Efficiency (AQA GCSE Combined Science: Trilogy: Physics): Revision Note

An electric motor has an efficiency of 35%. It lifts a 7.2 kg load through a height of 5 m in 3 s. Gravitational field strength = 9.8 N/kg.

Calculate the power of the motor.

Answer:

Step 1: List the known quantities

• Efficiency = 35%

• Mass of the load, m = 7.2 kg

• Height, h = 5 m

• Time, t = 3 s

• Gravitational field strength, g = 9.8 N/kg

Step 2: Write down the efficiency equation

• This equation is given on the Physics Equations Sheet. The question is about power, so use the power version:

$\text{efficiency}=\frac{\text{useful power output}}{\text{total power input}}$

Step 3: Convert the efficiency to a decimal

• Divide the percentage by 100:

$\text{efficiency}=\frac{35}{100}=0.35$

Step 4: Calculate the useful energy output

• The useful energy output is the energy transferred to the gravitational potential store of the load as it is lifted:

$E_p=m\times g\times h$

$E_p=7.2\times 9.8\times 5$

$E_p=352.8\text{ J}$

Step 5: Calculate the useful power output

• Power is the energy transferred per second, so divide the useful energy output by the time taken:

$\text{useful power output}=\frac{E}{t}=\frac{352.8}{3}$

$\text{useful power output}=117.6\text{ W}$

Step 6: Rearrange the efficiency equation to make total power input the subject

$\text{total power input}=\frac{\text{useful power output}}{\text{efficiency}}$

Step 7: Substitute the values and calculate the total power input

$\text{total power input}=\frac{117.6}{0.35}$

$\text{total power input}=336\text{ W}$

• The power of the motor is its total power input, 336 W

Efficiency can be given in a ratio (between 0 and 1) or percentage format (between 0 and 100%)

If the answer is required as a percentage, remember to multiply the ratio by 100 to convert it: if the ratio = 0.25, percentage = 0.25 × 100 = 25%

Only multiply by 100 when the question asks for a percentage. When you calculate a power or an energy from an efficiency (for example 0.75 × 0.24 W), do not multiply the final answer by 100. Convert a percentage efficiency to a decimal first (35% = 0.35)

Remember that efficiency has no units

To find an efficiency or a proportion from two energy values, divide useful output by total input. Subtracting the two values gives the wasted energy, not the efficiency. Check that both values use the same unit (for example kW and W) before you divide

Match the equation to the quantities in the question. If the question gives energy, use the energy equation. If it gives power, use the power equation. Do not mix the two (for example useful power output over total input energy)