14.1 Fluids, Density, and Pressure

If the reservoir in the example covered twice the area, but was kept to the same depth, would the dam need to be redesigned?

Which of the following substances are fluids at room temperature and atmospheric pressure: air, mercury, water, glass?

Explain how the density of air varies with altitude.

How is pressure related to the sharpness of a knife and its ability to cut?

Imagine that in a remote location near the North Pole, a chunk of ice floats in a lake. Next to the lake, a glacier with the same volume as the floating ice sits on land. If both chunks of ice should melt due to rising global temperatures, and the melted ice all goes into the lake, which one would cause the level of the lake to rise the most? Explain.

Atmospheric pressure exerts a large force (equal to the weight of the atmosphere above your body—about 10 tons) on the top of your body when you are lying on the beach sunbathing. Why are you able to get up?

Does atmospheric pressure add to the gas pressure in a rigid tank? In a toy balloon? When, in general, does atmospheric pressure not affect the total pressure in a fluid?

Gold is sold by the troy ounce (31.103 g). What is the volume of 1 troy ounce of pure gold?

What is the mass of a deep breath of air having a volume of 2.00 L? Discuss the effect taking such a breath has on your body’s volume and density.

Suppose you have a coffee mug with a circular cross-section and vertical sides (uniform radius). What is its inside radius if it holds 375 g of coffee when filled to a depth of 7.50 cm? Assume coffee has the same density as water.

A trash compactor can compress its contents to 0.350 times their original volume. Neglecting the mass of air expelled, by what factor is the density of the rubbish increased?

What is the density of 18.0-karat gold that is a mixture of 18 parts gold, 5 parts silver, and 1 part copper? (These values are parts by mass, not volume.) Assume that this is a simple mixture having an average density equal to the weighted densities of its constituents.

A glass tube contains mercury. What would be the height of the column of mercury which would create pressure equal to 1.00 atm?

Verify that the SI unit of $h \rho g$ is $\text{N}/\text{m}^{2}$.