Work

Work Done Equals Energy Transferred

Work done is the product of force and distance moved in the direction of the force. 📌

Whenever a force acts on an object and the object moves in the direction of that force, energy is transferred from one store to another. The amount of energy transferred is exactly equal to the work done. This principle applies to both mechanical work (a force moving an object through a distance) and electrical work (a potential difference driving charge through a component).

Because work done equals energy transferred, both quantities share the same SI unit: the joule (J). One joule of work is done when a force of one newton moves an object through a distance of one metre in the direction of the force.

A car engine, for example, does mechanical work against friction. Energy is transferred from the chemical store of the fuel to the thermal store of the brakes and surroundings. The work done by the friction force equals the energy transferred by heating.

MisconceptionStudents sometimes think work is done whenever a force exists. No displacement in the direction of the force means zero work done — even if a large force acts. A person holding a heavy box stationary does no mechanical work on the box because the box does not move.

Exam TipIf distance moved in the direction of the force is zero, state W = 0.

Calculating Work Done Using W = Fd

Key Equations

Mechanical work done:

$$W=F d=\Delta E$$

Variables:

• $W$ = work done, in joules (J)
• $F$ = force applied in the direction of motion, in newtons (N)
• $d$ = distance moved in the direction of the force, in metres (m)
• $\Delta E$ = energy transferred, in joules (J)

SI unit of $W$: J (equivalent to N m)

Rearrangements:

Starting from $W=Fd$:

Rearranging for $F$:

$$F=\frac{W}{d}$$

Rearranging for $d$:

$$d=\frac{W}{F}$$

ProportionalityWork done is directly proportional to force when distance is constant. Work done is directly proportional to distance when force is constant. Therefore, doubling the force (at constant distance) doubles the work done, and doubling the distance (at constant force) doubles the work done.

Reading the equation: The symbol $\Delta $ (delta) represents "change in." So $\Delta E$ means the change in energy — that is, the energy transferred during the process.

Because $W=Fd=\Delta E$, calculating the mechanical work done also gives the energy transferred. This connects force-and-motion problems directly to energy-transfer problems.