Engineering & Technology · Forces, Energy & Simple Engineering Systems

Work, power, efficiency and mechanical advantage

A ramp can make a small model load easier to move upward, but the input point travels farther than the load rises. The reduced force is useful; it does not mean the device creates energy.

Useful preparation is Measurement, Units & Engineering Evidence and Engineering Sketches, Models & Technical Communication. Be comfortable with multiplication, division, dimensions and reading a simple graph. The lessons introduce each force, motion and energy relationship without calculus. Supplied numerical values, device records, limits and SVG models are original constructed teaching cases, not equipment specifications, safe loads or instructions to operate machinery, electrical or heating equipment.

Back to the chapter

After reading, you can

Calculate simple work, distinguish power from energy and explain why mechanical advantage does not multiply energy.

Work connects force with movement

For a constant force acting in the same direction as displacement, work = force × distance. A 1 N force acting along 1 m transfers 1 J of work. When the force opposes movement, its work on the body is negative. A force perpendicular to displacement does zero work in this simple model. If force varies, multiplying one arbitrary force reading by the full distance is not enough.

The ideal ramp illustrates the force-distance trade. It has a 2 m path and a 1 m rise. Neglect friction and move a 20 N weight slowly so that kinetic energy does not change. A 10 N input force parallel to the ramp transfers 10 × 2 = 20 J. The gravitational energy gain is also 20 × 1 = 20 J. The contact force perpendicular to the ramp contributes no work along the path.

The ramp forms a right triangle with a 2 m sloping path and a 1 m vertical rise. A 20 N weight moved slowly on the ideal frictionless ramp needs 10 N force parallel to the path. Input work is 10 N×2 m=20 J; useful gravitational energy gain is 20 N×1 m=20 J. Normal contact does no work in this model.

Power describes how fast energy is transferred

Average power = transferred energy ÷ elapsed time. One joule per second is one watt, W. A process transferring 20 J in 10 s has average power 2 W; taking 5 s gives 4 W for the same energy amount. The unit symbol W means watt here; writing “work” in words avoids confusing it with a variable sometimes also named W.

Power and energy need matching intervals and boundaries. A short peak power, an average over a complete operation and a label on a device describe different things. If power is constant, energy = power × time. For a varying record, add the energy transferred during each part; an unweighted average of unrelated readings need not describe the operation.

A force ratio and an energy ratio answer different questions

Mechanical advantage is output force magnitude divided by input force magnitude. In the ideal ramp example it is 20 ÷ 10 = 2. The input point travels twice the vertical rise, preserving energy. The same principle appears in levers and gears, though their motion and force definitions must be specified carefully.

For the stated task, energy efficiency is useful energy delivered divided by supplied energy over the same interval. Real inputs can also increase stored energy or supply other outputs, such as warming and sound. Call an output useful because it serves the task, not because it keeps a preferred percentage high. A force advantage larger than one can coexist with an energy efficiency below one.

Add a recorded nonideal input to the ramp model

The ideal ramp transfers 20 J into the load’s gravitational energy. Suppose a separate constructed operating record for the same rise gives 25 J total supplied work, with no change in the device’s stored energy. The other 25 − 20 = 5 J must be accounted for in other destinations.

Useful-energy efficiency is 20 ÷ 25 = 0.8, or 80%. If the operation lasts 10 s, useful average power is 20 ÷ 10 = 2 W and supplied average power is 25 ÷ 10 = 2.5 W. The remaining average rate is 0.5 W.

The ideal 10 N input is not automatically the actual force in this nonideal record. If the real input force is constant and parallel over the full 2 m, its value would be 25 ÷ 2 = 12.5 N. Keep the ideal model and the supplied operating record identifiable instead of combining their favorable features.

Try the reasoning

A stationary support exerts a force on a motionless load. Has that force necessarily done mechanical work on the load during this interval?
Show the answer and reasoning
No. With zero displacement of its point of application in this simple model, the work is zero. Force can exist without that work transfer.
Two operations each transfer 20 J, one in 5 s and one in 10 s. Which has greater average power?
Show the answer and reasoning
The 5 s operation: 4 W rather than 2 W. The energy amounts are equal.
Does a mechanical advantage of two establish 200% energy efficiency?
Show the answer and reasoning
No. It is a force ratio. The ideal motion trades force for travel, and real energy accounting also includes other destinations and storage changes.

What to carry forward

Work combines force with displacement, power adds time and efficiency needs a declared useful output. Force multiplication does not create energy.

References

Teaching resources and research supporting this lesson’s explanations and examples.