How to play Force for Distance
- Choose a lever and read both arms, the load, and how far one end moves on the card.
- Both ends turn through the same angle, so each moves in proportion to its arm: s_l ÷ s_e = d_l ÷ d_e.
- For work, multiply each force by the distance it moves: the work in, F·s_e, equals the work out, W·s_l. Type your prediction and press Move.
- Watch the orange mark or line: it shows your prediction next to what really happens.
What does a lever trade?
A lever turns about its fulcrum, so both ends sweep through the same angle. The end farther from the fulcrum moves farther, and faster, in proportion to its distance: s_l ÷ s_e = d_l ÷ d_e. That is the price of mechanical advantage. A crowbar that lets you push with a fifth of the force makes you push five times as far. For a slow, frictionless lever no energy is lost, so the work you put in, F·s_e, equals the work you get out, W·s_l. A lever never saves work; it only trades force for distance. A class 3 lever, like your forearm or a fishing rod, makes the opposite trade: you push harder than the load, and in return the load moves farther and faster. That is why muscles attach close to joints, and why a bat, a racket, or a rod reaches so far.
A focused learning model
The lever is light and rigid and turns about a fixed fulcrum. One point, the load or the effort, is moved steadily for 2 s; each point then moves d·sin θ at right angles to the bar's starting line, so s_l ÷ s_e = d_l ÷ d_e at every moment, and the speeds keep the same ratio. The lever moves slowly with no friction, so the work in equals the work out. A prediction is right within 2%. Plays in real time.