Two hydraulic pistons are connected. The small piston has an area of 2 sq in and the large piston has an area of 20 sq in. If 100 lbs of force is applied to the small piston, what force is exerted by the large piston?

Pascal's principle: pressure applied to a confined fluid is transmitted equally throughout the fluid. Pressure = Force / Area. In a hydraulic system, pressure is the same in both pistons; force differs based on area. P = F/A is constant: F₁/A₁ = F₂/A₂. Calculation: F₁/A₁ = 100/2 = 50 psi. F₂ = P × A₂ = 50 × 20 = 1000 lbs. The larger piston multiplies force by the area ratio (10:1 in this case). Trade-off: distance moved is reduced by the same ratio. If small piston moves 10 inches, large piston moves 1 inch (volume is conserved: A₁ × d₁ = A₂ × d₂). Work in = work out (ignoring friction): 100 lbs × 10 in = 1000 lbs × 1 in = 1000 in-lbs. Real-world applications: hydraulic brakes (small force at pedal → large force at brake pad), hydraulic lifts (small pump pressure → lift heavy vehicles), hydraulic presses, excavator arms. Mechanical advantage of hydraulic system = A₂/A₁ (area ratio). Pneumatic systems work similarly but with compressed gas (less common in ASVAB). Fluid properties relevant to ASVAB MC: density, pressure increases with depth (P = ρgh in a fluid column), buoyancy (Archimedes' principle: buoyant force = weight of fluid displaced), incompressibility of liquids (vs compressibility of gases).