In everyday language, "work" means effort or activity. In physics it means something precise and often counterintuitive: work is done only when a force causes displacement in the direction of that force. A person holding a heavy weight perfectly still — exhausted, straining — does zero work in the physics sense. Understanding this definition is the gateway to the work-energy theorem, power, and the entire framework of energy in classical mechanics.
Work is done on an object when a force causes the object to be displaced in the direction of the force. Formula: W = Fd cosθ, where F is force (N), d is displacement (m), and θ is the angle between the force and displacement vectors. Work is a scalar measured in joules (J). 1 J = 1 N·m.
The Work Formula: W = Fd cosθ
The cosθ factor extracts only the component of force acting parallel to the displacement — the only component that does work. A force perpendicular to displacement does zero work, no matter how large.
| θ (angle) | cosθ | Work done | Example |
|---|---|---|---|
| 0° | 1 | W = Fd (maximum positive) | Pushing box horizontally |
| 90° | 0 | W = 0 | Gravity on horizontal motion; normal force |
| 180° | −1 | W = −Fd (maximum negative) | Friction opposing motion |
Positive, Negative, and Zero Work
Positive work (W > 0): Force has a component in the direction of motion. Energy is transferred to the object — kinetic energy increases. Example: engine pushing a car forward.
Negative work (W < 0): Force has a component opposite to motion. Energy is removed from the object — kinetic energy decreases. Example: friction on a sliding box; braking force.
Zero work (W = 0): Force is perpendicular to displacement. No energy transfer. Examples: (1) carrying a bag horizontally — gravity acts downward, displacement is horizontal, θ = 90°, cos 90° = 0; (2) centripetal force in circular motion — always perpendicular to velocity, so it does zero work and circular speed remains constant.
A weightlifter holding a barbell overhead at rest: displacement = 0, so W = Fd cosθ = 0. No work is done on the barbell in the physics sense. Muscles burn energy maintaining tension against gravity — but that energy goes into biochemical processes, not into the mechanical work on the barbell. This is one of the most cited examples of the physics definition differing from everyday intuition.
Worked Examples
Example 1: Horizontal push
A 40 N force pushes a box 5 m horizontally (θ = 0°):
Example 2: Inclined push
60 N force at 35° below horizontal moves a lawnmower 8 m:
Example 3: Work by gravity
A 2 kg ball falls 10 m. Work done by gravity (F = mg = 19.6 N, θ = 0°):
Example 4: Work by friction
Friction force of 15 N opposes a box moved 6 m (θ = 180°):
The Work-Energy Theorem
The net work done on an object equals the change in its kinetic energy. This result follows from Newton's second law and is one of the most useful relationships in classical mechanics. It lets you calculate final speeds without tracking forces through complex trajectories — you only need total work done.
Example: a 2 kg block slides down a frictionless ramp of height 5 m. Work by gravity = mgh = 98 J. Therefore KE at bottom = 98 J → v = √(2 × 98 / 2) = 9.9 m/s. The ramp shape is irrelevant — only height change matters.
Work Done by Gravity and Potential Energy
Gravity is a conservative force — work depends only on initial and final heights, not the path. When an object falls height h:
Lifting the object back requires work against gravity — stored as gravitational PE = mgh. This work-PE connection underlies the law of conservation of energy: work done against conservative forces stores energy that can be fully recovered.
Power: Rate of Doing Work
Power (watts) is work (joules) per unit time (seconds). The same work done faster requires more power. A 1,000 J task taking 10 s requires 100 W; the same task in 5 s requires 200 W.
Frequently Asked Questions
What is work done in physics?
Work is done when a force causes an object to be displaced in the direction of that force. Formula: W = Fd cosθ. Work is a scalar measured in joules (J). It represents energy transferred to or from an object by a force.
Can work be negative?
Yes. Work is negative when the force acts opposite to displacement (θ between 90° and 180°). Friction typically does negative work — it removes kinetic energy from objects. Negative work slows objects down.
When is work equal to zero?
Work is zero when: (1) force is zero, (2) displacement is zero, or (3) force is perpendicular to displacement (θ = 90°). Carrying a bag horizontally: gravity acts downward, displacement is horizontal — zero work done by gravity.
What is the unit of work?
The SI unit of work is the joule (J). 1 J = 1 N·m = 1 kg·m²/s². The joule is also the unit of energy, reflecting the deep connection between work and energy.
What is the work-energy theorem?
The work-energy theorem states that net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv_f² − ½mv_i². It is derived from Newton's second law and allows speed calculations without tracking forces through complex paths.
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Written by
Dr. James CarterPhysicist and educator with 15+ years teaching classical mechanics and thermodynamics at the university level. Former MIT OpenCourseWare contributor.
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