Work, Energy, Kinetic Energy and the Conservation of Energy

Work Work is the product of the force applied to an object and the distance the object moves in the direction of the force

Energy Energy is defined as the ability of an object to do work. Therefore, if an object has energy, it can apply a force and move an object through a distance.

Different Types of Energies An object can have an energy due to its position. This is a potential energy. There are different types of potential energy. Some examples are gravitational potential energy (the energy stored in the gravitational field), elastic potential energy (the energy stored in an elastic object), and electrical potential energy (the energy stored in an electric field). Potential energy is often thought of as a stored energy.

More on Different Types of Energy Another type of energy is the energy due to movement. This is known as Kinetic Energy. An object that is moving has the ability to do work due to the fact that the object has a mass and is moving (has a speed).

Kinetic Energy We are going to look at the amount of work that an object can do because it has a mass and a speed. We will call the mass m and the speed v. We will have it moving across a frictionless, horizontal surface when it runs into an object an applies a constant force of F to the object.

Calculating the Amount of Work = F ´ d but 2 ´ a ´ d = v ¢ 2 - v 2 or v ¢ 2 - v 2 d = 2 a

The Kinetic Energy Formula Therefore v ¢ 2 - v 2 W = m ´ a ´ 2 a or m ´ v 2 W = 2

Kinetic Energy The amount of work that the object can do because it is moving is the Kinetic Energy or Ek. Energy is measured in Joules, just like Work.

Elastic Collisions The Law of Conservation of Energy states that energy cannot be created or destroyed, it can only be converted from one form to another. Unfortunately, some energies are difficult to measure or contain. An example of this is the conversion of kinetic energy into heat. Potential Energies and Kinetic Energy are much easier to measure. These are known as the Mechanical Energies.

E E ¢ = total total Elastic Collisions If a collision conserves the mechanical energy, it is called an elastic collision. For an elastic collision, we are able to use the conservation of energy. E E ¢ = total total

Gravitational Potential Energy The gravtiational potential energy is the energy of an object due to its position in the gravitational field of the earth. The formula for the gravitational potential energy near the surface of the earth is: E = m g h

Elastic Potential Energy The elastic potential energy is the energy due to the position of an elastic object. The elastic energy is directly proportional to the change in the length of the elastic object. The formula for the elastic energy is: k D x 2 E = e 2

Total Energy We can now keep track of three types of energies in situations where the mechanical energy is conserved. m v 2 k D x 2 m v ¢ 2 k D x ¢ 2 + m g h + = + m g h ¢ + 2 2 2 2