D. Structures and Mechanisms · Systems in Action

Efficiency: Where Does the Energy Go?

D2.4 D2.7 D2.5 A1.2About 50 minutes

Learning goals

I can calculate the efficiency of a mechanical system from its work input and useful work output.
I can explain why no real machine is 100% efficient.
I can identify ways energy dissipates from mechanical systems (friction, sound, vibration, air resistance).
I can describe technological innovations that make mechanical systems more efficient.

Words to know

efficiency
The percentage of the input energy (or work) that becomes useful output. Efficiency = useful output ÷ input × 100%.

work input
The work you put into a machine: input force × input distance.

useful work output
The work the machine does on the load: output force × output distance.

dissipate
To spread out as forms that are not useful for the job, mostly thermal energy, so it cannot easily be used again.

friction
A force that resists motion when surfaces rub. It turns some kinetic energy into thermal energy.

law of conservation of energy
Energy cannot be created or destroyed. It can only change form or move from place to place.

lubricant
A substance, like oil or grease, that reduces friction between moving parts.

Hook: rub your hands

Rub your hands together quickly for ten seconds. They get warm. The work your arm muscles did did not disappear. It turned into thermal energy because of friction.

The same thing happens inside every machine: in a bicycle chain, in a car's wheel bearings, in a pulley's axle. Some of the energy you put in becomes warmth and sound instead of useful work. Engineers call this energy dissipated.

Close-up of a bicycle's rear gears, derailleur and oily chain. — Every link of the chain rubs on the gears. Oil reduces this friction, so less energy is dissipated as heat and sound. AI-generated image

Energy is never lost, but it can be wasted

The law of conservation of energy says energy cannot be created or destroyed. So where does the "lost" energy go? It dissipates: it spreads out into forms that do not help with the job.

Friction between moving parts turns energy into thermal energy.
Sound: squeaks, rattles and engine noise carry energy away.
Vibration: shaking parts use up energy.
Air resistance (drag) pushes against moving objects.
Electrical resistance warms wires and motors.

Because of this, the useful work output of a machine is always less than its work input.

Calculating efficiency

Efficiency = useful work output ÷ work input × 100%

Work input = input force × input distance
Useful work output = output force × output distance

Efficiency is always less than 100% for a real machine. A higher percentage means less energy is wasted.

Note: in Grade 7 you used "efficiency of a structure" to mean how much load a structure holds compared with its own mass. In this unit, efficiency means how much input energy becomes useful output.

Energy bars for the pulley in Example 1. Of the 1 000 J of work put in, 800 J lifted the box. The other 200 J was dissipated, mostly as thermal energy from friction, plus some sound. Efficiency = 80%.

Worked example

Example 1: Efficiency of a pulley system

A movable pulley lifts a 400 N box 2 m. The worker pulls with 250 N and pulls 4 m of rope. Find the work input, the useful work output and the efficiency. How much energy was dissipated?

Useful work output = 400 N × 2 m = 800 J.
Work input = 250 N × 4 m = 1 000 J.
Efficiency = 800 ÷ 1 000 × 100% = 80%.
Energy dissipated = 1 000 J − 800 J = 200 J, mostly thermal energy from friction in the pulley.

Efficiency = 80%; 200 J dissipated.

Worked example

Example 2: Efficiency of a ramp

Movers push a 500 N box up a ramp 4 m long onto a truck 1 m high. They push with 160 N. Find the efficiency.

Useful work output (lifting the box) = 500 N × 1 m = 500 J.
Work input = 160 N × 4 m = 640 J.
Efficiency = 500 ÷ 640 × 100% = 78.125%, about 78%.
140 J was dissipated by friction between the box and the ramp.

About 78% efficient.

Worked example

Example 3: Working backward

An electric winch is 75% efficient. It must do 300 J of useful work lifting a load. How much energy must go in?

Efficiency = output ÷ input, so input = output ÷ efficiency.
Input = 300 J ÷ 0.75 = 400 J.
Check: 300 ÷ 400 × 100% = 75%. ✓

400 J of input energy.

Innovations that make mechanical systems more efficient

Engineers fight energy dissipation in many ways:

Lubricants (oil and grease) let parts slide smoothly over each other. Engines, bike chains and door hinges all need them.
Ball bearings and roller bearings let wheels and axles roll instead of rubbing. Rolling friction is much smaller than sliding friction. Skateboards, bicycles, fans and cars all use bearings.
Streamlined shapes reduce air resistance. Think of a racing cyclist's helmet or the smooth nose of a high-speed train.
Low rolling-resistance tires and keeping tires properly inflated reduce energy wasted as tires squish.
Regenerative braking in electric and hybrid vehicles uses the motor as a generator when slowing down, turning some kinetic energy back into electrical energy stored in the battery instead of all of it becoming thermal energy in the brakes.
Lighter, stronger materials (like aluminum and carbon fibre) mean less energy is needed to move the machine itself.
Heat recovery: some systems capture waste thermal energy and reuse it, like the milk plant in the food processing lesson.
Maintenance: clean, tight, well-adjusted machines waste less energy.

