**Work done and Energy Transfers**

Derivation of the equations for gravitational Potential energy and also Kinetic energy:

**Gravitational Potential Energy:**

We begin with the equation for work done;

Since gravitational potential energy only changes if the height of the object is altered, the distance, d, must be solely related to the height, h. So

Now, any object that has a mass will have a weight, which is a force and acts downwards towards Earth. This can be written in the equation,

So, substituting this into equation (1) gives us:

Since work done is just energy, we can say that this type of energy is the gravitational potential energy:

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**Kinetic Energy**

We begin with the equation for work done;

In this case we can substitute in Newton’s 2nd law of motion;

We then use SUVAT and appropriate values for each quantity;

(we assume negligible air resistance)

X

Therefore we use the equation

Subbing the value from above in gives:

Subbing this into equation (1) gives:

Since the object has a velocity, we can say that the work done the transfer into kinetic energy:

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