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Science Grade XI Physics

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Chapter 5: Work, Energy and Power

Grade 11 Science | Chapter 5

Work, Energy and Power

Work transfers energy, and energy is conserved. This chapter defines work, kinetic and potential energy, proves the work energy theorem, and introduces power.

Core Concepts

Key Principles

Worked Examples

Practice Sets

Contents

Introduction: Work and Energy

Work Done by a Force

Kinetic Energy and the Work Energy Theorem

Potential Energy

Conservation of Mechanical Energy

Power

Key Reasoning (Principles)

Worked Examples (10)

Practice Sets A to D

10.

Summary and Exam Quick-Check

1. Introduction: Work and Energy

In physics, work is done when a force moves its point of application along the direction of the force, and doing work transfers energy. Energy is the capacity to do work; it takes many forms and can change between them, but the total is conserved. This chapter makes these ideas precise and proves the central result linking work to the change in kinetic energy.

Core idea

Work transfers energy: W = F s cosθ. The net work on a body equals its change in kinetic energy, and when only conservative forces act, the total mechanical energy stays constant.

2. Work Done by a Force

The work done by a constant force F when its point of application moves a displacement s is W = F s cosθ, where θ is the angle between the force and the displacement. Work is a scalar measured in joules. When the force is along the motion the work is positive; at right angles it is zero; and opposite to the motion it is negative, as with friction.

Diagram 1 – Work Done by a Force

A force at an angle to the displacement, with work equal to F s cosine of the angle

Fig 1. Only the component of the force along the displacement does work, so W equals F times s times the cosine of the angle between them.

3. Kinetic Energy and the Work Energy Theorem

Kinetic energy is the energy of motion, KE = ½ m v². The work energy theorem states that the net work done on a body equals its change in kinetic energy: W = ½ m v² minus ½ m u². It follows directly from the equation v² = u² + 2as combined with F = ma, and it lets us solve many problems without tracking the detailed motion.

4. Potential Energy

Potential energy is stored energy due to position or configuration. The gravitational potential energy of a mass raised through a height h is PE = m g h. The elastic potential energy stored in a stretched spring of stiffness k and extension x is ½ k x². Forces such as gravity and the spring force, for which the work done does not depend on the path, are called conservative.

5. Conservation of Mechanical Energy

When only conservative forces act, the total mechanical energy, the sum of kinetic and potential energy, stays constant. As a ball falls, its potential energy steadily converts into kinetic energy while the sum remains the same. Where non-conservative forces such as friction act, some mechanical energy is converted into heat, but the total energy of all forms is still conserved.

Diagram 2 – Conservation of Mechanical Energy

A falling ball showing potential energy converting to kinetic energy with constant total

Fig 2. As the ball falls, potential energy turns into kinetic energy, but their sum stays constant when only gravity acts.

6. Power

Power is the rate of doing work, or of transferring energy, P = work ÷ time. Its SI unit is the watt (W), one joule per second. For a force moving an object at velocity v, the instantaneous power is P = F v. Two machines may do the same work, but the more powerful one does it in less time.

7. Key Reasoning (Principles)

Principle 1: Only the along-motion component does work

Work is F s cosθ, so a force at right angles to the motion does no work, which is why circular motion at steady speed involves no work by the centripetal force.

Principle 2: Net work equals the change in kinetic energy

The work energy theorem, W = ½ m v² minus ½ m u², links force and motion through energy, often avoiding the need for the full equations of motion.

Principle 3: Mechanical energy is conserved for conservative forces

When only conservative forces act, kinetic and potential energy trade off while their sum stays constant; friction converts some of it to heat.

8. Worked Examples

Example 1

Q: A 10 N force moves a body 5 m along its direction. Find the work done.

▶ Show Solution

W = F s cos0 = 10 × 5 × 1.

= 50 J.

Answer: 50 J.

Example 2

Q: Find the work done by a 20 N force over 4 m at 60 degrees. (cos60 = 0.5)

▶ Show Solution

W = F s cosθ = 20 × 4 × 0.5.

= 40 J.

Answer: 40 J.

Example 3

Q: Find the kinetic energy of a 2 kg body moving at 5 m/s.

▶ Show Solution

KE = ½ m v² = ½ × 2 × 25.

= 25 J.

Answer: 25 J.

Example 4

Q: A 4 kg body speeds up from 2 m/s to 4 m/s. Find the work done on it.

▶ Show Solution

W = ½ m (v² minus u²) = ½ × 4 × (16 minus 4).

= 24 J.

Answer: 24 J.

Example 5

Q: Find the potential energy of a 5 kg body raised 4 m (g = 10 m/s²).

▶ Show Solution

PE = m g h = 5 × 10 × 4.

= 200 J.

Answer: 200 J.

Example 6

Q: A spring of stiffness 200 N/m is stretched 0.1 m. Find the energy stored.

▶ Show Solution

E = ½ k x² = ½ × 200 × 0.01.

= 1 J.

Answer: 1 J.

Example 7

Q: A machine does 600 J of work in 30 s. Find its power.

▶ Show Solution

P = work ÷ time = 600 ÷ 30.

