Conservation of Energy (Cambridge (CIE) O Level Physics): Revision Note

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. E_K → ∆E_P → ∆E_P → E_K

B. E_K → ∆E_P → E_K → ∆E_P

C. ∆E_P → E_K → E_K → ∆E_P

D. ∆E_P → E_K → ∆E_P → E_K

Answer: D

• At point A:

  • The rollercoaster is raised above the ground, therefore it has energy in its gravitational potential store

  • As it travels down the track, energy is transferred mechanically to its kinetic store  

• At point B:

  • Energy is transferred mechanically from the kinetic store to the gravitational potential store

  • As the kinetic energy store empties, the gravitational potential energy store fills 

• At point C:

  • Energy is transferred mechanically from the gravitational potential store to the kinetic store

• At point D:

  • The flat terrain means there is no change in the amount of energy in its gravitational potential store, the rollercoaster only has energy in its kinetic store

  • The kinetic energy store is full

   

• In reality, some energy will also be transferred to the thermal energy store of the tracks due to friction, and to the thermal energy store of the surroundings due to sound

   

• We say this energy is dissipated to the surroundings

  • The total amount of energy in the system will be constant

  • Total energy in = total energy out

It is helpful to think of energy stores as beakers and the total energy in the system as water. The water can be poured from one beaker into another back and forth as energy is transferred between stores. 

You may not always be given the energy transfers happening in the system in exam questions. By familiarising yourself with the energy stores and transfer pathways, you will be able to relate these to the situation in the question. For example, a ball rolling down a hill is transferring energy from the ball's gravitational potential energy store to its kinetic energy store mechanically, whilst a spring transfers energy from its elastic potential energy store to its kinetic energy store mechanically.

An electric motor is used to lift a weight. The total energy transferred to the motor is 500 J and the useful energy output is 120 J.

Calculate the amount of wasted energy.

Answer:

Step 1: State the conservation of energy

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

• This means that:

$\text{Total energy in}=\text{Useful energy out}+\text{Wasted energy}$

Step 2: Rearrange the equation for the wasted energy

$\text{Wasted energy}=\text{Total energy in}-\text{Useful energy out}$

Step 3: Substitute the values

$500-120=380\text{J}$