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.
More to read
7.2 Kinetic Energy and the Work-Energy Theorem
For a constant force along the motion, work is force times distance. A 10 N force acting along a box's 5 m motion does 50 J of work. The net work from all forces equals the change in kinetic energy. One force's work need not all become kinetic energy: friction may transfer some energy as heat. Efficiency compares useful output with total input. In an energy Sankey diagram, arrow widths are proportional to energy amounts.
7.3 Gravitational Potential Energy
Raising a mass m through height h near Earth's surface increases gravitational potential energy by mgh. Here g is gravitational acceleration. A 2 kg book raised 1.5 m gains 2 × 9.8 × 1.5 = 29.4 J. Work against gravity supplies that gain. During a fall, gravity transfers this energy into kinetic energy; air resistance can also transfer some to the surroundings.
9.5 Simple Machines
Machines can trade force for distance. A lever can reduce the force needed to lift a rock, while your hand moves farther. Input energy equals useful output plus wasted output when all transfers are counted. Efficiency is useful output work divided by input work. At 80% efficiency, 100 J of input supplies 80 J of useful work. The other 20 J is transferred elsewhere, often as heat from friction.
How Find Amps: 3 Easy Ways to Calculate
For steady voltage and current in a direct-current circuit, electrical power equals voltage times current. Energy transferred equals power times duration. A 60 W bulb running for 10 seconds uses 600 J. If 60 J becomes useful light, its efficiency is 60 ÷ 600 × 100 = 10%.
Key Terms
Efficiency is useful output work divided by input work. The joule is the unit of work and energy. For a constant force along the motion, work equals force times distance. Mechanical advantage is output force divided by input force. Power is energy transferred per unit time. Lifting a mass m through height h near Earth's surface increases gravitational potential energy by mgh.
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