## Changes in Energy

You need to be able to calculate changes in energy in a variety of different situations:

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The energy associated with a moving object

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The energy associated with a stretched spring

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The energy associated with an object raised above ground level.

###### Gravitational Potential Energy (G.P.E.)

Gravitational potential energy is the energy an object possesses because of its position in a gravitational field. When you lift an object some of your muscles transfer chemical energy, stored in the muscles, to the gravitational energy store of the object.

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The gravitational potential energy of an object depends on it's

- Mass

- Height

- The gravitational field strength acting upon it.

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This is why astronauts on the moon can lift objects more easily as the gravitational field strength on the Moon is around 6x weaker than on Earth.

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To work out the gravitational potential energy use the following equation:

Gravitational potential energy = Mass x Gravitational Field Strength x Height

(joules, J) (kg) (N/kg) (m)

###### Kinetic Energy (K.E.)

The energy of an object in motion is called its kinetic energy. It is dependent upon both its mass and speed. The formula for kinetic energy is:

Kinetic energy = 1/2 x mass x velocity²

(joules,J) (kg) (m/s)²

###### Linking G.P.E. and K.E.

What goes up, must come down. In the example shown as the rollercoaster carriage moves down the track the energy is transferred directly from G.P.E. to the K.E.

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From the example you should be able to work out the G.P.E or K.E. at any height.

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You should also be able to work out the K.E. at the end of the track.

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###### Elastic Potential Energy (E.P.E.)

When a rubber band or bungee cord is stretched then it contains a store of energy which is known as its elastic potential energy.

We can wor out how much energy is stored in a stretched elastic object using the following formula:

Elastic Potential Energy = 1/2 x Spring Constant x Extension²

(joules,J) (N/m) (m)²

Hooke's Law states that the extension of a spring is directly proportional to the force applied to it. We can use this to calculate the spring constant. Take any two points on a graph plotting extension against force and work out the gradient.