In everyday language, work means any kind of physical or mental activity - studying, playing, or carrying a load. But in physics, the word "work" has a precise meaning. Work is said to be done only when a force acts on an object and the object is displaced in the direction of the force. Similarly, energy has a specific scientific meaning; it is the capacity to do work.
An object that can do work possesses energy. When we push a trolley, when a moving car hits an obstacle, or when water falls over a dam to generate electricity, work is being done and energy is being transformed from one form to another.
In this chapter we study the scientific meaning of work, the different forms of energy - especially kinetic and potential energy - the law of conservation of energy, and the concept of power.
In science, work is done when a force acts on an object and there is a displacement of the object in the direction of the force. If a force F acts on an object and the object is displaced by a distance s in the direction of the force, then:
Work done (W) = Force (F) x Displacement (s)
The SI unit of work is the joule (J). One joule is the amount of work done when a force of 1 newton moves an object by 1 metre in the direction of the force. The CGS unit of work is the erg, and 1 J = 10^7 erg.
Conditions for work to be done: 1. A force must act on the object. 2. The object must be displaced. 3. The displacement must be in the direction of (or along) the force.
If there is no displacement, no work is done even if a large force is applied. For example, when we push a wall and it does not move, no work is done because there is no displacement. When we hold a weight above our head without moving it, no work is done in the scientific sense.
If the force and the displacement are perpendicular, no work is done. For example, when we carry a bag and walk horizontally, the force is vertically upward while the displacement is horizontal, so the work done by the force is zero.
Energy is the capacity of a body to do work. The amount of energy possessed by a body is equal to the amount of work it can do. Like work, the SI unit of energy is the joule (J). A bigger unit of energy used for practical purposes is the kilojoule (1 kJ = 1000 J) and, for electricity, the kilowatt hour (kWh).
Energy exists in many forms - kinetic energy, potential energy, chemical energy, heat energy, light energy, sound energy, electrical energy and nuclear energy. Energy can be transferred from one body to another and can be converted from one form to another.
The energy possessed by an object due to its motion is called kinetic energy. A moving object can do work because of its motion. For example, a moving hammer has kinetic energy and can drive a nail into wood, a fast-moving bullet can penetrate an object, and flowing water can turn a water wheel.
If an object of mass m moves with velocity v, its kinetic energy is given by:
Kinetic energy (KE) = (1/2) m v^2
The SI unit of kinetic energy is the joule. The kinetic energy depends on two factors: 1. The mass of the object - a heavier object has more kinetic energy. 2. The velocity of the object - kinetic energy increases with the square of the velocity. If the velocity doubles, the kinetic energy becomes four times.
The energy possessed by an object due to its position or configuration is called potential energy. For example, a stone raised above the ground has potential energy because of its height, a stretched rubber band has potential energy because of its stretched configuration, and water stored in a dam has potential energy.
When an object of mass m is raised to a height h above the ground, the work done against gravity is mgh, and this energy is stored in the object as potential energy:
Potential energy (PE) = m x g x h
The potential energy of an object depends on: 1. The mass of the object. 2. The height to which it is raised. 3. The acceleration due to gravity.
When the object falls, its potential energy is converted into kinetic energy. The potential energy of a stretched spring or a compressed spring is called elastic potential energy.
The law of conservation of energy states that energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy of a system remains constant.
For example, consider a body falling freely. At the top, it has maximum potential energy and zero kinetic energy. As it falls, its potential energy decreases and its kinetic energy increases. Just before hitting the ground, its potential energy is almost zero and its kinetic energy is maximum. At every point during the fall, the sum of potential and kinetic energy remains constant, equal to the initial potential energy.
Similarly, in a swinging pendulum, energy continuously changes between potential and kinetic forms, but the total energy remains constant (ignoring friction). A stone thrown upwards gains height (increase in potential energy) while losing speed (decrease in kinetic energy).
Power is the rate of doing work. It is the work done per unit time.
Power = Work done / Time taken
The SI unit of power is the watt (W). One watt is the power when 1 joule of work is done in 1 second. A larger unit is the kilowatt (1 kW = 1000 W) and the megawatt (1 MW = 10^6 W).
Another unit of power is the horsepower (hp); 1 hp = 746 W.
Power tells us not only how much work is done, but also how fast it is done. A machine that does the same work in less time has more power. The power of an engine is often expressed in horsepower.
The commercial unit of electrical energy is the kilowatt hour (kWh). One kilowatt hour is the energy consumed when 1 kilowatt of power is used for 1 hour. This is the unit in which electricity bills are calculated.
1 kWh = 1000 W x 3600 s = 3.6 x 10^6 J
| Quantity | Formula | SI Unit |
|---|---|---|
| Work | W = F x s | joule (J) |
| Kinetic energy | KE = (1/2) m v^2 | J |
| Potential energy | PE = mgh | J |
| Power | P = W / t | watt (W) |
| Energy Form | Description | Example |
|---|---|---|
| Kinetic | Energy of motion | Moving car |
| Potential | Energy of position/configuration | Stored water in a dam |
| Elastic potential | Energy of stretched/compressed spring | Stretched rubber band |
| Chemical | Energy stored in bonds | Food, batteries |
In this chapter we learned that work in physics is done only when a force causes a displacement in its direction, and that work is measured in joules. Energy is the capacity to do work, and it exists in many forms. We studied kinetic energy, which is the energy of motion, and potential energy, which is the energy of position or configuration, and derived their formulae. The law of conservation of energy reminded us that energy can only change form, never be created or destroyed. Finally, we defined power as the rate of doing work and understood the units of power and commercial energy. These ideas link physics to our daily lives - from the fuel used by a car to the electricity we consume at home.