š Hydraulic lift ā the same pressure, a bigger area, a bigger force
Press the small piston with force Fā. The pressure P = Fā/Aā appears undiminished everywhere in the trapped liquid, so on the large piston it produces Fā = PĀ·Aā = FāĀ·Aā/Aā ā enough to lift a car. The catch: the small piston must travel Aā/Aā times as far.
Push the small piston with Fā ā it presses on the trapped liquid.
P = Fā/Aā = ā (same everywhere) ·
Fā = FāĀ·Aā/Aā = ā N
the small piston travels Aā/Aā Ć farther ā work is conserved