#6 #11 #14 #16 #18 #206. A cube with a mass of 48 g is made from a metal with a density of 6 g/cubic centimeter. What is the volume of the cube and the length of each edge?
Since the density of a substance is its mass divided by its volume, the volume of the the cube is
Since it is a cube, its volume equals the edge length cubed, or l = 2 cm.
11. Given that atmospheric pressure drops by a factor of 2 for every gain in elevation of 18,000 ft, what is the height of a mercury barometer in an unpressurized compartment of an airliner flying at 36,000 ft?
At sea level, a mercury barometer has a height of about 760 mm. Under these conditions. the atmospheric pressure at sea level multiplied by the cross-section of the barometer's column equals the force of earth's gravity on the mercury column. This is
At 36,000 ft in elevation, the atmospheric pressure is one-fourth that at sea level. So,
14. If a cubic meter of water has a mass of 1000 kg, what is the pressure at a depth of 100 m? Is the atmospheric pressure important?
The pressure due to the water overhead is the gravitational force on the water column directly overhead divided by the cross-sectional area of the column. Taking this cross-section as A, we have
and
Atmospheric pressure is about 100,000 Pa, so its contribution is small in comparison.
16. A plastic fishing bobber has a volume of 12 cubic centimeters and a mass of 6 g. How much of the bobber will float above the surface?
By Archimedes' principle, the bobber will displace a volume of water with mass equal to its mass when floating. It has a mass of 6 g, so the water volume will be
The bobber has a volume of 12 cubic centimeters, so 6 cubic centimeters (half of its volume) will float above the surface.
18. A metal buoy has a volume of 2 cubic meters. How much of the buoy will be submerged if it has a mass of 500 kg?
The submerged volume will be
20. A ball has a volume of 5 cubic centimeters and a mass of 20 g. What will the ball weigh under water?
The ball's weight under water is its weight in air, less the buoyant force it experiences. The buoyant force is
Its weight in air is
Thus, its weight under water is
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