JEE · Physics

Work, Energy and Power

Decide whether force, energy, power, or momentum is the cleanest model for a mechanics problem, and use it with the correct system boundary.

Subject: Physics
Syllabus unit: Work, Energy and Power
Updated: 8 September 2026

Mapped to JEE Main 2026 and JEE Advanced 2026
Formulas carry their conditions
No invented weightage, question counts or trend percentages

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In short

Work transfers energy through force acting over displacement. The net work on a particle changes its kinetic energy. Mechanical energy stays constant only when the chosen system has no relevant non-conservative transfer. Power measures how fast work is done or energy is transferred.

The fastest solution is rarely the one with the most formulas. Start by choosing the system, listing initial and final states, and deciding whether the unknown depends on path or only on state.

Syllabus mapping

Syllabus mapping
Unit	Topics
Work, Energy and Power	Work by constant and variable force, Kinetic and potential energies, Work-energy theorem, Power, Spring potential energy, Mechanical-energy conservation, Conservative and non-conservative forces, Vertical-circle motion, Elastic and inelastic collisions in one and two dimensions, Conservation of linear momentum, Impulse

Unit
Work, Energy and Power
Topics
Work by constant and variable force, Kinetic and potential energies, Work-energy theorem, Power, Spring potential energy, Mechanical-energy conservation, Conservative and non-conservative forces, Vertical-circle motion, Elastic and inelastic collisions in one and two dimensions, Conservation of linear momentum, Impulse

What this chapter contains and why it matters

What this chapter contains and why it matters
Question	Direct answer
What is the chapter about?	How work, kinetic energy, potential energy, power, and momentum describe energy transfer and conservation in mechanics, and which model to pick first.
What is the central method choice?	Choose the system boundary, decide whether the unknown depends on path or only on state, and select work-energy, energy conservation, power, or momentum and impulse accordingly.
Where do most mistakes begin?	Confusing negative work on one body with total energy loss, applying conservation where non-conservative work is present, and assuming kinetic energy is conserved in every collision.
What should come before this chapter?	Vector resolution, free-body diagrams, force-position graphs, Newton's laws, and the distinction between velocity and speed.
What comes after it?	Rotational Motion extends energy and momentum ideas to rigid bodies, and Gravitation and Simple Harmonic Motion apply energy accounting in their own contexts.

Question
What is the chapter about?
Direct answer
How work, kinetic energy, potential energy, power, and momentum describe energy transfer and conservation in mechanics, and which model to pick first.
Question
What is the central method choice?
Direct answer
Choose the system boundary, decide whether the unknown depends on path or only on state, and select work-energy, energy conservation, power, or momentum and impulse accordingly.
Question
Where do most mistakes begin?
Direct answer
Confusing negative work on one body with total energy loss, applying conservation where non-conservative work is present, and assuming kinetic energy is conserved in every collision.
Question
What should come before this chapter?
Direct answer
Vector resolution, free-body diagrams, force-position graphs, Newton's laws, and the distinction between velocity and speed.
Question
What comes after it?
Direct answer
Rotational Motion extends energy and momentum ideas to rigid bodies, and Gravitation and Simple Harmonic Motion apply energy accounting in their own contexts.

The official JEE documents define content scope. They do not publish chapter weightage, so none is asserted here.

Official JEE syllabus mapping for Work, Energy and Power

Verified against the current JEE Main 2026 syllabus and JEE Advanced 2026 syllabus on 8 September 2026. This is a wording and scope mapping, not a claim about question difficulty or frequency.

Official JEE syllabus mapping for Work, Energy and Power
Concept group	JEE Main 2026	JEE Advanced 2026	Preparation note
Work and energy	Work by constant and variable force, kinetic and potential energies, and the work-energy theorem are explicitly listed.	Kinetic and potential energy, and work, are explicitly listed.	Confirm whether a force is constant before choosing a shortcut formula.
Power and springs	Power and spring potential energy are explicitly listed.	Power is explicitly listed.	Keep spring energy restricted to the linear Hooke-law range.
Conservation	Mechanical-energy conservation, and conservative and non-conservative forces, are explicitly listed.	Conservation of mechanical energy and linear momentum, and impulse, are explicitly listed.	State the system boundary before asserting any conservation.
Collisions and constrained motion	Vertical-circle motion, and elastic and inelastic collisions in one and two dimensions, are explicitly listed.	Elastic and inelastic collisions are explicitly listed.	Main and Advanced scope should not be assumed identical from a combined coaching outline. Keep both official documents available.

