5. Efficiency and Machine Data

Real machines lose some input energy to friction and heat, so useful output work is less than input work. Efficiency is:
\[ \text{Efficiency} = \frac{\text{useful output work}}{\text{input work}} \times 100\%. \]

Reading machine data (GED® skill). For formula questions, identify what is given, write the formula, substitute units, and solve. If a table compares ramps, longer ramps usually require less force but more distance.

Deep explanation. Efficiency measures how much of the input work becomes useful output work. Real machines are never perfectly efficient because friction, deformation, sound, and heat take away some useful energy. The "lost" energy is not destroyed; it is transformed into less useful forms.

Use the formula carefully: \(\text{efficiency} = \frac{\text{useful output work}}{\text{input work}} \times 100\%\). If useful output is \(180\text{ J}\) and input is \(240\text{ J}\), efficiency is \(180/240 \times 100\% = 75\%\). The remaining \(25\%\) became less useful energy forms.

Checking answers. Output work should not be greater than input work for a real machine. An efficiency of 125 percent usually means the numerator and denominator were reversed or the wrong numbers were used.

⚠️ Common misconception: an efficiency greater than 100% is realistic. It would mean output energy exceeds input energy, violating conservation of energy.

💡 Tip: no real machine is 100% efficient.