Ch 13 Exercises
what common liquid covers more than two-thirds of our planet, makes up 60% of our bodies, and sustains our lives and lifestyles in countless ways?
water
a balloon is weighed so that it is barely able to float in water. if it is pushed beneath the surface, will it return to the surface, stay at the depth to which it is pushed, or sink? explain. (does the balloons density change?)
the balloon will sink to the bottom because its density increases with depth. the balloon is compressible, so the increase in water pressure beneath the surface compresses it and reduces its volume, thereby increasing its density. density further increases as it sinks to regions of greater pressure and compression. think buoyant force: as its volume is reduced by increasing pressure as it descends, the amount of water it displaces becomes less. so buoyant force decreases as it descends.
a ship sailing from the ocean into a freshwater harbor sinks slightly deeper into the water. does the buoyant force on the ship change? if so, does it increase or decrease?
the buoyant force does not change. the buoyant force on a floating object is always equal to that object's weight, no matter what the fluid
in the hydraulic arrangement shown, the larger piston has an area that is 50 times that of the smaller piston. the strong man hopes to exert enough force on the large piston to raise the 10 kg that rest on the small piston. do you think he will be successful? defend your answer
the strong man will be unsuccessful. he will have to push with 50 times the weight of the 10 kg. the hydraulic arrangement is arranged to his disadvantage. ordinarily, the input force is applied against the smaller piston and the output force is exerted by the large piston-this arrangement is just the opposite
when the wooden block is placed in the beaker, what happens to the scale reading? answer the same question for an iron block
the total weight on the scale is the same either way, so the scale reading will be the same whether or not the wooden block is outside or floating in the beaker. likewise for an iron block, where the scale reading shows the total weight of the system.
which teapot holds more liquid?
the water can be no deeper than the spouts, which are at the same height, so both teapots hold the same amount of liquid.
why does water "seek its own level"?
water seeking its own level is a consequences of pressure depending on depth. in a bent U-tube full of water, for example, the water in one side of the tube tends to push water up the other side until the pressures at the same depth in each tube are equal. if the water levels were not the same, there would be more pressure at a given level in the fuller tube, which would move the water until the levels were equal
why will a volleyball held beneath the surface of water have more buoyant force than if it's floating?
when the ball is held beneath the surface, it displaces a greater weight of water
when an ice cube in a glass of water melts, does the water level in the glass rise, fall, or remain unchanged? does your answer change if the ice cube has many air bubbles? how about if the ice cube contains many grains of heavy sand?
when the ice cube melts, the water level at the side of the glass is unchanged (neglecting temperature effects). to see this, suppose the ice cube to be a 5g cube; then while floating it will displace 5 g of water. but when melted it becomes the same 5 g of water. hence the water level is unchanged. the same occurs when the ice cube with air bubbles melts. whether the ice cube is hollow or solid, it will displace as much water floating as it will melted. if the ice cube contains grains of heavy sand, however, upon melting, the water level at the edge of the glass will drop.
why will water flow more readily than cold water through small leaks in a car radiator?
when water is hot, the molecules are moving more rapidly and do not cling to one another as well as when they are slower moving, so the surface tension is less. the lesser surface tension of hot water allows it to pass more readily through small openings.
why is the buoyant force on a submerged submarine appreciably greater than the buoyant force on it while it's floating?
while floating, BF equals the weight of the submarine. when submerged, BF equals the submarine's weight plus the weight of the water taken into its ballast tanks. looked at another way, the submerged submarine displaces a greater weight of water than the same submarine floating
the density of a rock doesn't change when it's submerged in water, but your density changes when you are submerged. explain
you are compressible, whereas a rock is not, so when you are submerged, the water pressure tends to squeeze in on you and reduce your volume. this increases your density (be careful when swimming-at shallow depths you may still be less dense than water and be buoyed to the surface without effort, but at greater depths you may be passed to a density greater than water and you'll have to swim to the surface)
why does your body get more rest when you're lying down than when you're sitting? is blood pressure in your legs greater?
your body gets more rest when you're lying then when sitting or standing because when lying, the heart does not have to pump blood to the heights that correspond to standing or sitting
why is blood pressure measured in the upper arm, at the elevation of your heart?
your upper arm is at the same level as your heart, so the blood pressure in your upper arms will be the same as the blood pressure in your heart
the sketch shows a reservoir that supplies water to a farm. it is made of wood and is reinforced with metal hoops. (a) why is it elevated? (b) why are the hoops closer together near the bottom part of the tank?
