Cases – Chapter 5
1.A large ship floats motionless at the surface of a still sea, supported by the buoyant force. Its average density, including the air it contains, is less than that of the seawater.
a.What is the net force on the ship?
b.The ship is displacing both water and air. If the ship were to move upward a few centimeters, what would happen to the average density of the fluid the ship displaces?
c.If the ship were to move up a few centimeters, what would happen to the buoyant force on the ship?
d.If the ship were to move up a few centimeters, what would happen to the net force on the ship?
e.Show that the floating ship is in a stable equilibrium with respect to up and down motion.
f.Why does the ship settle deeper into the water when another passenger climbs aboard?
g.The ship’s captain can estimate how much cargo it’s carrying by how deep the ship rides in the water. How does that technique work?
h.Does the air exert a buoyant force on the ship? If so, why doesn’t the ship float in air?
2.Like all bony fish, a bass has a gas-filled sac or air bladder that allows it to float motionless below the surface of the water.
a.What forces act on the motionless bass, and what is the net force it experiences?
b.What is the bass’s average density?
c.Salt water is more dense than fresh water. What are the relative sizes of the air bladders in saltwater and freshwater bass?
d.A shark is a cartilaginous fish that lacks an air bladder. If it can’t move, it will sink. Why?
3.A scuba diver swims below the surface of the water, breathing air from the steel tanks of an aqualung.
a.It’s easiest for her to maintain a constant depth if the buoyant force on her and her equipment exactly balances their weight. Her wet suit floats so she wears a heavy weight belt to compensate. How should her average density compare with that of the water around her?
*b.When she is 20 m below the surface of the water, what is the pressure pushing inward on her chest?
c.When she breathes, she expects air to flow into her lungs. She can change the pressure in her lungs slightly, using the muscles in her chest and diaphragm. How must the pressure in her mouth compare with that in her lungs in order for air to begin flowing into her lungs?
d.If instead of taking compressed air with her, she were to try to breathe surface air through a straw, the air entering her mouth would be at atmospheric pressure. What would happen when she tried to breathe?
e.The special pressure regulator of an aqualung delivers air to her mouth at exactly the same pressure as that of the surrounding water. She can breathe this air easily. However, the deeper she dives, the faster she consumes air molecules from the tanks and the sooner she must return to the surface. Why does she exhaust her tanks faster by going deeper?
4.Blimps are compact versions of the great airships of the early 20th century. They are filled with helium and are propelled forward by fans. But a blimp has more to it than meets the eye. Inside the cigar-shaped exterior skin are several flexible containers called ballonets. The blimp’s buoyancy and orientation are controlled by pumping air into or out of these ballonets.
a.The exterior skin is rigid, so the blimp’s total volume doesn’t change. Why does pumping air into the ballonets cause the blimp to become less buoyant?
b.Why does pumping air from the forward ballonet to the rearward ballonet cause the blimp to tip its nose upward?
c.When the blimp flies into warmer air, what should it do with its ballonets in order to maintain a constant altitude?
d.The blimp is propelled forward by huge fans, which push the air backward. Why does this procedure help the blimp to move forward?
5.A traditional water cooler has a large bottle of water turned upside down so that its neck is submerged in a small chilled water reservoir at the top of the water cooler. The water level in the small reservoir remains just above the neck of the bottle. If you open the valve to let water out of the reservoir, bubbles of air rise up into the water bottle and the level of water in the bottle goes down.
a.Since there is no true seal between the neck of the bottle and the reservoir, what holds the water up inside the water bottle?
b.When you open the valve at the bottom of the water cooler, the water flows out into your glass. What provides the force needed to make the water accelerate?
c.Whenever the water level in the reservoir drops below the lip of the inverted water bottle, air bubbles enter the bottle and some water flows out. What force lifts the air bubbles upward inside the water bottle?
d.Once in a while the delivery person drops a water bottle and makes a tiny crack in its bottom (which is on top when the bottle is upside down on the water cooler). Although water can’t pass through the crack, air can. What will happen if you put the cracked bottle on the water cooler, and why will this happen?
6.Firefighters are battling a fire in a tall apartment building. The water pressure in the adjacent fire hydrant is about 500,000 Pa above atmospheric pressure.
*a. Some firefighters take their hose up the stairwell inside the building. What is the highest level at which they can expect water to flow out of their hose without additional pressure?
*b.Firefighters on the ground begin to spray water upward from their hoses. The water enters the hose traveling slowly at 500,000 Pa above atmospheric pressure. How fast will the water be traveling when it leaves the nozzle at atmospheric pressure?
*c.How high will the water in part b rise if the firefighters send it straight up?
*d.To boost the water pressure, the firefighters send it sequentially through pumps in two fire engines. Each pump boosts the pressure by 500,000 Pa, for a total of 1,500,000 Pa above atmospheric pressure. How high will this water rise in hoses carried up the stairs inside the building?
