Work, Energy, and Power Explained
Work, energy, and power are three closely related concepts that appear throughout mechanics, thermodynamics, and everyday life. Mastering these ideas — and knowing their units and formulas — allows you to analyse everything from a ball rolling down a slope to the efficiency of a car engine.
What Is Work?
In everyday language “work” means effort. In physics it has a precise definition: work is done when a force causes an object to move in the direction of that force. The formula is:
W = F × d
where W is work in joules (J), F is the applied force in newtons (N), and d is the displacement in metres (m) in the direction of the force. One joule equals one newton-metre: the work done when a force of 1 N moves an object 1 m in the direction of the force.
Two important consequences of this definition: (1) If there is no displacement, no work is done — holding a heavy bag stationary above your head is tiring, but in physics no work is being done on the bag. (2) Only the component of force in the direction of motion counts — for a force applied at an angle θ to the direction of motion, W = F d cosθ. A force acting at 90° to the displacement (like gravity on an object moving horizontally) does zero work.
Kinetic Energy
Kinetic energy (KE) is the energy an object has because of its motion:
KE = ½ m v²
where m is mass in kg and v is speed in m/s. The unit is joules. Notice that KE depends on the square of speed: doubling the speed quadruples the kinetic energy. This is why a car travelling at 60 mph is four times as dangerous as one at 30 mph in a collision — not twice as dangerous. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: Wnet = ΔKE. This means you can find the work done by calculating the kinetic energy change, and vice versa.
Gravitational Potential Energy
Gravitational potential energy (GPE) is the energy stored in an object due to its height above a reference level:
GPE = m g h
where m is mass (kg), g is gravitational field strength (9.8 m/s² on Earth), and h is the height above the reference level (m). When an object falls, GPE is converted to KE; when it rises, KE is converted to GPE. Choosing the reference level (usually the ground or the lowest point of interest) is your decision — only changes in GPE matter physically.
Conservation of Energy
One of the most powerful principles in physics is the conservation of energy: energy cannot be created or destroyed, only transferred from one form to another. In a closed system, the total energy remains constant.
Consider a ball dropped from height h. As it falls:
- At the top: all energy is GPE = mgh; KE = 0.
- Halfway down: GPE = mg(h/2); KE = mg(h/2) — the lost GPE has become KE.
- Just before hitting the ground: GPE = 0; KE = mgh.
In reality, air resistance converts some mechanical energy to heat, so KE just before impact is slightly less than mgh. When energy appears to be “lost”, it has actually been transferred to thermal energy (heat) through friction or air resistance. The total energy including heat is always conserved.
Energy Transfer Summary
| Situation | Energy transferred from | Energy transferred to |
|---|---|---|
| Ball falling freely | Gravitational PE | Kinetic energy |
| Car braking | Kinetic energy | Thermal (heat) in brakes |
| Stretching a spring | Kinetic / work done | Elastic potential energy |
| Burning fuel in engine | Chemical energy | Kinetic + thermal energy |
| Charging a battery | Electrical energy | Chemical energy |
Power
Power is the rate of doing work — how much energy is transferred per second:
P = W / t
The unit of power is the watt (W), equal to one joule per second. Since W = F × d, we can also write P = F × d / t = F × v, where v is the velocity of the object. This form is useful when a constant force acts on a moving object: a car engine exerting a driving force of 2000 N at a speed of 25 m/s is developing a power of 2000 × 25 = 50,000 W = 50 kW. Note that the watt symbol and the symbol for work are both “W” — context (units given) makes clear which is meant.
Efficiency
No real machine converts all input energy into useful output energy; some is always wasted as heat or sound. Efficiency measures the fraction of input energy that becomes useful output energy:
Efficiency = (useful energy output / total energy input) × 100%
An electric motor that takes in 500 J of electrical energy and produces 400 J of kinetic energy has an efficiency of (400/500) × 100% = 80%. The remaining 100 J has been lost as heat in the motor windings. Improving efficiency — through better insulation, lubrication, or design — is central to engineering and energy policy. No machine can ever be 100% efficient (this would violate the second law of thermodynamics), though high-quality electric motors can approach 95% efficiency.
Summary
Work equals force times displacement in the direction of the force, measured in joules. Kinetic energy depends on the square of speed (KE = ½mv²); gravitational potential energy depends on height (GPE = mgh). The conservation of energy principle guarantees that total energy is always constant — apparent losses appear as heat. Power (watts) measures the rate of energy transfer. Efficiency quantifies how well a device converts input energy to useful output. Together these concepts allow you to analyse nearly any mechanical system from first principles.