Class 11 Physics Chapter 5: Work, Energy and Power

Class 11 Physics Chapter 5: Work, Energy and Power

Work, Energy and Power is an important chapter of Class 11 Physics. It connects force and motion with the idea of energy and provides many useful methods for solving numerical problems.

Chapter Focus: Work, kinetic energy, potential energy, work-energy theorem, conservation of mechanical energy, power and collisions.

In this chapter:

• Work Done by a Force
• Work by Constant Force
• Work by Variable Force
• Energy
• Kinetic Energy
• Work-Energy Theorem
• Potential Energy
• Potential Energy of a Spring
• Conservation of Mechanical Energy
• Power
• Collisions

1. Work Done by a Force

In physics, work is said to be done when a force acting on an object produces displacement. Work is a scalar quantity.

If a constant force F acts on a body and produces displacement s at an angle θ with the force, then:

W = Fs cosθ

The SI unit of work is joule (J).

Positive Work

When the force and displacement are in the same direction, work done is positive.

θ = 0°   ⇒   W = Fs

Negative Work

When force acts opposite to displacement, the work done is negative.

θ = 180°   ⇒   W = -Fs

Zero Work

When the force is perpendicular to displacement, work done is zero.

θ = 90°   ⇒   W = 0

2. Work Done by a Constant Force

For a constant force, the work done depends on the magnitude of force, displacement and the angle between them.

W = F s cosθ

Condition	Work Done
Force and displacement in same direction	Positive
Force and displacement in opposite directions	Negative
Force perpendicular to displacement	Zero

3. Work Done by a Variable Force

When the magnitude or direction of force changes with position, the force is called a variable force. In such cases, work can be found from the area under the force-displacement graph.

W = ∫ F dx

For a variable force, the area between the force-displacement curve and the displacement axis represents the work done.

Exam Tip: Learn to interpret an F-x graph. The area under the graph is often directly used to calculate work.

4. Energy

Energy is the capacity of a body or system to do work. Energy is a scalar quantity and its SI unit is joule (J).

Some common forms of energy are kinetic, potential, thermal, electrical, chemical and nuclear energy.

5. Kinetic Energy

The energy possessed by an object due to its motion is called kinetic energy.

K = ½mv²

where m is the mass and v is the velocity of the object.

Kinetic energy is always non-negative because it depends on the square of velocity.

6. Work-Energy Theorem

The work-energy theorem states that the net work done on a body is equal to the change in its kinetic energy.

W_net = ΔK

Therefore:

W_net = K_f - K_i

or,

W_net = ½mv² - ½mu²

Key idea: Positive net work increases kinetic energy, while negative net work decreases kinetic energy.

7. Potential Energy

Potential energy is the energy associated with the position or configuration of an object in a force field.

Gravitational Potential Energy

Near the Earth's surface, the gravitational potential energy of an object at height h is:

U = mgh

The reference level for potential energy can be chosen conveniently. What matters physically is the change in potential energy.

8. Potential Energy of a Spring

A stretched or compressed spring stores elastic potential energy. For an ideal spring, the restoring force is given by Hooke's law:

F = -kx

The potential energy stored in the spring is:

U = ½kx²

Here, k is the spring constant and x is the extension or compression from the natural position.

9. Conservative and Non-Conservative Forces

A force is called conservative if the work done by it depends only on the initial and final positions, not on the path followed.

Examples include gravitational force and spring force.

Friction is an example of a non-conservative force because the work done by friction depends on the path travelled.

Conservative Force	Non-Conservative Force
Work is path independent.	Work depends on the path.
Work done in a closed path is zero.	Work done in a closed path is generally non-zero.
Example: gravitational force	Example: friction

10. Conservation of Mechanical Energy

Mechanical energy is the sum of kinetic energy and potential energy.

E = K + U

When only conservative forces act on a system, the total mechanical energy remains constant.

K + U = Constant

For an object moving under gravity:

½mv² + mgh = Constant

Important: Mechanical energy remains conserved when non-conservative forces such as friction do not cause energy loss from the mechanical system.

11. Power

Power is the rate at which work is done.

P = W/t

The SI unit of power is watt (W).

Instantaneous Power

Instantaneous power is given by:

P = F · v

For a force making an angle θ with velocity:

P = Fv cosθ

12. Collisions

A collision is an interaction between two or more bodies during which they exert large forces on each other for a short interval of time.

