Section 3.6: Efficiency
Efficiency measures how effectively a machine converts input energy (or work) into useful output energy (or work). It is always less than or equal to 100% due to energy losses (e.g., friction, heat).
\( \text{Efficiency} (\%) = \frac{\text{Useful Work Output}}{\text{Total Work Input}} \times 100 \)
Notes:
- Efficiency is unitless and expressed as a percentage.
- Energy losses reduce efficiency.
- For electrical devices: \( \text{Efficiency} = \frac{\text{Output Power}}{\text{Input Power}} \times 100 \)
Example 1
A motor does 500 J of useful work while consuming 600 J of energy. Find its efficiency.
\( \text{Efficiency} = \frac{500}{600} \times 100 = 83.3\% \)
Example 2
An electric heater converts 1500 J of electrical energy into 1200 J of heat energy delivered to a room. Calculate efficiency.
\( \text{Efficiency} = \frac{1200}{1500} \times 100 = 80\% \)
Practice Problems
- A crane lifts a 2000 N load 5 m while consuming 12000 J of work. Find the efficiency of the crane.
- A light bulb consumes 60 W of electrical power and emits 5 W as light. Calculate the efficiency.
- An engine produces 8000 J of useful work while consuming 10000 J. Determine its efficiency.
- A pump lifts 500 kg of water 10 m using 60000 J of energy. Find the efficiency.
- A machine requires 1000 J of input energy and delivers 750 J of useful work. Calculate efficiency.
- A motor delivers 200 W mechanical power but consumes 250 W electrical power. Find efficiency.
- An electric fan uses 50 W of power and moves air using 35 W. Determine its efficiency.
- A battery delivers 1000 J of energy to a load but stores 1200 J initially. Find efficiency.
- A lift consumes 5000 J to raise a load 4000 J. Calculate its efficiency.
- A gasoline engine converts 40000 J of chemical energy into 30000 J of mechanical work. Find efficiency.