the elastic PE of a spring is \(\tfrac12 kx^{2}\).

What is special about a conservative force?

The work done by it is path-independent and depends only on the initial and final positions; mechanical energy is conserved.

State the law of conservation of mechanical energy.

For conservative forces, the sum of kinetic and potential energy of a system remains constant.

Distinguish elastic and inelastic collisions.

In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision momentum is conserved but kinetic energy is not.

What is one electron-volt and one kilowatt-hour?

1 eV \(=1.6\times10^{-19}\) J is the energy gained by an electron across 1 volt; 1 kWh \(=3.6\times10^{6}\) J is the commercial unit of energy.

Work, Energy and Power

Class 11 Physics · Physics Part I · Chapter 5

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CBSE Class 11 · Physics

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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:

Flashcards & interactive practice