(a) the reservoir is elevated so as to produce suitable water pressure in the faucets that it serves. (b) the hoops are closer together at the bottom because the water pressure is greater at the bottom. closer to the top, the water pressure is not as great, so less reinforcement is needed there
a block of aluminum with a mass of 1 kg is placed in a beaker of water filled to the brim. water overflows. the same is done in another beaker with a 1 kg block of lead. does the lead displace more, less, or the same amount of water?
a 1 kg block of aluminum is larger than a 1 kg block of lead. the aluminum therefore displaces more water
why is a high mountain composed mostly of lead an impossibility on earth?
a mostly-lead mountain would be more dense than the mantle and would sink in it. guess where most of the iron in the world is-in the earth's center
a small aquarium half-filled with water is on a spring scale. will the reading of the scale increase or remain the same if a fish is placed in the aquarium? (will your answer be different if the aquarium is initially filled to the brim?)
if water doesn't overflow, the reading on the scale will increase by the ordinary weight of the fish. however, if the aquarium is brim filled so a volume of water equal to the volume of the fish overflows, then the reading will not change. we correctly assume here that the fish and water have the same density
when you are sunbathing on a stony beach, why do the stones hurt your feet less when you're standing in deep water?
in deep water, you are buoyed up by the water displaced and as a result, you don't exert as much pressure against the stones on the bottom. when you are up to your neck in water, you hardly feel the bottom at all
why will a block of iron float in mercury but sink in water?
mercury is more dense (13.6 g/cm3) than iron. a block of iron will displace its weight and still be partially above the mercury surface. hence it floats in mercury. in water it sinks because it cannot displace its weight
a piece of iron placed on a block of wood makes it float lower in the water. if the iron were instead suspended beneath the wood, would the wood float as low, lower, or higher? defend your answer
the block of wood would float higher if the piece of iron is suspended below it rather than on top of it. by the law of flotation: the iron and wood unit displaces its combined weight and the same volume of water whether the iron is on top or bottom. when the iron is on top, more wood is in the water, when on bottom, less wood in the water. or another explanation is that when the iron is below-submerged-buoyancy on it reduces its weight and less of the wood is pulled beneath the water line
compared with an empty ship, would a ship loaded with a cargo of styrofoam sink deeper into the water or rise in the water? defend your answer
when a ship is empty its weight is least and it displace the least water and floats highest. carrying a load of anything increases its weight and makes it float lower. it will float as low carrying a few tons of styrofoam as it will carrying the same number of tons of iron ore. so the ship floats lower in the water when loaded with styrofoam than when empty. if the styrofoam were outside the ship, below water line, then the ship would float higher as a person would with a life preserver
a block of aluminum with a weight of 10N is placed in a beaker of water filled to the brim. water overflows. the same is done in another beaker with a 10N block of lead. does the lead displace more, less, or the same amount of water. (why are these answers different from previous exercises)
a 10 N block of aluminum is larger than a 10 N block of lead. the aluminum therefore displaces more water. only in exercise 14 were the volumes of the block equal. in this and the preceding exercise, the aluminum block is larger.
in answer the question of why bodies float higher in saltwater than in freshwater, your friend replies that the reason is that saltwater is denser than freshwater (does your friend often answer questions by reciting only factual statements that relate to the answer but don't provide any concrete reasons?) how would you answer the same question?
a body floats higher in denser fluid because it does not have to sink as far to displace a weight of fluid equal to its own weight. a smaller volume of the displaced denser fluid is able to match the weight of the floating body.
if you release a ping pong ball beneath the surface of water, it will rise to the surface. would it do the same if it were inside a big blob of water floating weightless in an orbiting spacecraft?
a ping pong ball in water in a zero-g environment would experience no buoyant force. this is because buoyancy depends on a pressure difference on different sides of a submerged body. in this weightless state, no pressure difference would exist because no water pressure exists
you know that a sharp knife cuts better than a dull knife. do you know why this is so? defend your answer
a sharp knife cuts better than a dull knife because it has a thinner cutting area which results in more cutting pressure for a given force
if a submarine starts to sink, will it continue to sink to the bottom if no changes are made? explain
a sinking submarine will continue to sink to the bottom so long as the density of the submarine is greater than the density of the surrounding water. if nothing is done to change the density of the submarine, it will continue to sink because the density of water is practically constant. in practice, water is sucked into or blown out of a submarine's tanks to adjust its density to match the density of the surrounding water
if you've wondered about the flushing of toilets on the upper floors of city skyscrapers, how do you suppose the plumbing is designed so that there is not an enormous impact of sewage arriving at the basement level?
