Work, Energy, and Power

Syllabus Unit: Mechanics

Why it matters

Chapter overview

This topic threads one idea through four subtopics: energy transfer via a force acting over a displacement. It covers when work is positive, negative or zero, how kinetic and potential energy are defined and computed, how the work-energy theorem and power connect force to motion and time, and how mechanical energy is conserved whenever only conservative forces act.

Physics Syllabus Mechanics 30%–35% weightage

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Identify the force vector F and the displacement vector d

Find the angle θ between F and d

Apply W = Fd cosθ

Check the sign — positive, negative or zero — against the physical scenario

1Work Done by a Force

Work is done only when a force produces displacement along its own direction — pushing hard against a wall that doesn't move does zero physics-work, however tired you get.

Learning Objectives

Define work done by a constant force as W = Fd cosθ, and identify θ correctly in a given scenario.
Explain when work done is positive, negative, or zero, with a real example of each.
Compute work done as the area under a force-displacement graph for a variable force.
State the SI unit and dimensional formula of work.

Key Terms

WorkThe scalar product of force and displacement, W = F·d = Fd cosθ, measured in joules.

Positive WorkDone when the force has a component in the same direction as displacement (0°≤θ<90°), e.g. gravity on a falling object.

Negative WorkDone when the force opposes displacement (90°<θ≤180°), e.g. friction on a sliding block, or gravity on a rising object.

Zero WorkDone when force is perpendicular to displacement (θ=90°) or when displacement itself is zero, e.g. tension on a swinging pendulum bob.

In everyday language 'work' means effort; in physics it means something precise — a force must actually move its point of application, and only the component of force along that motion counts.

The formula and its angle

W = F·d = Fd cosθ

θ is the angle between the force vector and the displacement vector, not any other reference direction — this is the single most common source of error in work calculations.

Sign of work

Positive work (0°≤θ<90°) — force helps the motion, e.g. gravity doing work on a falling apple.
Negative work (90°<θ≤180°) — force opposes the motion, e.g. friction on a sliding box, or gravity on a ball thrown upward.
Zero work — force ⊥ displacement (e.g. centripetal force in circular motion, tension on a conical pendulum) or no displacement occurs at all (e.g. pushing an immovable wall).

Work by a variable force

When force varies with position, work equals the area under the Force vs displacement graph.

W = ∫ F dx (variable force)

Common MistakeCarrying a heavy bag while walking horizontally involves zero work by the 'carrying' (upward) force on the bag, since that force is perpendicular to the horizontal displacement — a classic NEET conceptual trap.

Exam TipSI unit of work is the joule (J) = N·m = kg·m²·s⁻²; dimensional formula [ML²T⁻²], identical to energy — they're the same physical dimension.