In a hydraulic system a 20.0-N force is applied to the small piston with cross sectional

area 25.0 cm2. What weight can be lifted by the large piston with cross sectional
area 50.0 cm2?

A flat-bottom river barge is 30.0 ft wide, 85.0 ft long, and 15.0 ft deep. (a) How many ft3 of water will it displace while the top stays 3.00 ft above the water? (b) What load in tons will the barge contain under these conditions if the empty barge weighs 160 tons in dry dock?

To determine the weight that can be lifted by the large piston in a hydraulic system, we need to apply Pascal's Law. According to Pascal's Law, the pressure exerted in a fluid is transmitted uniformly in all directions.

To solve this problem, we need to equate the pressure exerted on the small piston to the pressure exerted on the large piston.

Step 1: Convert the given force to the corresponding pressure.
- Force = 20.0 N
- Area of the small piston = 25.0 cm^2 = 0.0025 m^2 (since 1 cm^2 = 0.0001 m^2)
- Pressure on the small piston = Force/Area = 20.0 N / 0.0025 m^2 = 8,000 Pa

Step 2: Equate the pressure on the small piston to the pressure on the large piston.
- Area of the large piston = 50.0 cm^2 = 0.0050 m^2
- Pressure on the large piston = Force/Area (unknown)
- Since the pressure is the same throughout the hydraulic system:
Pressure on the small piston = Pressure on the large piston

Step 3: Rearrange the equation and solve for the unknown force.
- Pressure on the large piston = Pressure on the small piston = 8,000 Pa
- Force on the large piston = Pressure × Area
- Force on the large piston = 8,000 Pa × 0.0050 m^2 = 40 N

So, the weight that can be lifted by the large piston is 40.0 N.