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MFMcGrawChap 13d-Liquids - Revised 4-3-101 Chapter 13 LIQUIDS

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MFMcGrawChap 13d-Liquids - Revised 4-3-102 This lecture will help you understand: Pressure Pressure in a Liquid Buoyancy in a Liquid Archimedes’ Principle What Makes an Object Sink or Float Flotation Pascal’s Principle Surface Tension & Capillarity

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MFMcGrawChap 13d-Liquids - Revised 4-3-103 The force per unit area that one object exerts on another In equation form: Pressure depends on area over which force is distributed - a force “density.” Units: N/m 2, lb/ft 2, or Pa (Pascals) Pressure force area Pressure

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MFMcGrawChap 13d-Liquids - Revised 4-3-104 Pressure Pressure depends upon the surface area over which the force is applied. The vertical block exerts a greater force on the table than the horizontal block.

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MFMcGrawChap 13d-Liquids - Revised 4-3-105 Pressure Example: The teacher between nails is unharmed because force is applied over many nails. Combined surface area of the nails results in a tolerable pressure that does not puncture the skin.

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MFMcGrawChap 13d-Liquids - Revised 4-3-106 When you stand on one foot instead of two, the force you exert on the floor is less. B.the same. C.more. D.None of the above. Pressure CHECK YOUR NEIGHBOR-Trick Question

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MFMcGrawChap 13d-Liquids - Revised 4-3-107 When you stand on one foot instead of two, the force you exert on the floor is less. B.the same. C.more. D.None of the above. Comment: Distinguish between force and pressure! Pressure CHECK YOUR ANSWER - Did you get caught?

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MFMcGrawChap 13d-Liquids - Revised 4-3-108 When you stand on one foot instead of two, the pressure you exert on the floor is less. B.the same. C.more. D.None of the above. Pressure CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-109 When you stand on one foot instead of two, the pressure you exert on the floor is less. B.the same. C.more. D.None of the above. Explanation: Twice as much, in fact! Pressure CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1010 Characteristics of a Liquid Liquids can flow to fill up an arbitrary shape. Liquids can not support a shear stress. Liquids (for our purposes) are in compessive We can’t squeeze a given amount of liquid into a smaller volume. Liquids are not like nerf balls In general - fluid means a liquid or a gas.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1011 Pressure in a Liquid Force per unit area that a liquid exerts on an object Depth dependent and not volume dependent Example: Swim twice as deep, then twice as much weight of water above you produces twice as much pressure on you.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1012 Pressure in a Liquid Pressure acts equally in all directions Example: Your ears feel the same amount of pressure under water no matter how you tip your head. Bottom of a boat is pushed upward by water pressure. Pressure acts upward when pushing a beach ball under water. A shrunken styrofoam head bearing geologist Mike Rowe's signature and the scrawls and artwork of other science party members demonstates the effects of the deep-sea pressures that bear down on Alvin. Passengers inside the sub are protected by the vehicle's thick, titanium hull. This head began as a standard-sized wig form. Photograph: Sonya Senkowsky.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1013 What's the deal with the styrofoam heads? The styrofoam heads are something we do for fun on the research cruises when all of the work is done. We buy them from local stores in La Paz or a wholesaler in the US. They are the same size as a normal human head when we get them. We draw on them with Sharpies and then tie them in a dive bag on the side of the ROV so that when the ROV is at depth (10 meters of water depth = 1 atmosphere of pressure = 15 pounds per square inch) of say, 3000 meters, the head will be compressed to about 1/10 of its size! It's a bit like a souvenir from the deep. I've put pictures of the three that I've done at MBARI. http://www.mbari.org/staff/jones/shrunken.htmhttp://www.mbari.org/staff/jones/shrunken.htm A fluid can not support a shear stress.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1014 Pressure in a Liquid Independent of shape of container: Whatever the shape of a container, pressure at any particular depth is the same. In equation form: Liquid pressure weight density depth

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MFMcGrawChap 13d-Liquids - Revised 4-3-1015 Water pressure provided by a water tower is greater if the tower is taller. B.holds more water. C.Both A and B. D.None of the above. Pressure in a Liquid CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1016 Water pressure provided by a water tower is greater if the tower is taller. B.holds more water. C.Both A and B. D.None of the above. Explanation: Only depth, not amount of water, contributes to pressure. Pressure in a Liquid CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1017 Pressure Depends on Depth Independent of the volume of water behind the dam the size of the dam is determined by the depth of the water behind the dam.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1018 Pressure in a Liquid Effects of water pressure Acts perpendicular to surfaces of a container Liquid spurts at right angles from a hole in the surface. –The greater the depth, the greater the exiting speed.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1019 Pressure in a Liquid What happens to the water streaming out of the cup if you drop it?

