Chapter 13 - Liquids
47) rank the following from greatest to least for the percentage of its volume above the water line: a) basketball floating in fresh water b) basketball floating in saltwater c) basketball floating in mercury
C, B, A
A recipe calls for a specific amount of butter. How does the displacement method relate to the use of a kitchen measuring cup?
Put some water in the cup before you add the butter. Note the water-level reading on the side of the cup. Then add the butter and you'll note the water level rise. Because butter floats, poke it beneath the surface. When you subtract the lower-level reading from the higher-level reading, you know not only the volume of water displaced but also the volume of the butter.
Suppose that you raise one foot when you are standing on a bathroom scale. Does that pressure you exert on the scale change? Is there a difference in the scale reading?
When you shift your weight by standing on one foot, the pressure on the scale's surface doubles. But the scale doesn't measure pressure--it measures weight. Except for some jiggling as you shift your weight, the scale reading stays the same.
61) 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
69) your friend replies that the reason is that saltwater is denser than fresh water, how would you answer the 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
principle of flotation
a floating object displaced a weight of fluid equal to its own weight
97) a small, dry paper clip can rest on the surface of still water. why can't a heavier paper clip do the same without sinking?
a heavier clip would push deeper in the water surface, overcoming the small force of surface tension, whereupon it sinks
73) why is a high mountain composed mostly of lead an impossibility on earth?
a mostly-lead mountain would be more dense than earth's mantle and would sink in it. most of the iron is in the earth's center
23) what geometrical shape has the smallest surface area for a given volume?
a sphere has the smallest surface area for a given volume
11) distinguish between an immersed and a submerged body
a submerged body is completed immersed, totally beneath the surface
59) the sketch shows a wooden reservoir reinforced with metal hoops that supplies water to a farm 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
25) distinguish between adhesive and cohesive forces
adhesion is the attraction between unlike substances; cohesion is the attraction between like substances
archimedes' principle
an immersed body is buoyed up by a force equal to the weight of the fluid it displaces - if we immerse a sealed 1-L container halfway into the water, it will displace a half-liter of water and be buoyed up by a force equal to the weight of a half-liter of water--no matter what is in the container. - if we immerse it completely, it will be buoyed up by a force equal to the weight of a full liter of water (1 kg of mass). - if the container is fully submerged and doesn't compress, the buoyant force will equal the weight of 1 kg of water at ANY depth, this is because the container can displace no greater volume of water than its own volume and the weight of this displaced water (not the weight of the submerged object) is equal to a buoyant force ex) objects weigh more in air than in water. when a 3-kg block is submerged, the scale reading reduces to 1 kg. the "missing" weight is equal to the weight of the 2 kg of water displaced, which equals the buoyant force
91) we say that the shape of a liquid is the same as the shape of its container. but, with no container and no gravity, what is the natural shape of a blob of water? why?
because of surface tension, which tends to minimize the surface area of a blob of water, its shape without gravity and other distorting forces is a sphere--the shape with the smallest surface area for a given volume
9) how does the volume of a completely submerged object compare with the volume of water displaced?
both volumes are the same
7) why does buoyant force act upward on an object submerged in water?
buoyant force acts upward because there is more force beneath an object due to greater pressure at greater depth
67) if liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid?
buoyant force is the result of differences in pressure; if there are no pressure differences, there is no buoyant force.
77) why is it inaccurate to say that heavy objects sink and light objects float?
heavy objects may or may not sink, depending on their densities
45) your friend of mass 100 kg can just barely float in fresh water. calculate her approximate volume
human density is about the same as waters, 1000 kg/m3. from density = m/v, we have v=m/density (100 kg)/(1000 kgm/m3) = 0.1 m3
21) what happens to the pressure in all parts of a confined fluid if the pressure in one part is increased?
if the pressure in one part is increased, the same increase in pressure is transmitted to all parts
89) 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 if the aquarium is brim filled, so that a volume of water equal to the volume of the fish overflows, then the reading will not change
3) what is the relationship between liquid pressure and the depth of a liquid? between liquid pressure and weight density?
liquid pressure is proportional to depth and to weight density
71) why will a block of iron float in mercury but sink in water?
mercury is more dense 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 will sink because it cannot displace its weight
57) if water faucets upstairs and downstairs are turned fully on, will more water per second flow out of the upstairs faucets or the downstairs faucets?