For an isolated system, linear momentum is conserved during a collision.

Total momentum before collision = Total momentum after collision

Elastic Collision

In an elastic collision, both linear momentum and kinetic energy are conserved.

Inelastic Collision

In an inelastic collision, momentum is conserved but kinetic energy is not conserved. Some kinetic energy may be converted into heat, sound or deformation.

Perfectly Inelastic Collision

In a perfectly inelastic collision, the bodies stick together after collision and move with a common velocity.

m₁u₁ + m₂u₂ = (m₁ + m₂)v

Quick Revision

Concept	Formula
Work	W = Fs cosθ
Variable force	W = ∫F dx
Kinetic energy	K = ½mv²
Work-energy theorem	Wnet = ΔK
Gravitational potential energy	U = mgh
Spring potential energy	U = ½kx²
Mechanical energy	E = K + U
Average power	P = W/t
Instantaneous power	P = F · v

Important Questions – Work, Energy and Power

Very Short Answer Questions

1. Define work done by a force.
2. What is the SI unit of work?
3. When is work done by a force zero?
4. Define kinetic energy.
5. Write the expression for kinetic energy.
6. State the work-energy theorem.
7. What is potential energy?
8. Write the expression for gravitational potential energy near Earth's surface.
9. What is the SI unit of power?
10. Define instantaneous power.
11. What is a conservative force?
12. What is an elastic collision?

Short Answer Questions

1. Explain positive, negative and zero work with examples.
2. Why is work done by centripetal force zero in uniform circular motion?
3. Explain the difference between kinetic energy and potential energy.
4. State and explain the work-energy theorem.
5. Why is gravitational force considered conservative?
6. Why is friction called a non-conservative force?
7. Explain the conservation of mechanical energy.
8. Differentiate between average power and instantaneous power.
9. What is the difference between elastic and inelastic collisions?
10. Why is momentum conserved during an isolated collision?

Long Answer Questions

1. Derive the expression for kinetic energy of a moving body.
2. Prove the work-energy theorem for a constant force.
3. Derive the expression for potential energy stored in a stretched spring.
4. Explain the conservation of mechanical energy using the example of a freely falling body.
5. Derive the expression for instantaneous power in terms of force and velocity.
6. Explain elastic, inelastic and perfectly inelastic collisions.

Important MCQs

1. The SI unit of work is:
   (a) Watt   (b) Joule   (c) Newton   (d) Pascal
   Answer: (b) Joule
2. Work done by a force is zero when the angle between force and displacement is:
   (a) 0°   (b) 45°   (c) 90°   (d) 180°
   Answer: (c) 90°
3. The kinetic energy of a body is proportional to:
   (a) v   (b) 1/v   (c) v²   (d) √v
   Answer: (c) v²
4. The work-energy theorem states that net work done is equal to:
   (a) change in momentum
   (b) change in kinetic energy
   (c) change in potential energy
   (d) total energy
   Answer: (b) change in kinetic energy
5. Which of the following is a conservative force?
   (a) Friction   (b) Air resistance   (c) Gravitational force   (d) Viscous force
   Answer: (c) Gravitational force
6. The SI unit of power is:
   (a) Joule   (b) Newton   (c) Watt   (d) kg m/s
   Answer: (c) Watt
7. The potential energy stored in a spring is:
   (a) kx   (b) ½kx²   (c) k/x   (d) 2kx²
   Answer: (b) ½kx²
8. In an elastic collision, which quantities are conserved?
   (a) Only momentum
   (b) Only kinetic energy
   (c) Momentum and kinetic energy
   (d) Neither
   Answer: (c)

Numerical Problems

Numerical 1: Work Done

A force of 20 N moves an object through 5 m in the same direction as the force. Find the work done.

W = Fs
W = 20 × 5 = 100 J

Answer: 100 J

Numerical 2: Work at an Angle

A force of 10 N acts on a body through a displacement of 4 m at an angle of 60°. Find the work done.

W = Fs cos60°
W = 10 × 4 × ½
W = 20 J

Answer: 20 J

Numerical 3: Kinetic Energy

Calculate the kinetic energy of a 2 kg body moving with a speed of 10 m/s.

