How to play Hydraulic Lift
- Choose a job and read the load, the pistons, and the push or the rise on the card.
- The pressure is the same in all the oil: F₁ ÷ A₁ = F₂ ÷ A₂. A diameter 10 times bigger is an area 100 times bigger.
- For distances, the oil pushed in fills the other cylinder: A₁·d₁ = A₂·h₂. Type your prediction and press Push.
- Watch the bars: the lift grows toward the weight, or the two volumes of oil stay equal.
How does a hydraulic lift multiply force?
Squeeze a closed liquid anywhere and the extra pressure reaches every part of it equally: that is Pascal's principle. In a hydraulic lift, a push F₁ on a small piston of area A₁ makes a pressure p = F₁ ÷ A₁ in the oil. The large piston, of area A₂, feels that same pressure over its whole area, so it pushes up with F₂ = p·A₂. With pistons of 10 cm² and 1000 cm², a push of 118 N lifts a 1.2 t car. Areas grow with the square of the diameter, so a piston 10 times wider gives 100 times the force. There's a price. Oil doesn't squeeze, so the oil pushed out of the small cylinder must fill the large one: A₁·d₁ = A₂·d₂. To raise the car 1 cm, the small piston must travel 100 cm, and the work in, F₁·d₁, equals the work out, F₂·d₂. That is why a car jack needs many short strokes, the same trade as a lever's force for distance. Brakes, diggers, and barber chairs all work this way.
A focused learning model
The oil doesn't compress and has no weight of its own to speak of; the pistons slide without friction and the oil never leaks. The pressure is the same everywhere in it at once. The push grows steadily from zero for 2 s; the load lifts the moment p·A₂ reaches its weight (within 0.05% still lifts), and the small piston then travels 30 cm in 1 s. A set distance, or a number of 10 cm jack strokes, is made steadily over 2 s. Widths grow with the square root of the area and are not to scale; the pistons' moves are. A push or a piston size is right if it lifts the load with at most 2% to spare, a distance within 2%, and a number of strokes if it is the fewest that do the job. g = 9.8 m/s². Plays in real time.