Science Vault - Year 11 HSC Physics 8.4 - Moving About
8.4.3 - Work and Energy

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 work (more on work later). Kinetic energy is the energy of motion and it follows that any object with a velocity or which is moving is producing kinetic energy. The faster the body moves the more kinetic energy is produced. 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 is producing. The potential energy posseses 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:

Ek = ½mv2

where

Ek = kinetic energy in joules (J),
m = mass of the object in kilograms (kg),
v = the velocity of the object in metres per second (ms-1).

The net work done on an object is equal to the change in its kinetic or potential energy.

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 anbd it falls. A lift motor provides gravitational potential energy when lifting the car to higher floors. If the cable was cut the potential energy gained by the car would be transferred into kinetic energy as the car 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 energyis produced when the car is dropped. At the top floor the lift car has a huge amount of potential energy, but it has very little kinetic energy.

 Ep = work done = force x distance = mgh

PE = mgh

where

Ep is the potential energy in Joules (J),
g is the acceleration due to gravity in metres per second ( ms-2),
h is the height to which the obejct is lifted in metres (m).

Work

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. In equation form we can write:

W = Fs

where

F is the component of the constant force parallel to the displacement in Newtons (N),
s is the displacement in metres (m).

More generally we can write

W = Fscosθ

where

F is the constant force in Newtons (N),
is the displacement of the object in metres (m),
θ is the angle between the direction of the force and the net displacement.

The second equation becomes useful when, for example, a block is being pulled along a horizontal surface with a force that has both vertical and horizontal components. The force needs to be resolved into the direction of the displacement. The units of work are newton metres (Nm) or joules (J) and work is a scalar quantity.

You will sometimes hear work described as the process of converting energy from one form into another. This is correct but the definition above is more precise.

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 gravitaitonal potential energy. Work is done on the object to raise it against the gravitaitonal 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 gravitation 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 owrk 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 oenergy losses).

Δmgh = Δ½mv2

Energy and Collisions

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 paritcles 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 it 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.