Concept group
Work and energy
JEE Main 2026
Work by constant and variable force, kinetic and potential energies, and the work-energy theorem are explicitly listed.
JEE Advanced 2026
Kinetic and potential energy, and work, are explicitly listed.
Preparation note
Confirm whether a force is constant before choosing a shortcut formula.
Concept group
Power and springs
JEE Main 2026
Power and spring potential energy are explicitly listed.
JEE Advanced 2026
Power is explicitly listed.
Preparation note
Keep spring energy restricted to the linear Hooke-law range.
Concept group
Conservation
JEE Main 2026
Mechanical-energy conservation, and conservative and non-conservative forces, are explicitly listed.
JEE Advanced 2026
Conservation of mechanical energy and linear momentum, and impulse, are explicitly listed.
Preparation note
State the system boundary before asserting any conservation.
Concept group
Collisions and constrained motion
JEE Main 2026
Vertical-circle motion, and elastic and inelastic collisions in one and two dimensions, are explicitly listed.
JEE Advanced 2026
Elastic and inelastic collisions are explicitly listed.
Preparation note
Main and Advanced scope should not be assumed identical from a combined coaching outline. Keep both official documents available.

Sources: JEE Main 2026 syllabus and JEE (Advanced) 2026 syllabus, both linked in the sources section below.

Before this chapter

Prerequisites: what you should know before Work, Energy and Power

Prerequisites: what you should know before Work, Energy and Power
Prerequisite	You are ready if you can…	If not, repair this first
Vectors	Resolve vectors and compute a dot product.	Revisit vector components and the dot product before this chapter.
Free-body diagrams	Draw a free-body diagram and identify every force on a body.	Review Laws of Motion for force identification.
Force-position graphs	Read a force-position graph and identify its enclosed area.	Practise interpreting slope and area on force-position graphs.
Newton's laws	Apply Newton's second and third laws to a system.	Revisit Laws of Motion before this chapter.
Velocity versus speed	Distinguish signed velocity from unsigned speed.	Review Kinematics for velocity and speed definitions.

Prerequisite
Vectors
You are ready if you can…
Resolve vectors and compute a dot product.
If not, repair this first
Revisit vector components and the dot product before this chapter.
Prerequisite
Free-body diagrams
You are ready if you can…
Draw a free-body diagram and identify every force on a body.
If not, repair this first
Review Laws of Motion for force identification.
Prerequisite
Force-position graphs
You are ready if you can…
Read a force-position graph and identify its enclosed area.
If not, repair this first
Practise interpreting slope and area on force-position graphs.
Prerequisite
Newton's laws
You are ready if you can…
Apply Newton's second and third laws to a system.
If not, repair this first
Revisit Laws of Motion before this chapter.
Prerequisite
Velocity versus speed
You are ready if you can…
Distinguish signed velocity from unsigned speed.
If not, repair this first
Review Kinematics for velocity and speed definitions.

This is a readiness check, not a weightage or scoring-priority list.

Concepts in this chapter

1. Choose the system

A force internal to one system can be external to another.

Decide which bodies are inside the system. A force internal to one system can be external to another.

2. Identify transfer

Work is energy transferred through a force-displacement interaction.

Work is energy transferred through a force-displacement interaction. Its sign comes from the dot product of force and displacement.

3. Name the stores

Translational kinetic, gravitational potential, and elastic potential energy are common stores in this scope.

4. Account for non-conservative transfer

Friction converting mechanical energy into internal energy does not justify plain conservation.

Friction may convert mechanical energy into internal energy. It does not justify writing mechanical-energy conservation without an additional term.

5. Apply the constraint

Contact, string, spring, or circular-path conditions can decide whether an assumed motion is physically possible.

6. Switch model for collisions

Momentum can be conserved for an isolated collision while kinetic energy is conserved only for an elastic collision.

Linear momentum can be conserved for an isolated collision while kinetic energy is conserved only for an elastic collision.

Method selector: choose the model before the equation

Match the question signal to a first model, then validate the choice before calculating.

