# 1.20 The Principle of Conservation of Energy

## The Principle of Conservation of Energy

• The principle of conservation of energy is a law of Physics which always applies to a closed system • To apply conservation of energy, heat losses are usually ignored during the calculation stage
• In reality there are always some energy losses from the system
• These should be mentioned when comparing calculated, ideal values to real-life situations

• Conservation of energy is often applied in questions about exchanges between kinetic energy and gravitational energy
• Common examples include:
• A swinging pendulum
• Objects in free fall
• Sports such as skiing or skydiving where gravity is causing motion and few drag forces apply

• The gravitational potential energy stored initially is transferred to kinetic energy, or vice versa
• This allows either;
• Final velocity to be found from the distance the object moved, or
• Height of a drop from the final velocity

#### Worked example

The diagram below shows a skier on a slope descending 750 m at an angle of 25° to the horizontal. Calculate the final speed of the skier, assuming that he starts from rest and 15% of his initial gravitational potential energy is not transferred to kinetic energy.

Step 1: Write down the known quantities • Vertical height, h = 750 sin 25°
• Ek = 0.85 Ep

Step 2: Equate the equations for Ek and Egrav

Ek = 0.85 Egrav

½ mv2 = 0.85 × mgh

Step 3: Rearrange for final speed, v Step 4: Calculate the final speed, v #### Exam Tip

Gravitational energy:

• This equation only works for objects close to the Earth’s surface where we can consider the gravitational field to be uniform.

Kinetic energy:

• When using the kinetic energy equation, note that only the speed is squared, not the mass or the ½.
• If a question asks about the ‘loss of kinetic energy’, remember not to include a negative sign since energy is a scalar quantity. ### Get unlimited access

to absolutely everything:

• Unlimited Revision Notes
• Topic Questions
• Past Papers 