Work and Energy

In everyday life, any effort feels like work. In science, work has a precise meaning: work is done on an object only when a force is applied and the object moves in the direction of the force, or has a component of displacement along the direction of the force.

If no displacement takes place, or if the displacement is perpendicular to the applied force, the work done is zero according to physics.

A student pushing a heavy almirah that does not move has done no work in the physics sense, even though the student feels exhausted. Similarly, a coolie at a railway station who carries luggage on his head and walks horizontally exerts force upward but moves horizontally — since force and displacement are perpendicular, the work done by the coolie's upward force on the luggage is zero.

Work is positive when the force and displacement are in the same direction (θ = 0°). When you push a cart on a road in the same direction it moves, the work done by you is positive.

Work is negative when the force acts opposite to the displacement (θ = 180°). The work done by friction on a sliding box is negative because friction acts backward while the box moves forward.

Work is zero when force is perpendicular to displacement (θ = 90°). The tension in a string of a stone revolving in a horizontal circle does zero work because the tension is directed toward the centre while the motion is along the circle.

When you lift an object of mass m through a vertical height h, you do work against gravity. The force needed is at least equal to the weight mg, and the displacement is h upward.

The work done against gravity becomes stored as gravitational potential energy in the object. When the object is released, this stored energy can be converted back to kinetic energy.

Labourers in Indian construction sites who carry bricks or cement bags up several floors of a building are doing work against gravity with every step. The amount of work done depends on the mass of the load and the height gained.

A moving body has the capacity to do work because of its motion. This energy of motion is called kinetic energy.

Kinetic energy depends on both the mass and the speed of the body. If speed doubles, kinetic energy becomes four times larger. This is why accidents on national highways are far more dangerous at high speed than at low speed.

A cricket ball bowled by a fast bowler carries much more kinetic energy than a gentle slow ball because of the higher speed, even though the mass is the same. A loaded goods truck moving slowly can have more kinetic energy than a small car at the same speed because of its much greater mass.

The work-energy theorem states that the net work done on a body equals the change in its kinetic energy.

If the net force does positive work on a body, its kinetic energy increases and it speeds up. If the net force does negative work (like friction or brakes on a vehicle), kinetic energy decreases and the body slows down.

This theorem explains why a car needs much more braking force to stop from a high speed than from a low speed — the higher KE requires more work (larger force × larger distance) to reduce it to zero.

Potential energy is the energy possessed by a body because of its position or configuration. A body can store energy even when it is not moving.

A drawn bowstring, a compressed spring in a watch, a stretched rubber band, and a raised water tank on the rooftop of a building in Mumbai all have potential energy stored in them.

When the constraint is released — the bowstring is let go, the spring is released, the rubber band snaps — the stored potential energy converts into kinetic energy or other forms of energy.

Gravitational potential energy is the energy stored in a body when it is raised to a height above a reference level. The formula is PE = mgh.

Hydroelectric power plants like the Bhakra Nangal Dam in Punjab and the Tehri Dam in Uttarakhand use this principle on a massive scale. Water stored at a great height in a reservoir has huge gravitational potential energy. When released, this water falls and the potential energy converts to kinetic energy of the water, which then drives turbines to generate electrical energy.

The reference level for measuring height is chosen by the solver and is usually taken as the ground or the lowest point in the problem.

The law of conservation of energy states that energy can neither be created nor destroyed — it can only be converted from one form to another.

In a system where only gravity acts (no friction or air resistance), the sum of kinetic energy and potential energy remains constant. This sum is called mechanical energy.

A child on a garden swing in a park experiences this continuously. At the highest point, the swing moves slowly or stops — KE is minimum, PE is maximum. At the lowest point the swing moves fastest — KE is maximum, PE is minimum. The total mechanical energy stays the same throughout the motion.

Power is the rate at which work is done or energy is transferred. A powerful machine completes the same task faster than a less powerful one.

Two construction workers at a building site may lift the same total load to the same height, but the one who does it in less time has greater power.

The SI unit of power is the watt (W). One watt equals one joule of work done per second. Power is also sometimes expressed in horsepower (hp) in the context of engines and motor vehicles. 1 hp = 746 W.

In everyday commercial use, energy is measured in kilowatt-hours (kWh) rather than joules, because joule is too small a unit for household quantities.

One kilowatt-hour is the energy consumed by a device of 1000 W power running for 1 hour. On your electricity bill in India, each unit is 1 kWh. If electricity costs ₹5 per unit, a 1000 W geyser running for 2 hours uses 2 units and costs ₹10.

Converting kWh to joules: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. This large number explains why joule is not practical for billing purposes.

Energy exists in many forms: kinetic, potential, heat, light, sound, electrical, chemical, and nuclear. These forms can convert from one to another, but the total amount is always conserved.

When wood or dung cake (commonly used in rural India) burns in a hearth, chemical energy converts to heat and light. In a transistor radio or a mobile phone, electrical energy converts to sound energy. In a solar panel installed on Indian rooftops, light energy converts to electrical energy.

When we say energy is "wasted," we mean it has converted to a less useful form — usually heat that dissipates into surroundings. Energy is not lost; it simply becomes unavailable for further useful work. Improving efficiency means reducing the amount that converts to waste heat.

Work: . Work is zero when force ⊥ displacement.

Kinetic energy: . Potential energy: .

Work-energy theorem: .

Conservation: in absence of friction.

Power: . SI unit: watt (W).

Commercial energy unit: 1 kWh = 3.6 × 10⁶ J.