The kinetic energy of an object of mass m is the energy that it possesses due to its motion. If an object is in motion (whether vertically or horizontally), it has kinetic energy. As previously mentioned, there are many forms of kinetic energy- vibrational (the energy due to vibration), rotational (the energy due to rotation), and translational (the energy due to motion from one location to another). This year we mostly deal with translational kinetic energy, the amount of which is dependent on two variables: the mass (m) and the speed (V) of the object. If the object is moving at velocity V, then: 

From this equation we can see that the Kinetic Energy of an object is directly proportional to the square of its speed. This means that for twofold increase in speed the Kinetic Energy will increase by four, and for a threefold increase it will increase by nine etc. 

Kinetic Energy is a scalar quantity, meaning it does not have a direction only a magnitude. Like work and potential energy, the SI unit of measurement for kinetic energy is the Joule. As might be implied by the above equation, 1 Joule is equivalent to 1 kg*(m/s)^2.

An object can store energy as a result of its position, the energy stored due to position is called potential energy. For example a drawn bow is able to store energy due to its position. When in its normal position (when the bow is not drawn), no energy is stored in the bow, however when the bow is altered from its position of equilibrium it is able to store energy. Again, there are many different types of potential energy, some of which we will discuss below.

Gravitational Potential Energy (GPE)

Gravitational potential energy is the energy stored in an object as a result of its height. The energy is stored as the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of an object is dependent on two variables; the mass (m) and the height (h) of an object. There is a directly proportional relationship between the gravitational potential energy of an object and the mass of an object. The more massive an object the greater the potential energy it is capable of storing. Similarly, there is a directly proportional relationship between the height of an object and the gravitational potential energy of the object, the greater the height the greater the potential energy. These relationships are expressed by the following equation: 

PE_grav = mass • g • height / PE_grav = m *• g • h

Strain Energy 

Elastic potential energy (strain energy) is the energy stored in elastic materials as a result of their stretching or compressing, for example in trampolines, rubber bands, springs etc. The amount of  energy stored is related to the amount of stretch applied- the more stretch, the more stored energy.

A spring can store energy either via compression or stretching. A force is required to compress a string, the more compression there is the more force there is required in order to compress it further. Up until the limit of proportionality, for certain springs the force is directly proportional to the extension (x), with the constant of proportionality commonly known as the spring constant (k): 

F_spring = k • x

We can look at the force – extension relationship and see that a spring (or any elastic body) the amount of strain energy is given by the area under the force/extension graph.

The strain energy stored in the material  =   area under curve =   ½FX

And from the gradient K  = F / X so  F = K X

So, then Strain energy = ½KX X= ½K X2

Strain energy in an elastic material  = ½K X2 

Where

  K  =  stiffness (or springiness) of the spring in N/m

      also called the spring or force constant

  X  =  the elastic deformation in m

      also called the extension or increase/decrease in length