Science 8 · Mechanical systems
Every machine trades force for distance
A bicycle, a can opener and an excavator are all systems of simpler parts passing force and motion along. This unit takes them apart: the simple machines inside, gears, the work machines do and waste, and the liquids that let a small push lift a car.
- 1. The words, first
- 2. Simple machines, and machines as systems
- 3. Gears, speed ratios and force
- 4. Work, energy and efficiency
- 5. Hydraulics and pneumatics
- 6. What costs marks
The words, first
The idea: Mechanical advantage compares forces and speed ratio compares turns. Neither one is efficiency.
| Word | What it means |
|---|---|
| Machine / simple machine | A device that makes a task easier by changing the size or direction of a force / one of the six basic ones: lever, wheel and axle, pulley, inclined plane, wedge and screw. |
| System / subsystem / component | Parts working together for one purpose / a smaller system inside it, with its own job / a single part. |
| Input force / output force | The force you put into a machine, also called the effort / the force the machine puts on the load. |
| Fulcrum | The point a lever turns on. |
| Mechanical advantage (MA) | Output force ÷ input force: how many times a machine multiplies your force. Also called the force ratio. |
| Gear / driving / driven | A wheel with teeth / the gear turned by you or a motor / the gear it turns. Gears meshed together make a gear train. |
| Speed ratio | Turns of the driving gear for each turn of the driven gear. |
| Work (W) / joule (J) | Force × the distance moved in the direction of the force / the unit of work and energy: 1 J is a force of 1 newton moving something 1 metre. |
| Efficiency | Output work ÷ input work × 100%. |
| Friction | A force that resists surfaces sliding over each other, turning some energy into heat. |
| Pressure | Force ÷ area (Unit A). |
| Hydraulics / pneumatics | Using a liquid under pressure to pass a force along / using compressed air. |
| Piston | A plug that slides inside a cylinder, pushing on a fluid or pushed by it. |
Simple machines, and machines as systems
The idea: Every machine is built from simple machines, and every one trades something: less force, but over a longer distance.
| Simple machine | How it works | Examples |
|---|---|---|
| Lever | A bar turning on a fulcrum | Seesaw, crowbar, wheelbarrow, hockey stick |
| Wheel and axle | A large wheel fixed to a small axle, turning together | Doorknob, screwdriver, steering wheel |
| Pulley | A wheel with a rope; changes a force's direction, and several together reduce it | Flagpole, crane, window blind |
| Inclined plane | A slope: a smaller push over a longer path | Ramp, a road winding up a hill |
| Wedge | Two slopes back to back, forcing things apart | Axe, knife, doorstop |
| Screw | An inclined plane wrapped round a post | Jar lid, bolt, wood screw |
mechanical advantage = output force ÷ input force
Worked. A student pushes down on a crowbar with 150 N and lifts one edge of a rock with a force of 600 N. MA = 600 ÷ 150 = 4. Nothing is free: her end of the bar moves about four times as far as the rock does.
Machines as systems. A bicycle's drive subsystem — pedals, cranks, chain, gears — carries force from your legs to the back wheel. Steering sets the direction and braking slows it. Inside them are simple machines: each pedal and crank is a wheel and axle, each brake lever a lever. If the chain comes off, the drive fails and the bike goes nowhere, though every other part is fine.
Better over time. Ancient Egyptians lifted water a bucket at a time with the shadoof, a weighted lever. The Archimedes screw, turning inside a tube, lifts a steady stream. Electric pumps do most of it now: the same need, met faster.
Gears, speed ratios and force
The idea: When a small gear turns a big one, the big one turns more slowly but with more turning force. The teeth tell you by how much.
speed ratio = teeth on the driven gear ÷ teeth on the driving gear
Worked. A 12-tooth driving gear turns a 36-tooth driven gear. Speed ratio = 36 ÷ 12 = 3, often written 3:1: the big gear turns once for every three turns of the small one. If the small gear turns 90 times a minute, the big one turns 90 ÷ 3 = 30 times. Some books write the ratio the other way up, so say it in words too: “the driving gear turns 3 times for each turn of the driven gear.”
