# Energy Changes

## Gravitational Energy

In order to calculate energy in the gravitational store, we use this equation:This can also be written as **Ep = m g h**

Remember that you will be given the value for the gravitational field strength in the question (unless you are asked to calculate it!).

Notice that the 200**g** is changed to 0.2**kg**. It is really important to ensure that **kg** is always used. In order to convert grams to kilograms, just divide the number by 1000.

## Kinetic Energy

In order to calculate energy in the kinetic store, we use this equation:

Combination example

__Question: __Calculate the velocity of a 5kg object which was dropped from a height of 10m. g = 10N/kg

**Working: __The first step is to see that we need to find out we are missing. To calculate velocity, the only equation we know is __E**_{k}**= ½ x m x v².** We need to find **v** and have been given **m**; so we are missing **E**_{k}.

The question also gives us the height and a value for **g**. The only equation that suits this is **E**_{p}**=mgh**. We should remember that the kinetic energy at the bottom is the same value as the gravitational energy at the top.

Therefore: Ep= 5 x 10 x 10 = 500J

So: 500 = ½ x m x v²

v² = (500 x 2) / 10 = 100

Remember to square root both sides so:

v = 10m/s

## Sankey Diagrams

Sankey diagrams are used to show **efficiency of energy transfers**. They are simple to use and so are easy marks!

Often you will be asked to fill in one of the missing values when given the other two. Remember that the **total in must equal the total out**.

The **line width** of the arrow represents **how much energy is being transferred**. You may be asked to take a look at the **scale** (i.e. one box = 10J).

Try this: how much energy is being wasted?Answer: 50J - 36J = 14J

- What is the kinetic energy of a 3kg ball that is rolling at 2m/s?
- 6J
- What is the gravitational energy of a ball that is on the ground?
- 0J

Explanation:*The ball cannot fall, h=0* - What is the spring constant of a spring that took 0.7J of energy to stretch it 5cm?
- 560N/m