more water will flow from open faucets downstairs because of the greater pressure since pressure depends on depth, a downstairs faucet is effectively deeper than an upstairs faucet the pressure downstairs is greater by an amount = weight density x depth, where the depth is the vertical distance between faucets
If a friend commented that a hydraulic device is a common way of multiplying energy, what would you say?
no, although a hydraulic device can multiply force, it always does so at the expense of distance. energy is the product of force and distance. if you increase one, you decrease the other. no device has ever been found that can multiply energy
19) it was emphasized earlier that the buoyant force does not equal an object's weight but does equal the weight of the displaced water. now we say that the buoyant force equals the object's weight. isn't this a grand contradiction?
no. in the case of floating, the buoyant force equals both the weight of the object and the weight of the water displaced
93) 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 the principle have to do with their delight at your arrival?
part of whatever pressure you add to the water is transmitted to the hungry croc via pascals's principles. if the water were confined--that is, not open to the atmosphere--the crocs would receive every bit of pressure you exert. but even if you were able to slip into the pool to quietly float without exerting pressure, your displacement of water would raise the level in the pool
33) a 1-m tall barrel is filled with water (with a weight density of 10,000 N/m3) show that the water pressure on the bottom of the barrel is 10,000 N/m2, or equivalently 10kPa
pressure = weight density x depth 10,000 N/m3 x 1 m = 10,000 N/m2 = 10 kPa
35) the depth of water behind the Hoover Dam is 220 m. show that the water pressure at the base of this dam is 2200 kPa
pressure = weight density x depth = 10,000 N/m3 x 220 m = 2,200,000 N/m2 = 2200 kPa
1) how does pressure relate to force?
pressure is force / area
17) fill in the blanks: an object denser than water will ____ in water. an object less dense than water will ____ in water. an object that has the same density as water will ____ in water.
sink float neither sink nor float
83) 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
A 1-L container completely filled with lead has a mass of 11.3 kg and is submerged in water. What is the buoyant force acting on it?
the buoyant force equals the weight of the liter of water displaced--not the weight of the lead. one L of water has a mass of 1 kg and weighs 10 N. so the buoyant force on it is 10 N.
Two solid blocks of identical size are submerged in water. One block is lead and the other is aluminum. Upon which is the buoyant force greater?
the buoyant force is the same on both blocks because they displace the same volume of water. for submerged objects, the buoyant force is determined by only the volume of water displaced, not the object's weight.
As a boulder thrown into a deep lake sinks deeper and deeper into the water, does the buoyant force on it increase or decrease?
the buoyant force remains unchanged as the boulder sinks because the boulder displaced the same volume and the same weight of water at any depth
79) 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?
the buoyant force will remain unchanged on the sinking rock because it displaces the same volume and weight of water at any depth
As the automobile is being lifted, how does the oil-level change in the reservoir compare with the distance the automobile moves?
the car moves up a greater distance than the oil level drops, since the area of the piston is smaller than the surface area of the oil in the reservoir
43) a merchant sells you a solid gold 1-kg statue for a very reasonable price. when you get home, you wonder whether or not you got a bargain, so you lower the statue into a container of water and measure the volume of displaced water. show that, for pure gold, the volume of water displaced will be 51.8 cm3.
the density of gold is 19.3 g/cm3 your gold has a mass of 1000 grams, so 1000 g/V = 19.3 g/cm3 solving for v, we have v = 1000 g/19.3 g/cm3 = 51.8 cm3
101) 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. discuss whether or not this is possible
the event was quite reasonable because the force of the ocean on his finger would have been quite small. this is because the pressure on his finger has to do with only the depth of the water, specifically the distance of the leak below the sea level--not the weight of the ocean
87) one gondola in the falkirk wheel carries a 50-ton boat, while the other carries a 100-ton boat. why do the gondolas nevertheless weigh the same?
the gondolas weigh the same because they're brim full, and whatever the weight of a floating boat, the same weight of water was displaced when the boat entered the gondola
95) in the hydraulic arrangement, 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 is immaterial. what is your explanation to resolve this confusion?
the increase 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 ouput piston. however, the pressure increase is supplied by the mechanical pump, which has nothing to do with the area of fluid interface between the compressed air and the liquid. many hydraulic devices have a single piston upon which pressure is exerted.