a typical plumbing design involves short sections of pipe bent at 45 degree angles between vertical sections two-stories long. the sewage therefore undergoes a succession of two-story falls which results in a moderate momentum upon reaching the basement level
which do you suppose exerts more pressure on the ground-a 5000 kg elephant or a 50 kg lady standing on spike heels? (which will be more likely to make dents in a linoleum floor?) approximate a rough calculation for each
a woman with spike heels exerts considerably more pressure on the ground than an elephant. a 500 N woman with her 1 cm2 spike heels puts half her weight on each foot, distributed (let's say) half on her heel and half on her sole. so the pressure exerted by each heel will be 125 N/1 cm2 = 12.5 N/cm2. a 50,000 N elephant with 1000 cm2 feet exerting 1/4 its weight on each foot produces 12,500 N/1000 cm2 = 12.5 N/cm2; about 10 times less pressure (so a woman with spike heels will make greater dents in a new linoleum floor than an elephant will
we say that the shape of a liquid is that of its container. but, with no container and no gravity, what is the natural shape of a blob of water? why?
because of the surface tension, which tends to minimize the surface of a blob of water, its shape without gravity and other distorting forces will be a sphere-the shape with the least surface area for a given volume
how does water pressure 1 m beneath the surface of a lake compare with 1 m beneath the surface of a swimming pool?
both are the same, for pressure depends on depth
a block of aluminum with a volume of 10 cm3 is placed in a beaker of water filled to the brim. water overflows. the same is done in another beaker with a 10 cm3 block of lead. does the lead displace more, less, or the same amount of water?
both blocks have the same volume and therefore displace the same amount of water
what would you experience when swimming in water in an orbiting space habitat where simulated gravity is g? would you float in the water as you do on earth?
both you and the water would have half the weight density as on earth, and you would float with the same proportion of your body above the water as on earth. water splashed upward with a certain initial speed would rise twice as high, since it would be experiencing only half the "gravity force." waves on the water surface would move more slowly than on earth (at about 70% as fast since Uwave ~ square root g)
if liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid? explain
buoyant force is the result of differences in pressure, if there are no pressure differences, there is no buoyant force. this can be illustrated by the following example: a ping pong ball pushed beneath the surface of water will normally float back to the surface when released. if the container of water is in free fall, however, a submerged ping pong ball will fall with the container and make no attempt to reach the surface. in this case there is no buoyant force acting on the ball because there are no pressure differences-the local effects of gravity are absent
will a swimmer gain or lose buoyant force as she swims deeper in the water? or will her buoyant force remain the same at greater depths? defend your answer, and contrast it with the previous exercise' answer
buoyant force on a sinking swimmer will decrease as she sinks. this is because her body, unlike the rock in the previous exercise, will be compressed by the greater pressure of greater depths.
will a rock gain or lose buoyant force as it sinks deeper in water? or will the buoyant force remain the same at greater depths? defend your answer
buoyant force will remain unchanged on the sinking rock because it displaces the same volume and weight of water at any depth
would the water level in a canal lock go up or down if a battleship in the lock sank?
for the same reason as in the previous exercise, the water level will fall (try this one in the kitchen sink also. note the water level at the side of the dishpan when a bowl floats in it. tip the bowl so it fills and submerges, and you'll see the water level at the side of the dishpan fall)
there is a legend of a dutch boy who bravely held back the whole North sea by plugging a hole in a dike with his finger. is this possible and reasonable?
from a physics point of view, the event was quite reasonable, for the force of the ocean on his finger would have been quite small. this is because the pressure on his finger has only to do with the depth of the water, specifically the distance of the leak below the sea level-not the weight of the ocean.
why is it inaccurate to say that heavy objects sink and that light objects float? give exaggerated examples to support your answer
heavy objects may or may not sink, depending on their densities (a heavy log floats while a small rock sinks, or an ocean liner floats while a paper clip sinks, for ex). people who say that heavy objects sink really mean that dense objects sink. be careful distinguishing how heavy vs. how dense an object it
the relative densities of water, ice, and alcohol are 1.0, 0.9, and 0.8, respectively. do ice cubes float higher or lower in a mixed alcoholic drink? what comment can you make about a cocktail in which the ice cubes lie submerged at the bottom of the glass?
