BackIt's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, ρ = ρ₀ exp (-z/z₀), where z is the height above sea level, ρ₀ is the density at sea level (you can use the Table 14.1 value), and z₀ is called the scale height of the atmosphere. What is the density of the air in Denver, at an elevation of 1600 m? What percent of sea-level density is this?
A wooden cube, 1 m on all sides and having density 800 kg/m3 , is held under water in a large container by a string, as shown below. The top of the cube is exactly 2 m below the water line. Calculate the difference between the force applied by water to the top and to the bottom faces of the cube (Hint:calculate the two forces, then subtract.Use g=10 m/s2.)
Assume the supports of the uniform cantilever shown in Fig. 12–79 (m = 2900 kg) are made of wood. Calculate the minimum cross-sectional area required of each, assuming a safety factor of 9.0.
A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30 psi, but it's been a while since you've checked. You can't find a tire gauge in the car, but you do find the owner's manual and a ruler. Fortunately, you've just finished taking physics, so you tell your friend, 'I don't know, but I can figure it out.' From the owner's manual you find that the car's mass is 1500 kg. It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are 15 cm wide and the flattened segment of the tire in contact with the road is 13 cm long. What answer—in psi—will you give your friend?
Suppose a 65-kg person jumps from a height of 3.0 m down to the ground. Estimate the stress and determine if the tibia will break in a stiff-legged landing (d = 1.0 cm).
Estimate the total mass of the Earth’s atmosphere, using the known value of atmospheric pressure at sea level.
Intravenous transfusions are often made under gravity, as shown in Fig. 13–59. Assuming the fluid has a density of 1.00 g/cm3, at what height h should the bottle be placed so the liquid pressure is 52 mm-Hg?
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The deepest point in the ocean is 11 km below sea level, deeper than Mt. Everest is tall. What is the pressure in atmospheres at this depth?
You are designing a diving bell to withstand the pressure of seawater at a depth of 250 m. What is the gauge pressure at this depth? (You can ignore changes in the density of the water with depth.) At this depth, what is the net force due to the water outside and the air inside the bell on a circular glass window 30.0 cm in diameter if the pressure inside the diving bell equals the pressure at the surface of the water? (Ignore the small variation of pressure over the surface of the window.)
A closed container is partially filled with water. Initially, the air above the water is at atmospheric pressure (1.01×105 Pa) and the gauge pressure at the bottom of the water is 2500 Pa. Then additional air is pumped in, increasing the pressure of the air above the water by 1500 Pa. What is the gauge pressure at the bottom of the water?
A tall cylindrical beaker 10 cm in radius is placed on a picnic table outside. You pour 5 L of an 8,000 kg/m3 liquid and 10 L of a 6,000 kg/m3 liquid into. Calculate the total pressure at the bottom of the beaker. (Use g=10 m/s2.)
A steel cable is to support an elevator whose total (loaded) mass is not to exceed 3100 kg. If the maximum acceleration of the elevator is 1.8 m/s² , calculate the diameter of cable required. Assume a safety factor of 8.0.
A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?