Work, GPE & KE

GPE is gravitational potential energy
KE is kinetic energy
In many situations, energy is transferred between the GPE and KE stores

Whenever mechanical work is done (when a force acts over a distance), energy is transferred mechanically
- This is a consequence of conservation of energy

The amount of energy transferred (in joules) is equal to the work done (in joules or newton-metres)

energy transferred (J) = work done (J or N m)

GPE and KE calculations

In a perfect energy transfer, there is no wasted energy
Energy transfers can be assumed to be perfect if the wasted energy transfer is negligible
- Some exam questions will state to ignore air resistance for example
- In reality, there is no such thing as a perfect energy transfer

Ignoring wasted energy transfers is helpful in calculations because it allows energy values to be equated

Pendulums are often used as examples of perfect energy transfers
- All of the energy in the kinetic store of the pendulum is transferred mechanically into its gravitational potential store
- And then all of the energy in the gravitational potential store of the pendulum is transferred mechanically into its kinetic store
- Energy is transferred back and forth between these two stores as the pendulum swings
- Therefore, it can be said that:

$K E_{t o t a l} = G P E_{t o t a l}$

Worked example

The diagram shows a rollercoaster going down a track.

The rollercoaster takes the path A → B → C → D.

WE - Energy transfers question image, downloadable AS & A Level Physics revision notes

The rollercoaster begins at a height of 15 m above the ground and ends at ground level.

Breaking to stop the ride begins after it passes position D.

The mass of the rollercoaster is 100 kg.

Calculate the maximum speed of the rollercoaster at position D. Ignore any frictional effects before passing point D.

Answer:

Step 1: List the known quantities

Height, h = 15 m
Mass, m = 100 kg
Gravitational field strength, g = 10 N/kg

Step 2: Write out the equation for gravitational potential energy

$∆ G P E = m \times g \times ∆ h$

Step 3: Calculate the gravitational potential energy

$∆ G P E = 100 \times 10 \times 15$

$∆ G P E = 15 000 J$

Step 4: Use energy equivalency to equate the gravitational potential and kinetic energy

Frictional effects are to be ignored; therefore, a perfect energy transfer can be assumed

$∆ G P E = K E$

Step 5: Write out the equation for kinetic energy

$K E = \frac{1}{2} \times m \times v^{2}$

Step 6: Rearrange to make speed the subject:

$v = \sqrt{\frac{2 \times K E}{m}}$

Step 7: Calculate the maximum possible speed of the rollercoaster at position D

At position D the rollercoaster is at ground level
Therefore, all the energy has been transferred from the gravitational potential to the kinetic store
The maximum possible speed is based on the assumption of a perfect energy transfer

$v = \sqrt{\frac{2 \times 15 000}{100}}$

$v = 17 m / s$

Examiner Tip

When the question tells you to ignore the effects of resistance (ie wasted energy transfers), this is a clue that you may need to use energy equivalency to find the missing quantity needed for your calculation.

Work, GPE & KE (Edexcel IGCSE Physics: Double Science)

Revision Note

Work, GPE & KE

GPE and KE calculations

Worked example

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Author: Leander