Inside a ball bearing, with its side cover removed. The balls roll between the inner and outer rings, so the parts do not rub. Rolling friction is much smaller than sliding friction, so less energy is dissipated as thermal energy.

Efficiency = actual MA ÷ ideal MA

For simple machines, there is a shortcut: efficiency = actual MA ÷ ideal MA × 100%. In Example 1, actual MA = 400 ÷ 250 = 1.6 and ideal MA = 2, so efficiency = 1.6 ÷ 2 × 100% = 80%, the same answer.

Just for fun

That squeak from a rusty door hinge? That is energy escaping as sound. A drop of oil is basically a mute button for wasted energy.

Hands-on activity

Ramp friction test

You need: a smooth board or large cutting board as a ramp, books to prop it up, a small box with some cans or rice inside, a toy car or truck that the box can ride on (or 3 round pencils as rollers), a thick elastic band, a paper clip, a ruler, tape.

Safety: elastic bands can snap. Hold the band at arm's length, point it away from faces and do not over-stretch it. Keep the ramp low and stable.

Hook the elastic band to the box with the paper clip. Calibrate: hold the box hanging straight down from the band. Measure the band's stretch in cm. This represents the box's weight.
Prop the ramp so its top is a measured height (for example 15 cm). Measure the ramp's length along the slope.
Pull the box slowly and steadily up the ramp. Measure the stretch while it moves. This represents the input force.
Repeat with the box riding on the toy car (or rollers).
Estimate the efficiency each time: (stretch hanging × height) ÷ (stretch on ramp × length) × 100%. Because the stretch of the band grows with the force (roughly in step with it for small stretches), the stretch can stand in for force.

What to look for: the sliding box needs more stretch, so its efficiency is lower. The wheels reduce friction and give a higher efficiency. Results will not be exact, so repeat each test 3 times and average (A1.2). Explain the difference using the words friction, thermal energy and efficiency.

Your turn

What is efficiency?

A machine takes in 500 J and does 350 J of useful work. What is its efficiency?

Why can no real machine be 100% efficient?

Name two ways energy dissipates from a moving bicycle.

A pulley lifts a 300 N load 1.5 m. The input force is 200 N pulled over 3 m. Find the efficiency.

Name two innovations that reduce friction in machines.

How does regenerative braking make an electric car more efficient?

More practice: warm-up

What is the unit of energy?

Can energy be created or destroyed?

A machine has 100 J of input and 80 J of useful output. What is its efficiency?

What form of energy does friction mostly produce?

Why do we oil a squeaky hinge?

More practice: on your own

A 450 N box is pushed up a ramp 4 m long to a height of 0.8 m with a force of 120 N. Find the efficiency.

An electric motor is 60% efficient. It takes in 2 000 J of electrical energy. How much useful work does it do, and how much energy is dissipated?

A block and tackle with IMA 4 lifts a 1 000 N load 0.5 m. The worker pulls 320 N over 2 m. Find the actual MA and the efficiency.

Why do under-inflated car tires waste fuel?

Describe one technological innovation that makes a bicycle more efficient and explain how.

Challenge

A pulley system has an IMA of 5 and an actual MA of 4. What is its efficiency? Explain why the shortcut efficiency = actual MA ÷ IMA works.

An advertisement claims a new pulley is 110% efficient. Explain why this is impossible.

A 400 N box is pushed up a 4 m ramp to a height of 1 m. On a smooth ramp it takes 125 N. On a carpeted ramp it takes 160 N. Find both efficiencies. Which ramp dissipates more energy, and how much more?

Check your understanding

Quiz

Which formula gives efficiency?

A machine takes in 200 J and does 150 J of useful work. Its efficiency is...

Energy dissipated by friction mostly becomes...

Which innovation mainly reduces friction?

Which efficiency is possible for a real machine?

Regenerative braking turns some of a car's kinetic energy into...

Why is your hand warm after you rub it on the carpet?

For parents and teachers

Big idea (D2.4, D2.7): Students use the terms energy and efficiency and identify ways energy dissipates from mechanical systems, and describe technological innovations that make these systems more efficient. Efficiency = useful work output ÷ work input × 100%. Energy is conserved, but some always dissipates (mostly as thermal energy from friction), so real machines are below 100%.

How to help: Notice dissipation in daily life: a warm laptop, a squeaky bike, a hot car brake after driving down a hill. Ask, "Where did that energy come from? What could reduce it?" The ramp activity uses an elastic band as a homemade force meter; a luggage scale or spring scale works even better if you have one.

Common difficulties:

Putting input on top. Useful output always goes on top, so efficiency is under 100%.
Forgetting distances. Efficiency uses work (force × distance), not just force.
Thinking energy is destroyed. It is dissipated (spread out), not destroyed.
Mixing with Grade 7's structural efficiency. That compared load mass with structure mass; this is about energy.