CBSE Class 11 Physics Revision Notes Chapter 5 Work, Energy and Power

Work, energy and power explain how force transfers energy, changes motion and determines the rate of doing work.

In CBSE Class 11 Physics, these ideas connect force, displacement, kinetic energy, potential energy, springs and collisions.

Work has a precise meaning in physics. A force does work only when it produces displacement with a component along its direction. Energy measures the ability of a body or system to do work, while power measures how quickly work is done.

These CBSE Class 11 Physics Revision Notes Chapter 5 follow the 2026–27 chapter sequence. The notes cover the scalar product, work-energy theorem, mechanical energy, spring energy, power and collisions.

Key Takeaways

• Work: A constant force does work W = Fd cos θ over displacement d.
• Kinetic energy: A body of mass m and speed v has kinetic energy K = 1/2 mv².
• Mechanical energy: K + V remains constant when only conservative forces do work.
• Power: Instantaneous power is P = F·v.

Need help solving work-energy, spring and collision numericals?
Access interactive practice, chapter-wise notes and doubt-solving support on the Extramarks Learning App. Sign Up Free

Access Class 11 Physics Chapter 5 Work, Energy and Power Notes in 30 Minutes

These Work Energy and Power Class 11 Short Notes organise the chapter into linked concepts and formulas.

The same sequence makes these Work Energy and Power Class 11 Notes useful for quick concept revision.

Scalar Product Used in Work and Energy

Work involves force and displacement, which are vector quantities. Their scalar product gives work as a scalar quantity.

Dot Product of Two Vectors

The scalar product or dot product of vectors A and B is:

A·B = AB cos θ

Here, θ is the angle between the vectors.

The scalar product has magnitude but no direction.

Important properties include:

• A·B = B·A
• A·(B + C) = A·B + A·C
• A·A = A²
• A·B = 0 when A and B are perpendicular

For unit vectors:

i·i = j·j = k·k = 1

i·j = j·k = k·i = 0

Scalar Product in Component Form

For:

A = Axi + Ayj + Azk

B = Bxi + Byj + Bzk

The scalar product is:

A·B = AxBx + AyBy + AzBz

This form is useful when force and displacement are given through components.

Work Done by a Constant Force

The work done by a constant force equals the product of displacement and the force component along the displacement.

W = F·d

W = Fd cos θ

Here:

• F = magnitude of force
• d = magnitude of displacement
• θ = angle between force and displacement

Work is a scalar quantity.

Positive, Negative and Zero Work

The sign of work depends on the angle between force and displacement.

Positive work: Gravity does positive work on a falling object.

Negative work: Friction usually does negative work because it opposes motion.

Zero work: The normal reaction does zero work on a body moving horizontally.

A force also does zero work when displacement is zero.

Units and Dimensions of Work

The SI unit of work is joule.

1 J = 1 N m

One joule is the work done when a force of one newton produces one metre displacement along its direction.

The dimensions of work are:

[ML²T⁻²]

Work and energy have the same unit and dimensions.

Kinetic Energy and the Work-Energy Theorem

Kinetic energy depends on mass and speed. The work-energy theorem connects net work with the resulting change in motion.

Kinetic Energy

The kinetic energy of a body is the energy it possesses due to its motion.

K = 1/2 mv²

Here:

• m = mass
• v = speed

Kinetic energy is a scalar quantity.

It can also be written using momentum p:

K = p²/2m

A body moving at twice the speed has four times the kinetic energy.

Work-Energy Theorem for a Constant Force

Consider a body of mass m moving from speed u to v under a constant force.

The kinematic relation is:

v² − u² = 2as

Multiplying by m/2:

1/2 mv² − 1/2 mu² = mas

Since F = ma:

1/2 mv² − 1/2 mu² = Fs

Therefore:

Kf − Ki = W

The work-energy theorem states:

The work done by the net force on a particle equals the change in its kinetic energy.

Wnet = ΔK

Wnet = Kf − Ki

Positive net work increases kinetic energy. Negative net work decreases kinetic energy.

Work Done by a Variable Force

Most forces change with position. A variable force cannot always be treated through W = Fd cos θ over a large displacement.

Force-Displacement Graph

Suppose a force F(x) acts along the x-direction.

For a very small displacement Δx:

ΔW ≈ F(x)Δx

For the complete displacement from xi to xf:

W = ∫ from xi to xf F(x) dx

The work done by a variable force equals the area under its force-displacement graph.

• Area above the x-axis gives positive work.
• Area below the x-axis gives negative work.
• The algebraic sum gives net work.

Work-Energy Theorem for a Variable Force

For one-dimensional motion:

F = ma

F = m(dv/dt)

Since v = dx/dt:

F dx = mv dv

Integrating:

∫ F dx = ∫ mv dv

Therefore:

W = 1/2 mvf² − 1/2 mvi²

Hence:

W = Kf − Ki

The work-energy theorem remains valid for both constant and variable forces.

Potential Energy and Conservative Forces

Potential energy is stored energy associated with the position or configuration of a system.

Gravitational Potential Energy

Near the Earth’s surface, the gravitational potential energy of a body at height h is:

V = mgh

Here:

• m = mass
• g = acceleration due to gravity
• h = height above the chosen reference level

Potential energy depends on the selected zero level. Only changes in potential energy have direct physical significance.

For a body falling through height h:

Loss in potential energy = mgh

This energy appears as kinetic energy when air resistance is neglected.

