Work, Energy and Power - NEET Physics Notes, Formulas & Concepts

Chapter Introduction

Work, energy and power describe how forces transfer energy, how motion changes, and how quickly energy is transferred. These ideas connect gravity, springs, friction, connected bodies, collisions and circular motion.

Physics-first approach: Identify the system and what changes; choose the model; check its conditions; then apply the formula.

Chapter in One View

Central idea: Net work changes kinetic energy. Conservative forces transfer energy between kinetic and potential forms. Non-conservative work can change mechanical energy. Power tells how quickly energy is transferred.

Identify the system and displacement.
Find each force component along displacement.
Choose work–energy, mechanical-energy, power or momentum reasoning.
Check friction, external work and system boundaries.
For collisions, check external impulse before conserving momentum.
For connected bodies, write the string constraint before equations.
For circular motion, use energy for speed and radial dynamics for force.

Must-Know Concepts

Work: Scalar product of force and displacement; it can be positive, negative or zero.
Sign of work: Force component along displacement → positive; opposite → negative; perpendicular → zero.
Variable force: In one dimension, work is the signed area under the force–position graph.
Conservative force: Work depends only on initial and final positions; closed-path work is zero. Gravity and ideal spring force are examples.
Non-conservative force: Work depends on path. Kinetic friction commonly transfers mechanical energy into internal energy.
Kinetic energy: For translational motion, K = ½mv²; it is non-negative and depends on speed squared.
Potential energy: Energy associated with the arrangement of a system; its zero level is chosen by convention.
Work–energy theorem: Net work on a particle equals its change in kinetic energy.
Mechanical energy: E_mech = K + U; it is constant when net non-conservative work is zero.
Power: Average power is work divided by elapsed time; instantaneous power is F·v.
Efficiency: Useful output divided by input, expressed as a fraction or percentage.
Collisions: Momentum is conserved when external impulse is negligible. Kinetic energy is conserved only in an elastic collision.
Connected bodies: String constraints link displacements and speeds; derive the relation from the geometry.
Vertical circle: Use energy for speed and radial force balance for tension/normal force; check contact or taut-string conditions.

Formula + Meaning

Work by a Constant Force

W = Fs cos θ

Meaning: Only the force component along displacement contributes to work. Use: A constant force acts through a known displacement. Condition: θ is the angle between force and displacement; use displacement, not automatically total distance. Trap alert: A force perpendicular to displacement does zero work even if it is large.

Variable Force

W = ∫ F · dr; in 1D: W = ∫ F(x) dx

Meaning: Adds small work contributions along the path. Use: Force changes with position or direction. Condition: Use the force component along each small displacement. Trap alert: Area below the x-axis contributes negative work.

Work by Gravity

W_g = mg(h_i − h_f)

Meaning: Gravity does positive work when an object moves down and negative work when it moves up. Use: Height changes near Earth where g is approximately constant. Condition: Measure initial and final heights from the same reference. Trap alert: ΔU_g = mg(h_f − h_i) = −W_g.

Work by an Ideal Spring

W_s = ½k(x_i² − x_f²)

Meaning: Spring work depends on initial and final extensions/compressions. Use: An ideal spring changes from x_i to x_f. Condition: x is measured from natural length. Trap alert: Spring force is F_s = −kx; do not confuse force with potential energy.

Net Work

W_net = ΣW_i

Meaning: Adds the work done by every force on the chosen object. Use: Several forces act during a displacement. Condition: Calculate each force’s work with its direction and displacement. Trap alert: Work by one force is not necessarily net work.

Kinetic Energy and Work–Energy Theorem

K = ½mv²

W_net = ΔK = ½m(v_f² − v_i²)

Meaning: Net work determines the change in translational kinetic energy. Use: When speed change is needed and work is easier to find than acceleration or time. Condition: Use net work over the actual interval. Trap alert: Doubling speed makes kinetic energy four times as large. If predicted final K is negative, recheck the stopping point or assumed motion.

Conservative Force and Potential Energy

W_c = −ΔU

F_x = −dU/dx

Meaning: Conservative-force work and potential-energy change have opposite signs; force points toward decreasing potential energy along x. Use: Gravity or spring energy changes, or a one-dimensional U(x) graph is given. Condition: Applies to a conservative force in the stated coordinate. Trap alert: At equilibrium the slope is zero; stability depends on the nearby curve. Do not assign a unique potential-energy function to kinetic friction.

Mechanical Energy

E_mech = K + U

K_i + U_i = K_f + U_f

Meaning: Kinetic and potential energy trade while their sum remains constant. Use: Net non-conservative work is zero. Condition: Include all relevant potential terms and use a consistent reference. Trap alert: If friction or an external agent changes mechanical energy, use the non-conservative-work relation.

Non-Conservative Work

W_nc = Δ(K + U)

Meaning: Non-conservative work equals the change in mechanical energy. Use: Friction or an applied agent changes K + U. Condition: Define the system consistently and account for relevant work. Trap alert: Mechanical energy transferred away is not destroyed; it can become internal/thermal energy.

