Solved Examples: Calculating Efficiency in Mechanical Systems

📚 Quick Study Guide

• 🔍 Efficiency Definition: Efficiency is the ratio of useful energy output to the total energy input, usually expressed as a percentage.
• 💡 Formula: Efficiency ($\eta$) = $\frac{Output}{Input}$ x 100%
• 📝 Power: Power (P) is the rate at which energy is transferred or converted. It's often used in efficiency calculations. $P = \frac{Energy}{Time}$
• ⚙️ Mechanical Systems: These involve forces, motion, and energy transfer through mechanical components like gears, levers, and engines.
• 🌡️ Losses: Real-world systems always have losses due to friction, heat, and other factors, making efficiency always less than 100%.
• 🔢 Units: Ensure all values are in consistent units (e.g., Joules for energy, Watts for power) before calculating efficiency.

Practice Quiz

1. A motor consumes 1000 J of electrical energy to lift a 20 kg mass by 4 meters. What is the efficiency of the motor? (g = 9.8 m/s²)

   1. 28.4%
   2. 78.4%
   3. 68.4%
   4. 58.4%

2. An engine produces 5000 J of mechanical work while consuming 8000 J of fuel energy. What is the engine's efficiency?

   1. 52.5%
   2. 62.5%
   3. 72.5%
   4. 82.5%

3. A pump uses 250 W of power to lift water to a height of 5 meters at a rate of 2 kg/s. What is the efficiency of the pump? (g = 9.8 m/s²)

   1. 39.2%
   2. 49.2%
   3. 29.2%
   4. 59.2%

4. A gearbox has an input power of 100 W and an output power of 85 W. What is the efficiency of the gearbox?

   1. 95%
   2. 75%
   3. 85%
   4. 65%

5. A lever requires 50 J of input work to produce 40 J of output work. What is the efficiency of the lever?

   1. 60%
   2. 80%
   3. 70%
   4. 90%

6. An electric generator converts 3000 J of mechanical energy into 2700 J of electrical energy. Calculate the efficiency of the generator.

   1. 70%
   2. 80%
   3. 90%
   4. 60%

7. A pulley system has an efficiency of 75%. If the input work is 200 J, what is the output work?

   1. 100 J
   2. 150 J
   3. 200 J
   4. 250 J