buoyant force
the net upward force that a fluid exerts on an immersed object
pascal's principle
the pressure applied to a motionless fluid confined in a container is transmitted undiminished throughout the fluid - a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid
51) 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?
the pressure of the woman is greater because of the relatively small area of contact at the hell, which would hurt you more
5) how does the water pressure 1 m below the surface of a small pond compare with the water pressure 1 m below the surface of a huge lake?
the pressures are the same at the same depth
pressure
the ratio of force to the area over which that force is distributed: pressure = force/area liquid pressure = weight density x depth - the pressure a liquid exerts depends on its depth - the pressure of a liquid also depends on the density of the liquid (submerged in more dense than water, pressure would be greater)
capillarity
the rise of a liquid in a fine, hollow tube or in a narrow space
A beaker more than half full of water weighs 20 N. What will be the scale reading when a) a 5-N block of wood floats in it? b) a 8-N block of wood floats in it?
the scale readings will increase as weight is added: a) 20 N + 5 N = 25 N b) 20 N + 8 N = 28 N
63) in 1960, the u.s. navy's bathyscaphe descended to a depth of nearly 11 km in the marinanas 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
surface tension
the tendency of the surface of a liquid to contract in area and thus to behave like a stretched elastic membrane
13) if a 1-L container is immersed halfway into water, what is the volume of the water displaced? what is the buoyant force on the container?
the volume of the water displaced is 1/2 L the buoyant force is 5 N
53) why are persons who are confined to bed less likely to develop bedsores on their bodies if they rest on a water-bed rather than on an ordinary mattress?
there is less pressure with a waterbed due to the larger contact area
True of false? Archimedes' principles tells us that any object that displaces 10 N of liquid will be buoyed up with 10 N.
true. it's only the weight of the displaced liquid that counts.
103) suppose you wish to lay a level foundation for a house on hilly, brushy terrain. discuss how you could use a garden hose filled with water to determine equal elevations at distant points
using 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 the same elevation above sea level as the water surface at the other end of the hose
49) 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
65) why does water "seek its own level"?
water seeking its own level is a consequence of pressure depending on depth. in a bent u-tube full of water, 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
105) compared with an empty ship, would a ship loaded with a cargo of styrofoam sink deeper into the water or rise in the water?
when a ship is empty, its weight is least and it displaces the least water and floats highest. carrying a load of anything increases its weight and makes it float lower.
15) what is the condition in which the buoyant force on an object does equal the weight of the object?
when an object floats, its buoyant force equals its weight
75) why will a volleyball held beneath the surface of water have more buoyant force than if it is floating?
when the ball is held beneath the surface, it will displace a greater weight of water
If a fish makes itself denser, it will sink; if it makes itself less dense, it will rise. In terms of buoyant force, why is this so?
when the fish makes itself more dense by decreasing its volume, it displaces less water, so the buoyant force decreases. when the fish makes itself less dense by expanding its volume, more water is displaced and the buoyant force increases.
85) 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 in it? how about if the ice cube contains any gains of heavy sand?
when the ice cube melts, the water level at the side of the glass does not change the same occurs when the ice cube with the air bubbles melts, whether the ice cube is hollow or solid, it displaces as much water floating as when melted
41) a dike in holland springs a leak through a hole of area 1cm2 at a depth of 2 m below the water surface. how much force must a boy apple to the hole with his thumb to stop the leak? could he do it?
yes, first find the pressure weight density x depth = (10,000 N/m3)(2m) = 20,000 N/m2 or 20,000 Pa
81) the density of a rock doesn't change when it is 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
55) 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 down than when you are sitting or standing because the heart does not have to pump blood to the heights that correspond to standing or sitting
39) a 12-kg piece of metal displaces 2 L of water when submerged. show that its density is 6000 kg/m3. how does this compare with the density of water?
density = m/v 12 kg/2 L = 6 kg/L
The same beaker when brimful of water weighs 30 N. What will be the scale reading, after overflow, when a) a 5-N block of wood floats in it? b) a 8-N block of wood floats in it?
for the brimful beaker, the displacement of water by the floating blocks causes water to overflow a) the 5-N block causes an overflow of 5 N of water b) the 8-N block spills 8 N of water the scale reading doesn't change; it remains 30 N
37) calculate the average force per nail when sara, who weighs 120 pounds, lies on a bed of nails and is supported by 600 nails
force per nail is 120 pounds/600 nails = 0.2 pound per nail
