Conceptual Questions:
1. Describe "hydrostatic equilibrium." What determines the pressure at any one depth? To what materials does it apply? Under what conditions?
2. Which state of matter is associated with the very highest of temperatures?
a. liquid
b. plasma
c. gas
d. solid
3. What action gives rise to buoyancy in fluids? What happens if the density of the object equals the density of the fluid?
4. As ice floats in water, about 10% of the ice floats above the surface
of the water.
If we float some ice in a glass of water, what will happen to the water level
as the ice melts?
a. The water level will rise 10% of the volume of the ice that melts.
b. The water level will rise, but not as much as the 10% indicated in
answer a.
c. The water level will remain unchanged.
d. The water level will become lower.
Numerical Problems: answers link to a help page.
1. What is the total force on the bottom of a 2 m diameter by 1 m deep round wading pool due to the weight of air and the weight of the water? The pressure contribution from the atmosphere is 1.01x105 Pa, the density of water is 1000 kg/m3.
2. The standard kilogram is a platinum-iridium cylinder 39 mm in height and 39 mm in diameter. What is the density of the material?
3. The quantity "pressure" expressed in terms of the fundamental quantities (mass M, length L, time T) is equivalent to:
a. MLT-1.
b ML-1T-2.
c. M2L-1T-3.
d. a dimensionless quantity.
4. A 15,000 N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.04 m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car?
5. By what factor is the total pressure greater at a depth of 850 m of sea water than at the surface where pressure is one atmosphere? Water density = 1000 kg/m3, 1 atmospheric pressure = 1.01 x105 Pa.
6. If a column of mercury in a barometer stands at 72.6 cm, what is the atmospheric pressure? The density of mercury is 13.6 x103 kg/m3.
7. The pressure inside a commercial airliner is maintained at 1 ATM (1.0x105 N/m2). What is the outward force exerted on a 1 m x 2 m cabin door if the outside pressure (at 10 km height) is 0.3 ATM?
8. A Boeing 737 airliner has a mass of 20,000 kg. The total area of the wings is 100 m2. What must be the pressure difference between the top and bottom of the wings to keep the airplane up?
9. A spring balance is attached with string to a piece of aluminum
having density 2.7 gm/cm3 and mass 775 gm.
What reading will the balance register (gm) when the metal is submerged
in oil with density 0.75 gm/cm3?
Most spring balances are calibrated to read mass, not weight.
10. A ping pong ball has an average density of 0.084 grams/cm3 and a diameter of 3.8 cm. What force would be required to keep the ball completely submerged under water?
11. A cube of wood of density 0.78 gm/cm3 is 10 cm on a side. When placed in water, what height of the block will float above the surface? Water density = 1.00 gm/cm3.
12. The bottom of a flat-bottom aluminum boat has an area of 4.0 m2 and the boat's mass is 60 kg. When set afloat in water, how far below the water surface is the boat bottom? Water density = 1000 kg/m3.
13. A solid rock, suspended in air by a spring scale, has a measured mass of 9.0 kg. When the rock is submerged in water, the scale reads 3.3 kg. What is the density of the rock? Water density = 1000 kg/m3.