A wheel can change direction
With the fixed pulley, pulling the free end down raises the crate by the same distance. The pulley changes direction, but one rope segment supports the moving load. Its ideal force advantage is one.
How can a small pull lift a heavy load?
Rerig a dock crane. Pull the same length of rope, watch the crate rise, and see what you trade for an easier lift.
Enable JavaScript to change the conditions and run the interactive experiment.
Make a discovery
An ideal simple machine can reduce the force you supply by making you move farther. Force and distance belong together: a force advantage is not free energy.
Make a prediction
The moving-pulley rig halves the ideal effort. What happens to the rope travel for the same lift?
- It also halves
- It doubles
- It stays the same
Read the explanation
Two segments support the load, and each must shorten. To raise the crate 20 cm, pull 40 cm of rope.
Understand it
Support the moving wheel
In the second rig, one end is anchored above and the rope passes under a pulley attached to the crate, then over a fixed guide. Two rope segments support the moving assembly. Each supplies half its weight in this ideal model.
The same idea at a lever
In the lever bench, the pivot is the fulcrum. Moving the effort farther from the pivot increases its turning effect. Wheelbarrows, seesaws and crowbars arrange load, effort and pivot differently.
Look closer at the science
Count supporting segments
For a massless rope and frictionless wheels, the same tension T acts along the rope. With n vertical supporting segments, nT=mg. The crate and moving hardware are represented by the selected combined mass.
Travel pays for force
If the load rises h, all n supporting segments shorten by h, so the free end moves s=nh. Ideal input work Ts equals output work mgh. The crane reports force, rise and work together.
Balance turning effects
For the horizontal lever, effort force × perpendicular effort arm = load weight × perpendicular load arm. Real pulleys have friction; real levers have weight and bending. Those losses are absent here.
Try it yourself: Lift with a ruler
Supplies
- Ruler
- Round pencil
- Small eraser
- Stable tabletop
- Build the lever
Rest the ruler across the pencil. Place the eraser near one end and keep it low over the table.
- Move the pivot
Press the other end gently. Move the pencil closer to the eraser, then compare the effort. Keep the object and contact points otherwise the same.
- Look at both ends
Notice which end travels farther for the same tiny lift. Sketch the pivot, effort and load. Do not use heavy objects or fingers beneath the load.
Where should the pivot go to make the same object easier to lift?
Qualitative comparison only. A ruler bends and the pivot rolls; this activity does not measure an exact mechanical advantage.
Sources and model limits
- Two authored rope routes with ideal massless, inextensible rope; the rigging cannot be arbitrarily rearranged.
- Motion is prescribed slowly. Acceleration, rope stretch, pulley friction and crane stability are not simulated.
- The lever readout is horizontal static balance. Its inspection animation does not calculate dynamic lever forces.
Pulleys and levers trade ideal force against distance.
Figures 9.24–9.25 and equations 9.29–9.32 support segment counting, lever arms and ideal work.
OpenStax · Simple machinesA ruler and pencil can demonstrate a lever.
Original Ben Finio lesson. Our simplified procedure is an untrialed adaptation.
Science Buddies · Lever activityFriction can obscure a home pulley comparison.
Original procedure describes pencil-contact friction; the virtual model excludes that loss.
Science Buddies · Pulley activityIndependent subject review is pending.
Read the sources and model assumptions