# 2.3.6 Principle of Conservation of Energy

### Principle of Conservation of Energy

• The Principle of Conservation of Energy states that:

Energy cannot be created or destroyed, it can only be transferred from one form to another

• This means the total amount of energy in a closed system remains constant, although how much of each form there is may change

Types of Energy

Energy types can be separated into transfers or stores

#### Energy Dissipation

• When energy is transferred from one form to another, not all the energy will end up in the desired form (or place)
• Dissipation is used to describe ways in which energy is wasted
• Any energy not transferred to useful energy stores is wasted because it is lost to the surroundings
• These are commonly in the form of thermal (heat), light, or sound energy
• What counts as wasted energy depends on the system
• For example, in a television:

electrical energy ➝ light energy + sound energy + thermal energy

• Light and sound energy are useful energy transfers whereas thermal energy (from the heating up of wires) is wasted

Useful and wasted energy conversions for a television

• The energy changes in an electrical heater:

electrical energy ➝ thermal energy + sound energy + light energy

• In a gas cooker, the energy transfers are similar but the initial source of energy is different:

chemical energy ➝ thermal energy + sound energy + light energy

• In both these cases, thermal energy is useful, whereas sound and light are not

Useful and wasted energy conversions in an electric heater and gas cooker

#### Worked Example

The diagram shows a rollercoaster going down a track.
The rollercoaster takes the path A → B → C → D.

Which statement is true about the energy changes that occur for the rollercoaster down this track?

A.     KE – GPE – GPE – KE

B.     KE – GPE – KE – GPE

C.     GPE – KE – KE – GPE

D.     GPE – KE – GPE – KE

• At point A:
• The rollercoaster is raised above the ground, therefore it has GPE
• As it travels down the track, GPE is converted to KE and the roller coaster speeds up
• At point B:
• KE is converted to GPE as the rollercoaster rises up the loop
• At point C:
• This GPE is converted back into KE as the rollercoaster travels back down the loop
• At point D:
• The flat terrain means the rollercoaster only has KE

#### Applications of Energy Conservation

• Common examples of energy transfers are:
• A falling object (in a vacuum): gravitational potential energy ➝ kinetic energy
• A battery: chemical energy ➝ electrical energy ➝ light energy (if connected to a bulb)
• Horizontal mass on a spring: elastic potential energy ➝ kinetic energy

Energy transfers whilst jumping on a trampoline

• There may also be work done against resistive forces such as friction
• For example, if an object travels up a rough inclined surface, then

Loss in kinetic energy = Gain in gravitational potential energy + Work done against friction

#### Worked Example

A simple pendulum has a mass of 640 g and a length of 0.7 m. It is pulled out to an angle of 20° from the vertical.

The pendulum is released. Assuming negligible air resistance, calculate the maximum speed of the pendulum bob as it passes through the vertical position.

#### Spring Energy Conservation

• When a vertical spring is extended and contracted, its energy is converted into other forms
• Although the total energy of the spring will remain constant, it will have changing amounts of:
• Elastic potential energy (EPE)
• Kinetic energy (KE)
• Gravitational potential energy (GPE)
• When a vertical mass is hanging on a spring and it moves up and down, its energy will convert between the three in various amounts

• At position A:
• The spring has some EPE since it is slightly compressed
• Its KE is 0 since it is stationary
• Its GPE is at a maximum because the mass is at its highest point
• At position B:
• The spring has some EPE since it is slightly stretched
• Its KE is at a maximum as it passes through the equilibrium position at its maximum speed
• It has some GPE since the mass is still above the ground
• At position C:
• The spring has its maximum EPE because it is at its maximum extension
• Its KE is 0 since it is stationary
• Its GPE is at a minimum because it is at its lowest point above the Earth’s surface
• For a horizontal mass on a spring system, there is no gravitational potential energy to consider. The spring only converts between kinetic and elastic potential energy
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