In a machine shop, a hydraulic lift is used to raise heavy equipment for repairs. The sys- tem has a small piston with a cross-sectional area of 0.063 m2 and a large piston with a cross-sectional area of 0.172 m2. An engine weighing 2800 N rests on the large piston.

What force must be applied to the small piston in order to lift the engine?
Answer in Newtons

pressureSmall=pressureLarge (pascal's principle)

forceSmall/areaSmall=forceLarge/AreaLarge

forceSmall=.063*2800/.172

To solve this problem, you can use the principle of Pascal's law, which states that when a change in pressure is applied to a fluid, it is transmitted equally in all directions. Here's how you can calculate the force required to lift the engine:

1. Determine the pressure exerted on the large piston by the weight of the engine:
Pressure = Force / Area
Pressure = 2800 N / 0.172 m²
Pressure = 16279.07 Pa

2. Since Pascal's law states that the pressure is the same throughout the fluid, this pressure is also exerted on the small piston.

3. Calculate the force required to achieve the same pressure on the small piston:
Force = Pressure * Area
Force = 16279.07 Pa * 0.063 m²
Force = 1026.4 N

Therefore, the force that must be applied to the small piston in order to lift the engine is 1026.4 Newtons.