Work, energy and power

In everyday talk, studying for an exam is "hard work". In physics, the word has a precise meaning, and by that meaning a student sitting with a book is doing no work at all.

Work

Work is done only when a force acts on an object and the object moves in the direction of the force.

Work = Force × Displacement, or W = F × s

The SI unit of work is the joule (J). One joule of work is done when a force of 1 newton moves an object through 1 metre in its own direction.

• Push a wall with all your strength: the wall does not move, so no work is done, however tired you get.
• A coolie standing still with a load on the head does no work on the load in the scientific sense.
• Lift a 10 N bag through 2 m: W = 10 × 2 = 20 J.

Work can be negative. Friction acts opposite to the motion of a sliding box, so the work done by friction is negative.

Energy

Energy is the capacity to do work. It is also measured in joules. Energy exists in many forms: mechanical, heat, light, sound, electrical, chemical and nuclear. Mechanical energy is of two kinds.

Kinetic energy

The energy a body has because of its motion. A moving car, a flying ball, flowing water and blowing wind all have it.

Kinetic energy = ½ m v²

Because of the square, doubling the speed makes the kinetic energy four times as great. This is why speeding vehicles cause such severe accidents.

Potential energy

The energy a body has because of its position or shape. Water stored high in a dam, a stretched bow and a wound-up spring all have it. For a body of mass m raised to a height h:

Potential energy = m g h

Conservation of energy

Energy can neither be created nor destroyed. It can only be changed from one form into another. The total amount stays the same.

Hold a ball at a height: it has only potential energy. Let it fall: as it comes down, potential energy changes into kinetic energy. Just before it hits the ground, almost all the energy is kinetic. At every point, the sum of the two is the same (if we ignore air resistance).

• In a hydroelectric power station: potential energy of water → kinetic energy → electrical energy.
• In a bulb: electrical → light and heat.
• In a torch cell: chemical → electrical.
• In our body: chemical energy of food → heat and mechanical energy.

Power

Two students climb the same staircase. Both do the same work, but the one who runs up does it faster. That student has more power. Power is the rate of doing work.

Power = Work ÷ Time, or P = W ÷ t

The SI unit of power is the watt (W), named after James Watt. One watt is one joule of work done in one second. 1 kilowatt (kW) = 1,000 W.

Worked example: a pump does 6,000 J of work in 60 seconds. P = 6,000 ÷ 60 = 100 W.

Electricity bills use a bigger unit of energy, the kilowatt-hour (kWh), called simply a "unit". It is the energy used by a 1 kW appliance in one hour, and it equals 3.6 million joules.