K = ½mv²
K = ½ × 2 × 10²
K = 100 J

Answer: 100 J

Numerical 4: Potential Energy

Find the gravitational potential energy of a 5 kg object placed at a height of 10 m. Take g = 9.8 m/s².

U = mgh
U = 5 × 9.8 × 10
U = 490 J

Answer: 490 J

Numerical 5: Power

A machine performs 600 J of work in 20 seconds. Find its average power.

P = W/t
P = 600/20
P = 30 W

Answer: 30 W

Numerical 6: Spring Energy

A spring of force constant 200 N/m is compressed by 0.1 m. Find the energy stored in the spring.

U = ½kx²
U = ½ × 200 × (0.1)²
U = 1 J

Answer: 1 J

Assertion and Reason Questions

1. Assertion: Work done by centripetal force in uniform circular motion is zero.
   Reason: Centripetal force is perpendicular to instantaneous displacement.
   Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.
2. Assertion: Kinetic energy can never be negative.
   Reason: Kinetic energy is proportional to the square of velocity.
   Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.
3. Assertion: Mechanical energy remains constant when only conservative forces act.
   Reason: Conservative forces allow conversion between kinetic and potential energy without changing their total.
   Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.
4. Assertion: Momentum is conserved in an isolated collision.
   Reason: The net external force on an isolated system is zero.
   Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Exam Tips

• Remember that work is a scalar quantity.
• Always check the angle between force and displacement before calculating work.
• Practice F-x graph questions because area under the graph represents work.
• Learn the work-energy theorem carefully; it can simplify many numericals.
• Remember the difference between conservative and non-conservative forces.
• For collisions, carefully distinguish between conservation of momentum and conservation of kinetic energy.
• Practice numerical questions based on work, energy, power and spring energy.

Class 11 Physics Chapter 5 FAQs

1. What is Work, Energy and Power in Class 11 Physics?

Work, Energy and Power is Chapter 5 of Class 11 Physics. It deals with work done by forces, kinetic energy, potential energy, work-energy theorem, conservation of energy, power and collisions.

2. What is the formula for work?

For a constant force, work is given by W = Fs cosθ, where θ is the angle between force and displacement.

3. What is kinetic energy?

Kinetic energy is the energy possessed by a body due to its motion. Its formula is K = ½mv².

4. What is the work-energy theorem?

The work-energy theorem states that the net work done on a body is equal to the change in its kinetic energy.

5. What is potential energy?

Potential energy is energy associated with the position or configuration of an object in a force field.

6. What is the formula for gravitational potential energy?

Near Earth's surface, gravitational potential energy is U = mgh.

7. What is the potential energy stored in a spring?

The potential energy stored in an ideal spring is U = ½kx².

8. What is power?

Power is the rate at which work is done. Average power is P = W/t.

9. What is instantaneous power?

Instantaneous power is given by P = F · v.

10. What is an elastic collision?

An elastic collision is one in which both total linear momentum and total kinetic energy are conserved.

11. Is mechanical energy always conserved?

Mechanical energy remains constant when only conservative forces act on the system. Non-conservative forces such as friction can change mechanical energy into other forms.

Chapter 5 Formula Sheet

Topic	Formula
Work	W = Fs cosθ
Variable force	W = ∫F dx
Kinetic energy	K = ½mv²
Work-energy theorem	Wnet = ΔK
Gravitational potential energy	U = mgh
Spring force	F = -kx
Spring potential energy	U = ½kx²
Mechanical energy	E = K + U
Average power	P = W/t
Instantaneous power	P = F · v

One-Minute Revision

• Work: W = Fs cosθ.
• Kinetic energy: K = ½mv².
• Work-energy theorem: W_net = ΔK.
• Potential energy: U = mgh.
• Spring energy: U = ½kx².
• Mechanical energy: E = K + U.
• Average power: P = W/t.
• Instantaneous power: P = F · v.
• Elastic collision: Momentum and kinetic energy are conserved.
• Inelastic collision: Momentum is conserved, but kinetic energy is not conserved.

Conclusion

Class 11 Physics Chapter 5 – Work, Energy and Power is an important chapter for understanding the relationship between force, motion and energy. Students should focus especially on the work-energy theorem, conservation of mechanical energy, power, spring energy and collision-based numericals.

Regular practice of formula-based and conceptual questions can make this chapter much easier for CBSE examinations.