Conservation of Energy Calculations (SQA National 5 Physics): Revision Note

The diagram shows a rollercoaster going down a track.

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

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

The breaking which stops the ride begins after it passes position D.

The mass of the rollercoaster is 105 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 = 105 kg

• Gravitational field strength, g = 9.8 N/kg

Step 2: Write out the appropriate relationship

$E_p=mg∆h$

Step 3: Substitute in the known values to calculate the E_p

$E_p=105\times 9.8\times 15$

$E_p=15435\mathrm{J}$

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

$E_p=E_k$

Step 5: Write out the appropriate relationship

$E_k=\frac{1}{2}m{v}^2$

Step 6: Rearrange to make speed the subject:

$v=\sqrt{\frac{2\times E_k}{m}}$

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 converted from gravitational potential to kinetic energy E_p

• The maximum possible speed is based on the assumption of a perfect energy transfer

$v=\sqrt{\frac{2\times 15435}{105}}$

$v=17.146\mathrm{m}{\mathrm{s}}^{-1}$

Step 8: Round to an appropriate number of significant figures

• The least precise input value is 2 s.f.

• Therefore, the final answer can only be given to the same precision

$v=17\mathrm{m}{\mathrm{s}}^{-1}\left(2\mathrm{s}.\mathrm{f}.\right)$

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.