Spring and Gravitational Potential Energy

U_s = ½kx²

U_g = mgh

Meaning: Energy stored in an ideal spring relative to natural length; gravitational potential energy is measured relative to a chosen height. Use: Spring extension/compression or height is known. Condition: x = 0 at natural length; use the same zero-height reference for initial and final states. Trap alert: Absolute potential energy depends on reference; changes in potential energy do not.

Power

P_avg = W/Δt; P = dW/dt = F · v = Fv cos θ

Meaning: Power measures the rate of work or energy transfer. Use: The question asks how quickly work is done or energy is transferred. Condition: For instantaneous power, use instantaneous force and velocity. Trap alert: Force and velocity need not be parallel; use the dot product.

Efficiency

η = (useful output / total input) × 100%

Meaning: Fraction of input energy or power delivered as useful output. Use: Input and useful output are given or can be found. Condition: Compare energy with energy or power with power. Trap alert: Use useful output, not total output including losses.

Impulse and Coefficient of Restitution

J = Δp

e = separation speed / approach speed

Meaning: Impulse changes momentum; coefficient of restitution compares relative speeds before and after impact along the line of impact. Use: Impact questions involving force over time or one-dimensional collision speeds. Condition: Momentum conservation requires negligible net external impulse. Trap alert: e = 1 for an ideal elastic collision; e = 0 for a perfectly inelastic collision. Momentum conservation alone does not guarantee kinetic-energy conservation.

Scope note: K = ½mv² is translational kinetic energy. If rotational motion is part of the question, rotational kinetic energy may also be required.

Formula Selection Guide

See This Situation	Think This Model	Use This Relation / Action
Constant force and displacement	Work by a force	W = Fs cos θ
Force varies with position	Variable-force work	W = ∫F(x) dx; signed area on F–x graph
Initial/final speeds; net work known	Work–energy theorem	W_net = ΔK
Height changes near Earth	Gravitational energy	U_g = mgh; W_g = −ΔU_g
Spring changes extension	Spring work/energy	U_s = ½kx²; W_s = −ΔU_s
Friction/external work changes K + U	Non-conservative work	W_nc = Δ(K + U)
“How quickly?”	Power	P_avg = W/Δt; P = F·v
Input and useful output given	Efficiency	η = useful output/input × 100%
Collision over short interval	System momentum	Check external impulse; conserve momentum if negligible
Collision asks about energy retention	Collision type	Elastic: K conserved; inelastic: K generally not conserved
String/pulley links bodies	Constraint relation	Relate displacements/speeds from geometry first
Speed/tension in vertical circle	Energy + radial dynamics	Energy for v; ΣF_radial = mv²/r

When to Use / When Not to Use

Mechanical-energy conservation

Use when: Net non-conservative work is zero.

Do not use blindly when: Friction, an applied force or another non-conservative interaction changes K + U.

Instead: Use W_nc = Δ(K + U), with a clear system boundary.

Work–energy theorem

Use when: Net work over a displacement can be found and speed change is needed.

Do not: Replace net work with one force’s work unless other forces do zero work.

Momentum conservation in collisions

Use when: Net external impulse on the selected system is zero or negligible during impact.

Do not: Infer kinetic-energy conservation from momentum conservation; check collision type.

Vertical-circle condition

Use energy to connect speeds at different heights; use radial force balance to find tension or normal force.

At the top of a string-supported circle, the limiting taut-string case is T = 0. Then mg = mv²/r and v_min = √(gr) at that instant.

Important: This is a limiting condition, not a universal speed for every vertical-circle problem; starting point and energy loss matter.

Connected bodies

Choose the system and derive the string/constraint relation before applying energy. Do not assume all connected bodies have the same displacement or speed unless the constraint geometry proves it.

Common Misconceptions

Wrong idea: “A force always does work.” → Correct Physics: Work is zero if there is no displacement or the force is perpendicular to it. → Why it matters: Direction and displacement matter.

Wrong idea: “Zero net work means the object is at rest.” → Correct Physics: Kinetic energy is unchanged; the object may keep moving at constant speed. → Why it matters: Work changes kinetic energy.

Wrong idea: “Mechanical energy is always conserved.” → Correct Physics: Non-conservative work can change K + U. → Why it matters: Mechanical energy may transfer into internal energy.

Wrong idea: “Momentum conservation means kinetic-energy conservation.” → Correct Physics: Momentum can be conserved in an inelastic collision while kinetic energy decreases. → Why it matters: The laws have different conditions.

Wrong idea: “Negative work gives negative kinetic energy.” → Correct Physics: Negative net work reduces K. If predicted K becomes negative, the assumed motion cannot continue as stated. → Why it matters: Check the stopping point.

Exam Traps

Using total distance automatically instead of displacement/path information.
Forgetting the sign of the force component along displacement.
Calling one force’s work “net work”.
Treating all F–x graph area as positive.
Assuming K + U is constant despite friction or external work.
Confusing energy with power.
Conserving kinetic energy in every collision.
Using momentum conservation without checking external impulse.
Ignoring string constraints in connected-body problems.
Finding speed from energy but forgetting radial force balance.
Measuring spring extension from a point other than natural length.

