Why Machines?
MA, VR, efficiency — and the cheat that never works
What this lesson covers
Why it matters
One mechanic lifts an 800 N engine with one hand. No magic, no muscle — a machine traded her small force over a long pull for a big force over a short lift. Machines are honest bankers: they never lend.
The idea in plain words
Three letters that grade every machine. Tap them.
MA = load/effort · VR = dE/dL · η = MA/VR
A machine lifts 800 N with 250 N of effort; VR = 4. Find MA and η.
MA = 3.2, η = 80% — 20% fed the friction
- no unit: MA — mechanical advantage — how many times the machine multiplies your force
- no unit: VR — velocity ratio — how many times farther YOU move than the load (fixed by geometry)
- fraction or %: η — efficiency = MA/VR = useful work out ÷ work in — friction keeps it below 1
- MA = 800 ÷ 250 = 3.2
- η = MA ÷ VR = 3.2 ÷ 4 = 0.8
Predict first
Can a machine ever give out MORE energy than you put in?
Machines multiply FORCE (or speed, or change direction) — never energy. Efficiency = output/input is always below 100%.
- Never — friction guarantees you get out LESS — correct
- Yes, that's what machines are for
- Yes, if it's well oiled
What you do
Lift the engine, then try to cheat the machine with a too-small effort — and see exactly why η can't beat 100%.
Check yourself
An IDEAL machine is one where…
Ideal = frictionless fiction. Real machines always have MA < VR.
VR of a machine depends on…
VR is built into the design; MA is what friction lets you actually get.
A machine with VR = 5 and η = 60% gives MA =
MA = η × VR = 0.6 × 5 = 3.
- MA = VR and η = 100% (no friction, weightless parts) — correct
- MA is greater than VR
- no effort is needed at all
- its geometry alone — arm lengths, rope count — correct
- how hard you pull
- the load's weight
- 3 — correct
- 5
- 8.3