Simple machines simulator covering three fundamental mechanisms: the lever (class 1, 2 and 3), the block-and-tackle pulley system, and the inclined plane. All modes assume an ideal, frictionless machine, so work in equals work out: F_in × d_in = F_out × d_out. For a lever the mechanical advantage is the effort-arm length divided by the load-arm length (a/b). For a pulley system it equals the number of rope segments supporting the load (N). For an inclined plane it equals the ramp length divided by its height, which is 1/sin(theta). Adjust arm lengths, rope segments or ramp angle and watch the required input force, mechanical advantage and input/output distances update live.
A simple machine changes the size or direction of a force without adding energy of its own. The key idea is mechanical advantage (MA): the ratio by which a machine multiplies an input force to produce an output force. A lever's MA is the effort-arm length divided by the load-arm length (a/b); a pulley system's MA equals the number of rope segments supporting the moving load (N); an inclined plane's MA equals the ramp length divided by its height, 1/sin(θ). In every case, so long as friction is ignored, the machine conserves work: Fin × din = Fout × dout. Whatever force you save, you pay back in distance — pull the effort end of a lever further than the load moves, haul in far more rope than the load rises, or push a crate a longer distance up a shallow ramp than the height it gains.
These three machines appear everywhere. A crowbar and a pair of scissors are class-1 levers, with the fulcrum between the effort and the load; a wheelbarrow and a bottle opener are class-2 levers, with the load between the fulcrum and the effort, giving mechanical advantage greater than one; tweezers and a fishing rod are class-3 levers, with the effort between the fulcrum and the load, trading force for speed and reach even though their mechanical advantage is less than one. A block-and-tackle rig, familiar from sailing ships and construction cranes, lets one person hoist a load many times their own strength by adding more supporting rope segments. Ramps for loading trucks, wheelchair access ramps and mountain roads are all inclined planes, letting a gentler, longer push replace a short, hard lift.
What does this simulation actually show?
It lets you switch between three simple machines — a lever, a block-and-tackle pulley system and an inclined plane — and see a live schematic of each with force arrows for the input force you must apply and the output force (the load's weight). As you change arm lengths, rope segments or ramp angle, the telemetry panel updates the mechanical advantage, required input force, input and output distances, and confirms that ideal work in equals work out.
What is the difference between the three lever classes?
All levers pivot around a fulcrum, but the arrangement of fulcrum, effort and load differs. Class 1 has the fulcrum between effort and load, like a crowbar, a see-saw or a pair of scissors. Class 2 has the load between the fulcrum and the effort, like a wheelbarrow or a bottle opener, which always gives mechanical advantage greater than one. Class 3 has the effort between the fulcrum and the load, like tweezers, a fishing rod or your own forearm lifting a weight — mechanical advantage is less than one, but you gain speed and reach at the load end.
Why does a pulley system with more rope segments need less force but more rope pulled?
Each supporting rope segment carries an equal share of the load's weight, so N segments each carry W/N of the load, meaning you only need to pull with force W/N. But that same rope has to be pulled in through every one of those N segments to raise the load by a given height, so you pull N times more rope than the load actually rises. This is exactly the work-conservation trade-off: force divided by N, distance multiplied by N.
Only the component of the load's weight that acts along the slope, W·sin(θ), has to be overcome to push the load up a frictionless ramp — the rest is carried by the ramp's normal force. A shallower ramp (smaller θ) reduces that component, so you push with less force, but you must travel the full ramp length L = h/sin(θ) to reach the same height h, which is longer than h itself. Less force, more distance, same total work.
In lever mode, the class buttons rearrange the fulcrum, effort and load along the beam, and the arm-length sliders set the effort arm a and load arm b. In pulley mode, the rope-segment slider sets how many strands of rope support the moving pulley block, from 1 to 6. In inclined-plane mode, the angle slider sets the ramp's steepness from 5° to 80° against a fixed 2 m height. The load-weight slider and the output-displacement slider apply to every mode, since they define the task the machine has to do.
An ideal machine loses none of the input work to friction, heat or deformation, so all the work you put in comes out as useful work: efficiency = 100%. Real machines always fall short — bearings, rope and ramp surfaces all generate friction, so some of the input work is wasted as heat, and real efficiency is always below 100%. That means a real machine needs a slightly larger input force than this ideal simulation predicts to move the same load the same distance.
Mechanical advantage below one means you must apply more force than the load weighs, which sounds like a bad trade — but the payoff is speed and distance at the load end. Because din/dout = MA < 1, the load end moves further and faster than the effort end for the same effort motion. That is exactly what you want from tweezers picking up something delicate, a fishing rod flicking a lure a long way, or your forearm swinging a hammer — reach and speed matter more than raw force.
For any chosen output displacement dout, the simulator computes the matching input displacement din = MA × dout, then multiplies each distance by its corresponding force: work in = Fin × din, work out = Fout × dout. Because Fin = Fout/MA and din = MA × dout, these two products are always mathematically identical in the frictionless case, which the telemetry panel displays side by side.
Levers appear in crowbars, scissors, wheelbarrows, bottle openers, nail clippers and tweezers. Pulley systems lift sailboat sails, hoist engine blocks in a garage, and raise materials on construction cranes and elevators. Inclined planes appear as loading ramps for trucks, wheelchair access ramps, switchback mountain roads and even the ramps ancient builders likely used to raise heavy stone blocks. All three let a smaller or more convenient force do the job of a larger, less convenient one.