= 20 W.

Answer: 20 W.

Example 8

Q: A force of 50 N moves a body at 4 m/s. Find the power.

▶ Show Solution

P = F v = 50 × 4.

= 200 W.

Answer: 200 W.

Example 9

Q: A 1 kg ball is dropped from 5 m. Find its speed just before landing (g = 10 m/s²).

▶ Show Solution

By conservation, ½ m v² = m g h, so v² = 2gh = 100.

v = 10 m/s.

Answer: 10 m/s.

Example 10

Q: How much work is done by gravity on a body moving horizontally?

▶ Show Solution

Gravity is at right angles to a horizontal displacement, so cos90 = 0.

Work done = 0.

Answer: Zero.

9. Practice Sets A to D

Set A – Multiple Choice (Basic)

1. The SI unit of work is the: (a) newton (b) watt (c) joule (d) pascal

2. Kinetic energy is given by: (a) mgh (b) ½ m v² (c) Fs (d) mv

3. The work energy theorem says net work equals the change in: (a) momentum (b) kinetic energy (c) power (d) force

4. Power is the rate of doing: (a) force (b) work (c) distance (d) mass

5. A force at 90 degrees to the motion does work equal to: (a) Fs (b) zero (c) maximum (d) negative

▶ Reveal Answers

1. (c) joule.

2. (b) ½ m v².

3. (b) kinetic energy.

4. (b) work.

5. (b) zero.

Set B – Short Answer (Understanding)

1. Define work and give its unit.

2. State the work energy theorem.

3. What is a conservative force?

4. State the law of conservation of mechanical energy.

5. Write the relation between power, force and velocity.

▶ Reveal Answers

1. Work is force times displacement along the force, W = F s cosθ, measured in joules.

2. The net work done on a body equals its change in kinetic energy.

3. A force for which the work done does not depend on the path taken, such as gravity.

4. When only conservative forces act, the total mechanical energy stays constant.

5. P = F v, power equals force times velocity.

Set C – Application and Reasoning

1. Find the work done by a 15 N force over 6 m along its direction.

2. Find the kinetic energy of a 3 kg body at 4 m/s.

3. Find the potential energy of a 2 kg body at 10 m (g = 10 m/s²).

4. A motor does 900 J in 45 s. Find its power.

5. Why does the centripetal force do no work in circular motion?

▶ Reveal Answers

1. W = 15 × 6 = 90 J.

2. KE = ½ × 3 × 16 = 24 J.

3. PE = 2 × 10 × 10 = 200 J.

4. P = 900 ÷ 45 = 20 W.

5. Because it is always at right angles to the velocity, so cos90 = 0 and no work is done.

Set D – Higher Order (Challenge)

1. Derive the work energy theorem from F = ma and v² = u² + 2as.

2. A 2 kg body is raised 5 m then dropped (g = 10 m/s²). Find its speed on return to the start.

3. A pump raises 100 kg of water through 10 m in 50 s (g = 10 m/s²). Find the power.

4. Explain why kinetic energy quadruples when speed doubles.

5. A 1000 kg car at 20 m/s brakes to rest. Find the work done by the brakes.

▶ Reveal Answers

1. Multiply F = ma by s: Fs = mas; using as = (v² minus u²) ÷ 2 gives Fs = ½ m v² minus ½ m u², the change in kinetic energy.

2. By conservation, the speed on return equals v² = 2gh = 100, so v = 10 m/s.

3. Work = mgh = 100 × 10 × 10 = 10000 J; power = 10000 ÷ 50 = 200 W.

4. Because KE = ½ m v² depends on the square of the speed, so doubling v multiplies energy by four.

5. Work = change in kinetic energy = 0 minus ½ × 1000 × 400 = minus 200000 J, so the brakes do 200000 J of work.

Chapter Summary

Work

W = F s cosθ, in joules; zero at right angles, negative when opposing motion.

Kinetic Energy

KE = ½ m v², the energy of motion.

Work Energy Theorem

Net work equals the change in kinetic energy.

Potential Energy

mgh for gravity, ½ k x² for a spring.

Conservation

Total mechanical energy is constant for conservative forces.

Power

Rate of doing work, P = work ÷ time = F v, in watts.

Quantity

Unit

Symbol

Work and energy

joule

Power

watt

Kinetic energy

½ m v²

8-Point Exam Quick-Check

Work W = F s cos(angle), measured in joules.

A force at right angles to the motion does no work.

Kinetic energy = half m v squared.

Work energy theorem: net work = change in kinetic energy.

Gravitational PE = mgh; spring PE = half k x squared.

Mechanical energy is conserved when only conservative forces act.

Power = work divided by time = F v, in watts.

Doubling the speed quadruples the kinetic energy.

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Class 11 Physics Chapter 5: Work, Energy and Power, Complete Notes and Practice

This revision guide follows the current NCERT Class 11 Physics syllabus and develops work and energy, covering work done by a force, kinetic energy and the work energy theorem, gravitational and elastic potential energy, the conservation of mechanical energy, and power, with two diagrams, ten worked examples and graded practice. Visit SchoolRevise.com to revise, practise and excel.