7.A canoe is a particularly simple type of boat. Most modern canoes are made of aluminum or plastic. Suppose that you and a friend are paddling an aluminum canoe in a lake.
a.Aluminum is denser than water, so how can an aluminum canoe weigh less than the water it displaces?
b.The canoe has gas-filled foam inserts in its ends to ensure that it will float even when filled with water. The foam is closed-pore and doesn’t soak up water like a sponge. Why is it important that the foam not soak up water when the canoe tips over?
c.How does pulling the paddles backward through the water cause the boat to accelerate forward?
d.If both of you paddle the canoe on the right hand side, it will tend to turn toward the left. Like most effectively free objects, the canoe naturally pivots about its center of mass. What causes the canoe to begin turning toward the left? (Draw a picture.)
8.Most sink drains have traps. A trap is an S-shaped pipe that carries water from the drain first downward, then upward, then downward to the sewer. Water fills the bottom of the trap and prevents unpleasant smells from working their way out of the drain.
a.As water pours down the drain, it begins to flow up the middle portion of the trap. What is lifting that water against the force of gravity?
b.If you drop a gold ring down the drain, it will usually remain in the first curve of the trap. Why won’t the ring travel up the middle portion of the trap with the water?
c.If the trap fills up with debris, it may prevent the sink from draining. One way to clear the trap, without disassembling it, is to create a very high water pressure in the drain. A plumber’s helper resembles a large suction cup and can be used to squeeze the water in the drain and raise its pressure. How does this high pressure unblock the trap?
d.Even without a trap, there is no overall movement of air in the drainpipe. What allows odor molecules to travel from the sewer to the drain?
9.A submarine hovers below the surface of the water, supported by the buoyant force. Although it also pushes on the water to propel itself forward and to adjust its height, the submarine’s most important depth control is its average density.
a.If a submarine is hovering motionless, 50m below the surface of the water, what is the net force it’s experiencing?
b.What is the motionless submarine’s average density?
c.A submarine has ballast tanks that control its buoyancy. To start descending, the submarine floods these tanks with outside seawater. How does this flooding affect the submarine’s average density and the net force on the submarine?
d.To ascend, the submarine uses compressed air to purge the seawater from its ballast tanks. How does eliminating this seawater affect the submarine’s average density and the net force on the submarine?
e.To control the submarine’s tilt, water is pumped between tanks in the front and back of the vessel. Why doesn’t this transfer of water affect the submarine’s buoyancy?
10.When a person donates blood, the nurse inserts a narrow, hollow needle into the donor’s vein. Blood passes through the needle, through a wider plastic tube, and collects in a plastic bag. The tube and bag are at the same height as the needle.
a.The donor’s blood pressure is higher than atmospheric pressure. Why is that important to the flow of blood through the needle?
b.As blood flows through the needle and the tube, and into the bag, where is its pressure highest?
c.Where is its pressure lowest?
d.What factors determine how long it will take to collect a unit of blood?
e.Would lowering the collecting bag below the height of the needle change the time it would take to collect a unit of blood? Why?
f.How would raising the collecting bag above the height of the needle affect the blood collecting process?
g.Use your answer to f to explain how blood or other fluids can be administered to patients using gravity alone.
11.Some banks and businesses use pneumatic tubes to move documents or cash from one place to another. These items travel inside a cylindrical canister that fits snugly inside a tube and is propelled through that tube by air pressure. While friction is important, we’ll neglect it for now.
a.To start the motionless cylinder moving forward through a level tube, how must the air pressure in front of the cylinder compare to the air pressure behind it?
b.To keep the cylinder moving forward through the level tube at constant velocity, how must the air pressure in front of the cylinder compare to the air pressure behind it?
c.The cylinder begins to rise up a vertical section of tube at constant velocity. How must the air pressure above the cylinder compare to the air pressure below it?
d.The cylinder reaches another level section and begins to slow down for arrival. How must the air pressure in front of the cylinder compare to the air pressure behind it as it decelerates?
e.How could you propel the cylinder through the tube if all you had was a device that produced low pressure (like a vacuum cleaner)?
f.How could you propel the cylinder through the tube if all you had was a device that produced high pressure (like a bicycle pump)?
12.Because the earth’s crust floats on the surface of the molten mantle, supporting tall mountains is problematic.
a.How does the density of the earth’s crust compare to the density of the mantle (more, less, the same)?
b.If you began to build a mountain by piling rocks over one region of the earth’s crust, how would the crust respond?
c.What does your answer to b tell you about the thickness of the crust in the vicinity of a tall mountain?
d.The earth’s crust is never more than about 80km (50miles) thick. Why does that small crust thickness impose a limit on the heights of the earth’s mountains?