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Chapter 14: Q. 2 (page 383)
Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0o C. The diameter of cylinder B is half that of cylinder A, and cylinder B is filled with glycerin. What is the ratio of the fluid mass in cylinder B to that in cylinder A?
The ratio is 1760: 1
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A U-shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is deep. How far upward from its initial position does the mercury in the right arm rise?
In addition to the buoyant force, an object moving in a liquid experiences a linear drag force , direction opposite the motion), where is a constant. For a sphere of radius , the drag constant can be shown to be , where is the viscosity of the liquid. Consider a sphere of radiusand density that is released from rest at the surface of a liquid with density .
a. Find an expression in terms of , and the densities for the sphere's terminal speed as it falls through the liquid.
b. Solve Newton's second law to find an expression for , the sphere's vertical velocity as a function of time as it falls. Pay careful attention to signs!
c. Water at has viscosity Pas. Aluminum has density . If a -mm-diameter aluminum pellet is dropped into water, what is its terminal speed, and how long does it take to reach of its terminal speed?
A tree loses water to the air by the process of transpiration at the rate of . This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000 vessels, each in diameter, what is the upward speed of the sap in each vessel? The density of tree sap is
A 3.0-cm-diameter tube is held upright and filled to the top with mercury. The mercury pressure at the bottom of the tube— the pressure in excess of atmospheric pressure—is 50 kPa. How tall is the tube?
A spring with spring constant 35 N/m is attached to the ceiling, and a 5.0-cm-diameter, 1.0 kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position. When in equilibrium, what length of the cylinder is submerged?
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