ice cubes will float lower in a mixed drink because the mixture of alcohol and water is less dense than water. in a less dense liquid a greater volume of liquid must be displaced to equal the weight of the floating ice. in pure alcohol, the volume of alcohol equal to that of the ice cubes weighs less than the ice cubes, and buoyancy is less than weight and ice cubes will sink. submerged ice cubes in a cocktail indicate that it is predominantly alcohol
if the gravitational field of earth were to increase, would a fish float to the surface, sink, or stay at the same depth?
if the gravitational field of the earth increased, both water and fish would increase in weight and weight density by the same factor, so the fish would stay as its prior level in water
in the hydraulic arrangement shower in figure 13.22, the multiplication of force is equal to the ratio of the areas of the large and small pistons. some people are surprised to learn that the area of the liquid surface in the reservoir of the arrangement shown in figure 13.23 is immaterial. what is your explanation to resolve this confusion?
in figure 13.22, the increased pressure in the reservoir is a result of the applied force distributed over the input piston area. this increase in pressure is transmitted to the output piston. in figure 13.23, however, the pressure increase is supplied by the mechanical pump, which has nothing to do with this area of fluid interface between the compressed air and the liquid. many hydraulic devices have a single piston upon which pressure is exerted
if water faucets upstairs and downstairs are turned fully on, will more water per second flow out of the upstairs faucets or downstairs?
more water will flow from a downstairs open faucet because of the greater pressure. since pressure depends on depth, the downstairs faucet is effectively "deeper" than the upstairs faucet. the pressure downstairs is greater by an amount= weight density x depth, where the depth is the vertical distance between faucets.
the mountains of the Himalayas are slightly less dense than the mantle material upon which they "float". do you suppose that, like floating icebergs, they are deeper than they are high?
mountain ranges are very similar to icebergs: both float in a denser medium, and extend farther down into that medium than they extend above it. mountains, like icebergs, are bigger than they appear to be. the concept of floating mountains is isostacy-Archimedes' principe for rocks
when you're standing, blood pressure in your legs is greater than in your upper body. would this be true for an astronaut in orbit? defend your answer
no, in orbit where support is absent there are no pressure differences due to gravity
the weight of the human brain is about 15 N. the buoyant force supplied by fluid around the brain is about 14.5 N. does this mean that the weight of fluid surrounding the brain is at least 14.5 N? defend your answer
no, there does not have to actually be 14.5 N of fluid in the skull to supply a buoyant force of 14.5 N on the brain. to say that the buoyant force is 14.5 N is to say that the brain is taking up the space that 14.5 N of fluid would occupy if fluid instead of the brain was there. the amount of fluid in excess of the fluid that immediately surrounds the brain does not contribute to the buoyancy on the brain. (a ship floats the same in the middle of the ocean as it would if it were floating in a small lock just barely larger than the ship itself. as long as there is enough water to press against the bull of the ship, it will float. it's not important that the amount of water in this tight-fitting lock weigh as much as the ship
so you're on a run of bad luck, and you slip quietly into a small, calm pool as hungry crocodiles lurking at the bottom are relying on Pascal's principle to help them to detect a tender morsel. what does Pascal's principle have to do with their delight at your arrival?
part of whatever pressure you add to the water is transmitted to the hungry crocodiles, via Pascal's principle. if the water were confined, that is, not open to the atmosphere, the crocodiles would receive every bit of pressure you exert. but even if you were able to slip into the pool to quiet float without exerting pressure via swimming strokes, your displacement of water raises the water level in the pool. this ever-so-slight rise, and accompanying ever-so-slight increase in pressure at the bottom of the pool, is an ever-so-welcome signal to the hungry crocodiles
which is more likely to hurt-being stepped on by a 200 lb man wearing loafers or being stepped on by a 100 lb woman wearing heels?
pressure would be appreciably greater by the woman, which would hurt you more
suppose that you're given the choice between two life preservers that are identical in size, the first a light on filled with styrofoam and the second a very heavy one filled with gravel. if you submerge these life preservers in the water, upon which will the buoyant force be greater? upon which will the buoyant force be ineffective? why are your answers different?
since both preservers are the same size, they will displace the same amount of water when submerged and be buoyed up with equal forces. effectiveness is another story. the amount of buoyant force extend on the heavy gravel-filled preserver is much less than its weight. if you wear it, you'll sink. the same amount of buoyant force exerted on the lighted styrofoam preserver is greater than its weight and it will keep you afloat. the amount of the force and the effectiveness of the force are two different things
a chunk of steel will sink in water. but a steel razor blade, carefully placed on the surface of water, will not sink. what is your explanation?
