What a learner can do afterwards
- Calculates efficiency as a percentage from given input and useful output energy values
- Draws a Sankey diagram to represent energy transfers in a device, with arrow widths proportional to energy amounts
- Uses W = Fd to calculate work done when a force moves through a distance
- Identifies which energy transformations in a Sankey diagram are useful and which are wasted
- Calculates work against gravity using weight = mg and work = mgh near Earth's surface.
- Calculates useful output energy or work from a percentage efficiency and total input.
1 · Read
Efficiency compares useful output energy with total input: efficiency (%) = useful ÷ input × 100. For the same useful job, a more efficient machine needs less input energy. Some output may be unwanted heat, sound, or light. A lamp's light is useful; its heat is usually wasted. When all output is counted as useful or wasted, useful = input minus wasted. To find useful output from efficiency, multiply input by efficiency ÷ 100.
In a model heater, 500 J enters. It transfers 450 J as useful heat to water and 50 J as unwanted sound. Efficiency = 450 ÷ 500 × 100 = 90%. The remaining 10% is wasted in this model.
A Sankey diagram uses arrow widths proportional to energy amounts. One input arrow splits into useful and wasted outputs. Twice the width means twice the energy. Outgoing widths add to the incoming width because energy is conserved. A large useful share means high efficiency. In a car engine, energy not transferred usefully can heat the engine and surroundings, or leave as sound.
Work transfers energy through a force. For a constant force along the motion, W = F × d: work in joules, force in newtons, distance in metres. A 20 N push along a trolley's 5 m motion does 100 J of work. To lift against gravity, use weight F = mg, so work = mgh. Here m is mass in kilograms, g is gravitational acceleration, and h is the height gained in metres.
Efficiency compares useful output with input. Sankey widths show energy amounts. For a constant force along the motion, work = force × distance.
2 · Watch
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Where it sits
Where this leads
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14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.