OPOpenPithMake curiosity visiblePhysics lab / Simple machines

About this lab

Five experiments, one thread: saving force costs distance.

Levers, pulleys, ramps and wheels look different, but they share one fact: without friction, the work you do equals the energy the load gains. Use less force and your hand must travel farther; no machine saves both force and distance. The last experiment adds friction and the machine’s own weight: total work always exceeds useful work, so efficiency is always below 100 %.

Every reading, curve and table row comes from the same physical model, not a pre-drawn animation. Change one parameter and all the data is recalculated together.

What the five experiments show

Five common ideas, overturned by data

01 Lever: “the arm is the distance from the pivot to where you push”

Two masses hang 15 cm left of the pivot and the meter pulls straight down 10 cm to the right: it reads 1.47 N. Keep the same point but pull 60° from vertical and it reads 2.94 N. The arm is the distance from the pivot to the line of the force; at 60° it halves, so the force doubles. The law of the lever is F₁l₁ = F₂l₂.

02 Pulleys: “a fixed pulley saves force, and pulling another way changes it”

Four masses on a fixed pulley read 1.96 N whether you pull straight down or at an angle: a fixed pulley only changes direction. With a 50 g movable pulley it reads 1.23 N, a little more than half, because the pulley must be lifted too; the rope end moves twice as far as the load.

03 Ramp: “a longer ramp saves force, so it saves work too”

Pull the same crate up a 30 cm high wooden ramp: the 0.5 m ramp needs 4.31 N and 2.16 J; the 1 m ramp needs only 3.11 N but 3.11 J. The useful work is 1.47 J both times. A longer ramp saves force, but the path is longer and friction wastes more work.

04 Windlass: “a wheel and axle saves both force and distance”

With a 25 cm crank on a 5 cm axle, a 3 kg bucket needs only 5.88 N at the handle, a fifth of its weight; but to raise it 50 cm the hand travels 2.5 m around the circle. FR = Gr: what you save in force you pay in distance.

05 Efficiency: “a machine’s efficiency is fixed, whatever it lifts”

The same pulley block is only 30.7 % efficient with one mass and 76.8 % with ten: the extra work from the pulley’s weight and friction changes little, so more useful work means a larger share. Efficiency does not depend on the height lifted, and it is always below 100 %.

Model and sources

Model and sources

  • Lever: F₁l₁ = F₂l₂; the arm l is the distance from the pivot to the line of the force, so pulling at α gives l₁ = L₁·cosα.
  • Pulleys: ignoring rope weight and friction, F = (G + G_pulley) / n and the rope end moves s = n·h.
  • Ramp: F = G sinθ + μG cosθ; W_useful = Gh, W_total = FL.
  • Wheel and axle: FR = Gr; one turn moves the hand 2πR and lifts the bucket 2πr.
  • Efficiency: η = W_useful / W_total = G / (nF).

g is the textbook 9.8 N/kg and each mass is 50 g. Every process is slow and steady: the pull comes from balance, with no change in kinetic energy. The ramp friction coefficients (rollers 0.02, steel 0.15, wood 0.35) and the axle friction (each pulley passes on 96 % of the tension) are teaching assumptions for comparison only. Arrow lengths are only proportional sketches.

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