surface tension accounts for the "floating" of the razor blade. the weight of the blade is less than the restoring forces of the water surface that tends to resist stretching
why does an inflated beach ball pushed beneath the surface of water swiftly shoot above the water surface when released?
the buoyant force on the ball beneath the surface is much greater than the force of gravity on the ball, producing a large upward force and large acceleration
the photo shows physics instructor Marshall Ellenstein walking barefoot on broken glass bottles in his class. what physics concept is Marshall demonstrating, and why is he careful that the broken pieces are small and numerous? (the band-aids on his feet are for humor)
the concept of pressure is being demonstrated. marshall is careful that the pieces are small and numerous so that his weight is applied over a large area of contact. then the sharp glass provides insufficient pressure to cut the feet
a can of diet soda floats in water, whereas a can of regular soda sinks. explain this phenomenon first in terms of density, then in terms of weight versus buoyant force
the diet drink is less dense than water, whereas the regular drink is denser than water (water with dissolved sugar is denser than pure water) also, the weight of the can is less than the buoyant force that would act on it if totally submerged. so it floats, where buoyant force equals the weight of the can
how much force is needed to hold a nearly weightless but rigid 1-L carton beneath the surface of water?
the force needed will be the weight of 1L of water (9.8 N). if the weight of the carton is not negligible, then the force needed would be 9.8 N minus the carton's weight, for then the carton would be "helping" to push itself down
in 1960, the U.S. Navy's bathyscaphe Trieste (a submersible) descended to a depth of nearly 11 km in the Marianas Trench near the Philippines in the Pacific Ocean. instead of a large viewing window, it had a small circular window 15 cm in diameter. what is your explanation for so small a window?
the smaller the window area, the smaller the crushing force of water on it
suppose that you wish to lay a level foundation for a home on hilly and bushy terrain. how can you use a garden hose filled with water to determine equal elevations for distant points?
the use of a water-filled garden hose as an elevation indicator is a practical example of water seeking its own level. the water surface at one end of the hose will be at the same elevation above sea level as the water surface at the other end of the hose
a barge filled with scrap iron is in a canal lock. if the iron is thrown overboard, does the water level at the side of the lock rise, fall or remain unchanged? explain
the water level will fall. this is because the iron will displace a greater amount of water while being supported than when submerged. a floating object displaces its weight of water, which is more than its own volume, while a submerged object displaces only its volume. (this may be illustrated in the kitchen sink with a dish floating in a dishpan full of water. silverware in the dish takes the place of the scrap iron. note the level of water at the side of the dishpan, and then throw the silverware overboard. the floating dish will float higher and the water level at the side of the dishpan will fall. will the volume of the silverware displace enough water to bring the level to its starting point? no, not as long as it's denser than water
why are persons who are confined to bed less likely to develop bedsores on their bodies if they rest on a waterbed rather than an ordinary mattress?
there is less pressure with a waterbed due to the greater contact area
there is a story about Pascal's assistant climbing a ladder and pouring a small container of water into a tall, thing, vertical pipe inserted into a wooden barrel full of water below. the barrel burst when the water in the pipe reached about 12 m. this was all the more intriguing because of the weight of added water in the tube was very small. what is your explanation, and how does this relate to Plug-and-Chug 4?
this dramatically illustrates that water pressure depends on depth, which directly relates to plug-and-chug 4
the weight of the container of water, as shown in (a), is equal to the weight of the stand and the suspended solid iron ball. when the suspended ball is lowered into the water as shown in (b), the balance is upset. challenge your friends and ask if the additional weight needed on the right side to restore balance is greater than, equal to, or less than the weight of the solid iron ball
when the ball is submerged (but not touching the bottom of the container), it is supported partly by the buoyant force on the left and partly by the string connected to the right side. so the left pan must increase its upward force to provide the buoyant force in addition to whatever force is provided before, and the right pan's upward force decreases by the same amount, since it now supports a ball lighter by the amount of the buoyant force. to bring the scale back to balance, the additional weight that must be put on the right side will equal twice the weight of water displaced by the submerged ball. why twice? half of the added weight makes up for the loss of upward force on the right, and the other half for the equal gain in upward force on the left (if each side initially weighs 10 N and the left side gains 2 N to become 12 N, the right side loses 2 N to become 8 N. so an additional weight of 4 N, not 2 N is required on the right side to restore balance). because the density of water is less than half the density of the iron ball, the restoring weight, equal to twice the buoyant force, will still be less than the weight of the ball.