84D - Energy and Work

In physics, energy is an indirectly observed quantity which comes in many forms, such as kinetic energy, potential energy, radiant energy, and many others. The question "what is energy?" is difficult to answer in a simple, intuitive way, although energy can be rigorously defined in theoretical physics. In the words of Richard Feynman, "It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount." However, it is clear that energy is always an indispensable prerequisite for performing mechanical work. The natural basic units in which energy is measured are those used for mechanical work; they always are equivalent to a unit of force multiplied by a unit of length.

84D1 - Energy and Work

Here you will learn to:

Identfy different types of energy,

Apply the law of conservation of energy to energy transformations,

Calculate kinetic energy for moving objects,

Calculate the gravitational potential energy of objects close to the Earth, and

Calculate the work done in situations where multiple forces are acting.

What Is Energy?

Energy is needed to do useful work. It can move, heat, cool, join and cut things; make noise and light; and power our electronics. Food contains energy your body needs to operate. But what is energy? It's not possible to give a one-line definition. The best we can do is list its properties.

Loosely speaking, energy is the ability to cause motion. Sometimes energy doesn't immediately cause motion: it can be stored for later. While energy does other things besides cause motion, we'll stick to motion for now.

Common examples of energy are:

  • energy of motion - kinetic energy

  • stored energy - potential energy, such as gravitational, elastic and chemical

  • energy in hot objects - thermal energy (loosely termed heat)

  • light energy, sound energy, electrical energy and others.

Energy is a scalar: it has no direction, so the mathematics tends to be easier. Its SI unit is the joule
(J or kg m2 s-2).

Law of Conservation of Energy

To scientists, conservation of energy is not saving energy. The law of conservation of energy says that energy is neither created nor destroyed. When we use energy, it doesn't disappear. We change it from one form of energy into another. A car engine burns petrol, converting the chemical energy in petrol into kinetic energy. Solar cells change light energy into electrical energy. Energy changes form, but the total amount of energy in the universe stays the same.

Kinetic and potential energy are often involved in a particular dance where they exchange one form of energy for another. When we lift an object, it is given gravitational potential energy. Work is done on the object to raise it against the gravitational field of the Earth. For a car driving to the top of a hill, the chemical energy in the petrol is used by the engine to give the car gravitational potential energy. Work is being done by the engine on the car because energy is being transformed from one form into another. The same principle can be applied to a lift except the gravitational potential energy is being supplied by an electric motor.

When the car gets to the top of the hill it can coast down the other side of the hill because now the Earth's gravitational field is doing work on the car to convert potential energy into kinetic energy. At the bottom of the hill the car has maximum velocity and maximum kinetic energy but zero potential energy. All of the potential energy has been converted into kinetic energy in the process of the Earth's gravitational field doing work on the car. The change in potential energy is always equal to the change in kinetic energy, assuming there are no other energy losses.

The law of conservation of energy is an empirical law of physics. It states that the total amount of energy in an isolated system remains constant over time (i.e. is said to be conserved over time). A consequence of this law is that energy can neither be created nor destroyed; it can only be transformed from one state to another. The only thing that can happen to energy in a closed system is that it can change form, for instance chemical energy can become kinetic energy.

Said another way, the energy out of a system has to be the same as the energy being put into a system. During the collision of a car with a tree, the kinetic energy of the car before the collision is high because it is moving with considerable velocity. After the collision, the kinetic energy of the system is zero. The tree has done work to deform the car so kinetic energy is lost and the car comes to rest. Some kinetic energy is also transformed into heat and sound as the car comes to rest.

When objects collide, like when a car hits another car or when two billiard balls collide, the total kinetic energy is rarely conserved. A collision where kinetic energy is conserved is called an elastic collision. These types of collision are rare in the macroscopic world and generally only occur between the particles of an ideal gas. Inelastic collisions are ones where kinetic energy is not conserved. When one car runs into the back of another car, some of the total kinetic energy is lost because it is converted into sound energy and thermal energy as the atoms of each car vibrate slightly faster. Some kinetic energy is also lost because work is done by each car in deforming the shape of the other car. This uses some of the original kinetic energy of each car. The total energy is always conserved in the collision, but the collision is inelastic because the total kinetic energy of the system is not conserved.

Kinetic Energy

The word 'kinetic' is derived from the modern Greek word, 'kinesis', meaning 'to move'. In physics, if an object has energy then we say it has the ability to do work (more on work later). Kinetic energy is the energy of motion and it follows that any object that is moving or with a velocity possesses kinetic energy. The faster the body moves the more kinetic energy it has. The greater the mass and speed of an object the more kinetic energy there will be. As a car accelerates down a hill, its velocity increases and so does the kinetic energy it has. The gravitational potential energy possessed by the car at the top of the hill is being changed into kinetic energy.

Kinetic energy is often defined informally as energy of motion. It is better defined as the work it would take to get an object of mass, m, moving with velocity, v, and is given by the formula on the right. The net work done on an object is always equal to the change in its kinetic energy.

Gravitational Potential Energy

Potential energy is the same as stored energy. There are many different types of potential energy such as chemical, elastic and electrical potential energy. The stored energy is held within some kind of field and in the case of gravitational potential energy it is the Earth's gravitational field. When you lift a heavy object against the gravitational field, you exert energy or give the object energy as you lift it. This potential energy later becomes kinetic energy if you let go of the object and it falls. A lift motor provides gravitational potential energy when lifting an elevator to higher floors. If the cable was cut the potential energy gained by the elevator would be transferred into kinetic energy as it fell back towards the Earth. It would have maximum potential energy at the highest floor and maximum kinetic energy when it hit the Earth at the ground floor. The higher the lift car is lifted by the motor, the more potential energy is produced and this means that a greater amount of kinetic energy is produced when the elevator is dropped. At the top floor the lift car has a huge amount of potential energy, but would have very little kinetic energy at that height if it was falling. For an object being lifted off the ground, work is being done on the object by whatever is lifting it. This work is being converted into potential energy as follows according to the equation on the right.


The word work has a variety of meanings in everyday language. But in physics, work is given a very specific meaning to describe what is accomplished by the action of a force when it makes an object move through a distance. Specifically, the work done on a particle or object by a constant force (constant in both magnitude and direction) is defined to be the product of the magnitude of the displacement times the component of the force parallel to the displacement.

To a physicist, doing work means using a force to displace an object resulting in either of the following:

  • a transfer of energy from one object to another

  • a transformation of energy from one form to another.

Therefore, work equals the amount of energy transferred or transformed by the force. Work (W) is a scalar. Its SI unit is the joule (J).

Work has been done on an object by a force only if it experiences a component of displacement in the direction of that force. If the object doesn't move when you push it, you are doing no work, like pushing against a wall. For example, if you lift an object through a height h, the force of your hand causes the object's GPE to increase; therefore, you've done work on that object. The work done by that force equals the object's potential energy increase (mgh). In this case, it's simple - the work done equals the energy increase.

Stuff to Do

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