Answer the following problems.
1. Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a hydraulic system. The piston chambers and the connecting tube are filled with an incompressible fluid. The cross-sectional areas of piston 1 and piston 2 are A1 and A2, respectively. A force F1 is exerted on piston 1. Rank the resultant force F2 on piston 2 that results from the combinations of F1, A1, and A2 given from greatest to smallest. If any of the combinations yield the same force, give them the same ranking. (Use only “>” or “=” symbols. Do not include any parentheses around the letters or symbols.)
- F1 = 6.0 N; A1 = 1.1 m2; and A2 = 2.2 m2
- F1 = 3.0 N; A1 = 1.1 m2; and A2 = 0.55 m2
- F1 = 3.0 N; A1 = 2.2 m2; and A2 = 4.4 m2
- F1 = 6.0 N; A1 = 0.55 m2; and A2 = 2.2 m2
- F1 = 6.0 N; A1 = 0.55 m2; and A2 = 1.1 m2
- F1 = 3.0 N; A1 = 2.2 m2; and A2 = 1.1 m2
2. A bicycle tire pump has a piston with area 0.49 in2. If a person exerts a force of 24 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump?
3. A large truck tire is inflated to a gauge pressure of 82 psi. The total area of one sidewall of the tire is 1,330 in2. What is the net outward force (in lb) on the sidewall because of the air pressure? (Enter the magnitude.)
4. A viewing window on the side of a large tank at a public aquarium measures 59 in. by 69 in. The average gauge pressure from the water is 7 psi. What is the total outward force on the window?
5. The total mass of the hydrogen gas in the Hindenburg zeppelin was 18,000 kg. What volume did the hydrogen occupy? (Assume that the temperature of the hydrogen was 0°C and that it was at a pressure of 1 atm.)
6. A large balloon used to sample the upper atmosphere is filled with 590 m3 of hydrogen. What is the mass of the hydrogen (in kg)?
7. Find the gauge pressure (in psi) at the bottom of a freshwater swimming pool that is 18.6 ft deep.
8. The depth of the Pacific Ocean in the Mariana Trench is 36,198 ft. What is the gauge pressure at this depth?