Conservative and Non-Conservative Forces

A conservative force has the following properties:

• Its work depends only on initial and final positions.
• Its work does not depend on the path followed.
• Its work over a closed path is zero.
• A potential-energy function can be defined for it.

Examples include gravitational force and spring force.

A non-conservative force has path-dependent work.

Friction is a common non-conservative force. It converts mechanical energy into other forms, usually thermal energy.

Force and Potential Energy Relation

For a conservative force in one dimension:

F(x) = −dV/dx

The negative sign shows that the force acts towards decreasing potential energy.

The work done by a conservative force is:

Wc = Vi − Vf

Therefore:

Wc = −ΔV

Conservation of Mechanical Energy

Mechanical energy is the sum of kinetic and potential energy.

E = K + V

The conservation of mechanical energy applies when only conservative forces do work.

Ki + Vi = Kf + Vf

Mechanical Energy During Free Fall

Consider a body released from height H.

At the top:

K = 0

V = mgH

Total energy:

E = mgH

At height h:

K = 1/2 mv²

V = mgh

Therefore:

E = 1/2 mv² + mgh

At the ground:

V = 0

K = 1/2 mvf²

The total remains:

mgH = 1/2 mvf²

Therefore:

vf = √(2gH)

Potential energy decreases while kinetic energy increases by the same amount.

Effect of Non-Conservative Forces

When both conservative and non-conservative forces act:

ΔK = Wc + Wnc

Since:

Wc = −ΔV

We get:

ΔK + ΔV = Wnc

Therefore:

Ef − Ei = Wnc

If friction does negative work, the final mechanical energy is less than the initial mechanical energy.

Potential Energy of a Spring

A spring stores elastic potential energy when stretched or compressed.

Hooke’s Law

For an ideal spring:

Fs = −kx

This is Hooke’s law.

Here:

• Fs = spring force
• k = spring constant
• x = displacement from equilibrium

The negative sign shows that spring force acts opposite to displacement.

The SI unit of k is N m⁻¹.

A spring with a large k is stiffer than a spring with a small k.

Work Done by a Spring

The force varies linearly with displacement.

Fs = −kx

The work done by the spring from xi to xf is:

Ws = ∫ from xi to xf (−kx) dx

Ws = 1/2 kxi² − 1/2 kxf²

For extension from 0 to x:

Ws = −1/2 kx²

The work done by an external force during slow extension is:

Wext = 1/2 kx²

Energy of a Block-Spring System

The potential energy of a spring is:

V = 1/2 kx²

At maximum displacement xm:

K = 0

V = 1/2 kxm²

At equilibrium:

V = 0

K is maximum.

For a frictionless block-spring system:

1/2 mv² + 1/2 kx² = 1/2 kxm²

The kinetic and potential energies vary, but their sum remains constant.

Power and Rate of Energy Transfer

Two machines may do the same work in different times. The machine completing it faster delivers more power.

Average Power

Average power is the work done per unit time.

Pavg = W/Δt

It can also be written as:

Pavg = ΔE/Δt

The SI unit of power is watt.

1 W = 1 J s⁻¹

Instantaneous Power

Instantaneous power is:

P = dW/dt

Since:

dW = F·dr

Therefore:

P = F·(dr/dt)

P = F·v

For force and velocity in the same direction:

P = Fv

If the angle between F and v is θ:

P = Fv cos θ

Watt, Kilowatt-Hour and Horsepower

Common power units include:

1 kilowatt = 1000 W

1 horsepower ≈ 746 W

A kilowatt-hour is a unit of energy:

1 kWh = 3.6 × 10⁶ J

It is not a unit of power.

These relations are important Work Energy and Power Formulas for machine and electricity-based numericals.

Collisions in Class 11 Physics Chapter 5

A collision is a short interaction during which bodies exert large forces on each other.

The forces during collision are internal to the system. If external force is negligible, total momentum remains conserved.

Elastic and Inelastic Collisions

An elastic collision conserves both:

• Total linear momentum
• Total kinetic energy

An inelastic collision conserves momentum but not total kinetic energy.

In a completely inelastic collision, the bodies stick together after impact.

One-Dimensional Elastic Collision

Consider masses m1 and m2 with initial velocities u1 and u2. Their final velocities are v1 and v2.

Momentum conservation gives:

m1u1 + m2u2 = m1v1 + m2v2

Kinetic-energy conservation gives:

1/2 m1u1² + 1/2 m2u2² = 1/2 m1v1² + 1/2 m2v2²

For a one-dimensional elastic collision:

u1 − u2 = −(v1 − v2)

Therefore:

Relative speed of approach = Relative speed of separation

The final velocities are:

v1 = [(m1 − m2)u1 + 2m2u2]/(m1 + m2)

v2 = [2m1u1 + (m2 − m1)u2]/(m1 + m2)

If the second body is initially at rest:

u2 = 0

Then:

v1 = [(m1 − m2)/(m1 + m2)]u1

v2 = [2m1/(m1 + m2)]u1

Completely Inelastic Collision

Suppose two bodies stick together and move with common velocity v.

Momentum conservation gives:

m1u1 + m2u2 = (m1 + m2)v

Therefore:

v = (m1u1 + m2u2)/(m1 + m2)

Kinetic energy is not conserved in this inelastic collision.

The loss in kinetic energy appears as heat, sound or deformation.

Work, Energy and Power Formula Sheet

These formulas make the Class 11 Work Energy and Power Notes easier to revise before solving numericals.

These Work Power Energy Class 11 Notes link every formula with its physical meaning rather than treating them as isolated equations.

Important Differences for Quick Revision

Useful Links for Class 11 Physics