Method selector: choose the model before the equation
Question signal	Best first model	First check
Force varies with position	Work integral or area under an F-x graph	Sign and integration limits
Only initial and final speeds or heights matter	Work-energy or energy accounting	System boundary and dissipative work
Time or rate is requested	Power	Instantaneous versus average
Very short interaction or collision	Momentum and impulse	External impulse and collision type
Vertical loop or constrained path	Energy plus radial dynamics	Contact or tension condition

Question signal
Force varies with position
Best first model
Work integral or area under an F-x graph
First check
Sign and integration limits
Question signal
Only initial and final speeds or heights matter
Best first model
Work-energy or energy accounting
First check
System boundary and dissipative work
Question signal
Time or rate is requested
Best first model
Power
First check
Instantaneous versus average
Question signal
Very short interaction or collision
Best first model
Momentum and impulse
First check
External impulse and collision type
Question signal
Vertical loop or constrained path
Best first model
Energy plus radial dynamics
First check
Contact or tension condition

Formula sheet

Work equals the integral of force dotted with displacement along the path from A to B.
Work done by a force F along the actual path from A to B.
F
force acting on the chosen body (N)
r
position along the path (m)
W
work done (J)
Use when — Use the force acting on the chosen body; a constant force gives W = F s cos(theta).
Common trap — Replacing a varying force by an endpoint value.
Net work equals the change in translational kinetic energy.
Net work on a body changes its translational kinetic energy K.
W_net
net work done by all external forces (J)
K
translational kinetic energy (J)
Use when — Particle or centre-of-mass translation with all external-force work included.
Common trap — Using the work of one force as if it were the net work.
Kinetic energy equals one half mass times speed squared.
Translational kinetic energy.
m
mass (kg)
v
speed (m/s)
K
kinetic energy (J)
Use when — Non-relativistic point particle or the translational part of a rigid body.
Common trap — Assigning a sign to kinetic energy from the velocity direction.
Spring potential energy equals one half the spring constant times extension squared.
Ideal spring potential energy for extension or compression x.
k
spring constant (N/m)
x
extension or compression from natural length (m)
U_s
spring potential energy (J)
Use when — Linear Hooke-law range, with x measured from the spring's natural length.
Common trap — Using k x squared without the one-half factor, or measuring x from an arbitrary origin.
Work by a conservative force equals the negative of the change in potential energy.
Work done by a conservative force equals the negative change in its potential energy.
W_c
work by the conservative force (J)
U
potential energy (J)
Use when — A potential-energy function exists for the force.
Common trap — Applying it to kinetic friction, which has no potential-energy function.
Initial kinetic plus initial potential plus non-conservative work equals final kinetic plus final potential.
Mechanical-energy accounting including non-conservative work W_nc.
K_i
initial kinetic energy (J)
U_i
initial potential energy (J)
W_nc
non-conservative work done on the system (J)
K_f
final kinetic energy (J)
U_f
final potential energy (J)
Use when — A consistent sign convention is kept for every term.
Common trap — Writing K + U as constant when W_nc is not zero.
Power equals the time derivative of work, equivalently force dotted with velocity.
Instantaneous power is the rate of energy transfer.
P
instantaneous power (W)
F
force (N)
v
velocity (m/s)
Use when — Force and velocity are evaluated at the same instant.
Common trap — Using speed times force without the angle between force and velocity.
Impulse equals the integral of force over time and equals the change in momentum.
Impulse of the resultant force changes momentum.
J
impulse (N s)
p
linear momentum (kg m/s)
Use when — Resultant external impulse acts on the chosen system.
Common trap — Treating impulse as if it were energy.

Worked examples

A block starts from rest and slides a distance s down an incline of angle theta with kinetic-friction coefficient mu_k. Find its speed at the bottom.

Answer: v squared equals 2 g s (sin theta minus mu_k cos theta), provided the block actually slides and remains on the plane.

Choose the block as the system.
Gravity decreases potential energy by m g s sin(theta).
The normal force does no work because it is perpendicular to the displacement.
Kinetic friction does work equal to minus mu_k m g cos(theta) s.
Apply energy accounting: (1/2) m v^2 = m g s sin(theta) - mu_k m g cos(theta) s.
Mass cancels, giving v^2 = 2 g s (sin(theta) - mu_k cos(theta)).