Speed or force, not both. The slower driven gear turns with more turning force: ideally three times as much, a little less because of friction. Let the big gear drive the small one instead, and the small one spins three times as fast with a third of the force. Meshed gears turn in opposite directions; gears joined by a chain turn the same way.
Worked: bicycle gears. A 42-tooth front gear drives a 14-tooth rear gear through the chain. Speed ratio = 14 ÷ 42 = 1/3: the back wheel turns 3 times for each turn of the pedals, fast on flat ground. On a hill, a bigger rear gear means fewer wheel turns per pedal turn, and an easier push.
Work, energy and efficiency
The idea: Work is done when a force moves something. A machine can reduce the force you need, but never the work, and some of the work you put in is always turned to heat by friction.
work = force × distance · W = F × d · newtons × metres = joules
efficiency = output work ÷ input work × 100%
Worked: a ramp. A mover needs to get a 200 N box onto a platform 1.5 m high. Lifting it straight up takes a force of 200 N. Instead he pushes it 5.0 m up a ramp with a force of 80 N.
- Output work, what the job needs: 200 N × 1.5 m = 300 J.
- Input work, what he actually does: 80 N × 5.0 m = 400 J.
- Efficiency: 300 ÷ 400 × 100% = 75%. Mechanical advantage: 200 ÷ 80 = 2.5.
The ramp let him push with 80 N instead of lifting with 200 N, but over 5.0 m instead of 1.5 m, and in total he did more work, not less. With no friction, 300 J over 5.0 m would need a push of only 300 ÷ 5.0 = 60 N. The other 20 N went into overcoming friction, and the extra 100 J became heat.
No machine is 100% efficient. Friction in every joint, axle and gear turns some input work into heat. The energy is not destroyed; it just does nothing useful. Oil, grease and ball bearings cut friction.
No movement, no work. Holding a heavy box still is tiring, but it does no work on the box, because the box does not move.
Hydraulics and pneumatics
The idea: Push on a liquid in a closed system and the pressure spreads equally through all of it. A small force on a small piston becomes a large force on a large piston, which moves only a short way.
Pascal's principle. In the 1600s, Blaise Pascal showed that pressure applied to a fluid in a closed container is passed on equally to every part of it, in every direction. Hydraulic machines use liquids because they barely compress, so the push is passed on, not soaked up.
Worked: a hydraulic jack. Push down on the 2 cm² piston with 50 N:
pressure = 50 N ÷ 2 cm² = 25 N on every square centimetre, everywhere in the liquid
Each of the large piston's 40 square centimetres is pushed up with 25 N, so its force is 25 × 40 = 1000 N: twenty times the push. The price is distance. Pushing the small piston down 20 cm moves 20 × 2 = 40 cm³ of liquid, which lifts the large piston only 40 ÷ 40 = 1 cm. Work in: 50 N × 0.20 m = 10 J. Work out: 1000 N × 0.01 m = 10 J, before friction takes its share.
Where you find them. Hydraulics: car brakes, excavators, garage lifts, a barber's chair. Pneumatics: jackhammers, nail guns, the air brakes on buses and big trucks. Air compresses, so pneumatic machines are a little springy and less precise, but air is free, and a leak sprays nothing but air. That is also why air in a car's brake lines is a fault: the pedal feels spongy, because pushing it squeezes the bubbles first.
What costs marks
The idea: Six, and the first is the idea the whole unit is built on.
- Thinking a machine saves work. It reduces the force and makes up for it with distance.
- Flipping the speed ratio. Driven teeth ÷ driving teeth: 36 ÷ 12 = 3. Then check it in words.
- Calling mechanical advantage efficiency. MA compares forces; efficiency compares work and is never above 100%.
- Using centimetres in W = F × d. 50 N over 20 cm is 50 × 0.20 = 10 J, not 1000 J.
- Saying the big piston moves as far as the small one. Twenty times the force means a twentieth of the distance.
- Counting work when nothing moves. No distance, no work.