See This → Think This

See This	Think This	Recognition Cue
Force at an angle to displacement	Use the parallel component	W = Fs cos θ
Force–position graph	Signed area gives work	Count area above and below x-axis with signs
Speed changes	Relate net work to ΔK	W_net = ΔK
Height changes with no non-conservative work	Compare K + U	Mechanical energy remains constant
Spring stretches/compresses	Measure x from natural length	U_s = ½kx²
Friction acts	Check whether mechanical energy changes	W_nc = Δ(K + U)
“How quickly?”	Think power, not just work	P = F·v
Bodies collide	Define system and check external impulse	Momentum is a vector
Collision asks about energy loss	Identify elastic/inelastic behaviour	Momentum and kinetic energy have different conditions
Pulley/string connects bodies	Derive displacement constraint	Use geometry before equations
Vertical circle	Energy for speed; radial equation for force	ΣF_inward = mv²/r
Potential-energy graph	Force is the negative slope	F_x = −dU/dx

Key Diagrams / Graphs

Force-displacement graph showing signed work areas — **Force–displacement graph.** Work is the signed area between the F–x curve and the x-axis. Add positive and negative areas algebraically to find work by that force.

Potential energy curve showing slope and equilibrium — **Potential-energy curve.** F_x = −dU/dx. At equilibrium, dU/dx = 0. A local minimum is stable equilibrium; a local maximum is unstable equilibrium. Assess the curve around the point.

Energy pathway between kinetic, potential and thermal energy — **Energy pathway.** Conservative interactions exchange K and U; friction can transfer mechanical energy into internal/thermal energy. Define the system and track where energy goes rather than saying energy is destroyed.

Vertical circular motion diagram showing forces at the top — **Vertical-circle top-point schematic.** At the top, inward is downward. Gravity and tension, when present, point inward there. Apply ΣF_inward = mv²/r. In the limiting taut-string case T = 0, gravity alone supplies the centripetal requirement.

Collision Quick Comparison

This comparison assumes an isolated system during collision and the usual one-dimensional coefficient-of-restitution model.

Collision Type	Momentum (isolated system)	Kinetic Energy	Restitution
Elastic	Conserved	Conserved	e = 1
Inelastic	Conserved	Not conserved in general	0 < e < 1 in ordinary 1D impacts
Perfectly inelastic	Conserved	Not conserved; bodies move together after impact	e = 0

Quick Checks

Q: What part of a constant force contributes to work? → The component along displacement.

Q: What does area under an F–x graph represent? → Work by that force, with sign.

Q: Relation between work by gravity and potential-energy change? → W_g = −ΔU_g.

Q: When is mechanical energy conserved? → When net non-conservative work is zero.

Q: Can a moving object have zero net work over an interval? → Yes; kinetic energy can remain unchanged.

Q: What does power measure? → Rate of work or energy transfer.

Q: Does momentum conservation guarantee kinetic-energy conservation? → No; only elastic collisions conserve kinetic energy.

Q: What must be checked before conserving momentum? → Net external impulse on the chosen system.

Q: From where is spring extension x measured? → From natural length.

Q: What tools are combined in vertical-circle questions? → Energy for speed and radial force balance for force.

Q: A potential-energy graph has zero slope. What does it indicate? → An equilibrium point; stability depends on the nearby curve.

Q: A block is predicted to have negative final K. What should you check? → Whether it stops before the assumed final point.

Mini Exam Reasoning

Case A — Block slides down a rough slope

Clue: Height decreases and friction acts. → Physics situation: Gravitational energy changes while friction transfers energy. → Model: Work–energy / non-conservative work. → Relation: W_nc = Δ(K + U). → Check: Friction work is negative for motion down the slope.

Case B — Two bodies collide

Clue: A short collision interval is given. → Physics situation: Internal forces dominate during impact. → Model: System momentum. → Relation: Conserve total momentum if external impulse is negligible. → Check: Conserve kinetic energy only for an elastic collision.

Case C — Body moves in a vertical circle

Clue: Speed or tension is asked at the top. → Physics situation: Speed changes with height and the path curves. → Model: Energy + radial dynamics. → Relation: Energy gives v; ΣF_inward = mv²/r. → Check: Verify string/contact condition and inward force directions.

One-Minute Recall

Work → force component along displacement.
Net work → change in kinetic energy.
Conservative force → path-independent work; closed-path work is zero.
W_c = −ΔU; F_x = −dU/dx.
K + U stays constant when net non-conservative work is zero.
Non-conservative work → change in mechanical energy.
Power → rate of energy transfer.
Efficiency → useful output / input.
Collision → momentum may be conserved; kinetic energy depends on collision type.
Connected system → derive the constraint relation.
Vertical circle → energy for speed; radial balance for force.
Negative predicted K → assumed motion/state needs rechecking.

Download the Work, Energy and Power Concept Summary PDF

Prefer studying offline? Download the same Work, Energy and Power — NEET Physics Essentials concept summary as a PDF.

Download PDF

Practice MCQs

Test your understanding with formula-wise MCQs, special ratios, and solutions.

For MCQs, visit the [Current Lesson] MCQ Index