Common mistakes and what they actually indicate

Calling every negative work term an energy loss
Knowledge gap
Why it happens
Negative work on one chosen body may be positive transfer elsewhere in a larger system.
How it is corrected
Track where the energy goes across the full system boundary before calling it lost.
Using path-independent potential energy for a non-conservative force
Knowledge gap
Why it happens
A potential-energy function only exists for a conservative force.
How it is corrected
Represent friction and similar forces as a work term, never as a potential energy.
Conserving kinetic energy in every collision
Decision / selection error
Why it happens
Kinetic energy is conserved only in an elastic collision, not in every collision.
How it is corrected
Classify the collision first, then decide which quantities are conserved.
Forgetting that the normal force can do work when the constraint itself moves
Knowledge gap
Why it happens
The zero-work rule for a normal force assumes the contact surface is stationary along the direction of motion.
How it is corrected
Re-examine whether the constraining surface itself has a displacement component.
Solving a vertical-circle speed by energy and never testing contact or tension
Decision / selection error
Why it happens
Energy accounting alone does not confirm the body stays on the path; the constraint condition must also hold.
How it is corrected
Check the minimum-speed or minimum-tension condition alongside the energy equation.
Dropping the angle between force and velocity when computing power
Execution error
Why it happens
Power is a dot product, so using speed times force without the angle overstates or misassigns the rate of transfer.
How it is corrected
Always write power as force dotted with velocity and evaluate the angle explicitly.

Diagnose the first wrong decision

Diagnose the first wrong decision
Primary label	Evidence in a failed solution	Corrective action
Knowledge Gap	Cannot explain why potential energy belongs to a system	Rebuild system and interaction definitions.
Recall Gap	Correct model, but the spring energy or power relation is unavailable	Retrieve the formula with units and condition.
Execution Error	Sign, dot product, algebra, or graph area is wrong	Rework the same model with a transfer ledger.
Decision / Selection Error	Uses force equations through a long path when endpoint energy is sufficient, or conserves kinetic energy in an inelastic collision	Mark question signals before calculation.
Needs Review	Assumes a contact, friction state, or collision classification not established by the prompt	Send the assumption and complete solution for academic review.

Primary label
Knowledge Gap
Evidence in a failed solution
Cannot explain why potential energy belongs to a system
Corrective action
Rebuild system and interaction definitions.
Primary label
Recall Gap
Evidence in a failed solution
Correct model, but the spring energy or power relation is unavailable
Corrective action
Retrieve the formula with units and condition.
Primary label
Execution Error
Evidence in a failed solution
Sign, dot product, algebra, or graph area is wrong
Corrective action
Rework the same model with a transfer ledger.
Primary label
Decision / Selection Error
Evidence in a failed solution
Uses force equations through a long path when endpoint energy is sufficient, or conserves kinetic energy in an inelastic collision
Corrective action
Mark question signals before calculation.
Primary label
Needs Review
Evidence in a failed solution
Assumes a contact, friction state, or collision classification not established by the prompt
Corrective action
Send the assumption and complete solution for academic review.

Only Knowledge Gap, Recall Gap, Execution Error, Decision / Selection Error, and Needs Review are used as primary labels.

Official-paper handling

Official-paper handling
Practice question	Direct answer
Where should I practise Work, Energy and Power questions?	Use official JEE Main and JEE Advanced paper archives directly.
How are questions classified by topic?	Filters for variable-force work, conservation, power, vertical-circle constraints, and collisions are shown only after a reviewer verifies each classification.
Are counts, trends, or predicted frequencies published here?	No. Counts, trend charts, predicted frequency, and expected questions stay hidden until they can be evidenced.

Practice question
Where should I practise Work, Energy and Power questions?
Direct answer
Use official JEE Main and JEE Advanced paper archives directly.
Practice question
How are questions classified by topic?
Direct answer
Filters for variable-force work, conservation, power, vertical-circle constraints, and collisions are shown only after a reviewer verifies each classification.
Practice question
Are counts, trends, or predicted frequencies published here?
Direct answer
No. Counts, trend charts, predicted frequency, and expected questions stay hidden until they can be evidenced.

Official-paper links are evidence-safe practice pointers, not a claim about this chapter's exam weightage.

FAQ