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MFMcGrawChap 13d-Liquids - Revised 4-3-1020 Fountain Height

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MFMcGrawChap 13d-Liquids - Revised 4-3-1021 Buoyancy in a Liquid Buoyancy Apparent loss of weight of a submerged object Amount equals the weight of water displaced

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MFMcGrawChap 13d-Liquids - Revised 4-3-1022 Buoyancy in a Liquid Displacement rule: A completely submerged object always displaces a volume of liquid equal to its own volume. Example: Place a stone in a container that is brimful of water, and the amount of water overflow equals the volume of the stone.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1023 Buoyant Force and Overflow Weight

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MFMcGrawChap 13d-Liquids - Revised 4-3-1024 A cook who measures a specific amount of butter by placing it in a measuring cup with water in it is using the principle of buoyancy. B.displacement rule. C.concept of density. D.All of the above. Buoyancy in a Liquid CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1025 A cook who measures a specific amount of butter by placing it in a measuring cup with water in it is using the principle of buoyancy. B.displacement rule. C.concept of density. D.All of the above. Buoyancy in a Liquid CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1026 Buoyancy in a Liquid Buoyant force Net upward force that a fluid exerts on an immersed object = weight of water displaced Example: The difference in the upward and downward forces acting on the submerged block is the same at any depth

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MFMcGrawChap 13d-Liquids - Revised 4-3-1027 Buoyant Force

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MFMcGrawChap 13d-Liquids - Revised 4-3-1028 How many forces act on a submerged body at rest in a fluid? One—buoyancy B.Two—buoyancy and the force due to gravity C.None—in accord with the equilibrium rule, F = 0 D.None of the above. Buoyancy in a Liquid CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1029 How many forces act on a submerged body at rest in a fluid? One—buoyancy B.Two—buoyancy and the force due to gravity C.None—in accord with the equilibrium rule, F = 0 D.None of the above. Buoyancy in a Liquid CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1030 Buoyancy in a Liquid Sink or float? Sink when weight of submerged object is greater than the buoyant force. Neither sink nor float when weight of a submerged object is equal to buoyant force—object will remain at any level. Float when weight of submerged object is less than the buoyant force it would have when submerged — when floating, buoyant force = weight of floating object.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1031 Archimedes’ Principle Archimedes’ principle: Discovered by Greek scientist Archimedes. Relates buoyancy to displaced liquid. States that an immersed body (completely or partially) is buoyed up by a force equal to the weight of the fluid it displaces. Applies to gases and liquids.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1032 Archimedes’ Principle Apparent weight of a submerged object Weight out of water — buoyant force Example: If a 3-kg block submerged in water apparently “weighs” 2 kg, then the buoyant force or weight of water displaced is 1 kg.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1033 On which of these blocks submerged in water is the buoyant force greatest? 1 kg of lead B.1 kg of aluminum C.1 kg of uranium D.All the same. Archimedes’ Principle CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1034 On which of these blocks submerged in water is the buoyant force greatest? 1 kg of lead B.1 kg of aluminum C.1 kg of uranium D.All the same. Explanation: The largest block is the aluminum one. It displaces more water and therefore experiences the greatest buoyant force. All blocks are 1 kg, therefore the material with the smallest density has the largest volume. Archimedes’ Principle CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1035 When a fish expands its air bladder, the density of the fish decreases. B.increases. C.remains the same. D.None of the above. Archimedes’ Principle CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1036 When a fish expands its air bladder, the density of the fish decreases. B.increases. C.remains the same. D.None of the above. Archimedes’ Principle CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1037 When a fish decreases the size of its air bladder, the density of the fish decreases. B.increases. C.remains the same. D.None of the above. Archimedes’ Principle CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1038 When a fish decreases the size of its air bladder, the density of the fish decreases. B.increases. C.remains the same. D.None of the above. The bladder is normally empty, if the it is decreased then it is replaced with more dense tissue. Therefore the density of the fish increases. Archimedes’ Principle CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1039 When a submarine takes water into its ballast tanks, its density decreases. B.increases. C.remains the same. D.None of the above. Archimedes’ Principle CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1040 When a submarine takes water into its ballast tanks, its density decreases. B.increases. C.remains the same. D.None of the above. Archimedes’ Principle CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1041 When a submerged submarine expels water from its ballast tanks, its density decreases. B.increases. C.remains the same. D.None of the above. Archimedes’ Principle CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1042 When a submerged submarine expels water from its ballast tanks, its density decreases. B.increases. C.remains the same. D.None of the above. Explanation: This is how a submerged submarine is able to surface. Archimedes’ Principle CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1043 Flotation Principle of flotation: –A floating object displaces a weight of fluid equal to its own weight. Example: A solid iron 1-ton block may displace 1/8 ton of water and sink. The same 1 ton of iron in a bowl shape displaces a greater volume of water—the greater buoyant force allows it to float. Archimedes’ Principle

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MFMcGrawChap 13d-Liquids - Revised 4-3-1044 The reason a person finds it easier to float in saltwater compared with freshwater is that in saltwater the buoyant force is greater. B.a person feels less heavy. C.Neither of these. D.None of the above. Archimedes’ Principle CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1045 The reason a person finds it easier to float in saltwater compared with freshwater is that in saltwater the buoyant force is greater. B.a person feels less heavy. C.Neither of these. D.None of the above. Explanation: A floating person has the same buoyant force whatever the density of water. A person floats higher because a smaller volume of the denser saltwater is displaced. Archimedes’ Principle CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1046 On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoam-filled preservers. He apparently doesn’t know his physics. B.He is correct. Archimedes’ Principle Hewitt Turns Sadistic

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MFMcGrawChap 13d-Liquids - Revised 4-3-1047 On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoam-filled preservers. He apparently doesn’t know his physics. B.He is correct. Explanation: He’s correct, but what he doesn’t tell you is you’ll drown! Your life preserver will submerge and displace more water than those of your friends who float at the surface. Although the buoyant force on you will be greater, the net force downward is greater still! Archimedes’ Principle Hewitt Turns Sadistic

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MFMcGrawChap 13d-Liquids - Revised 4-3-1048 You place an object in a container that is full to the brim with water on a scale. The object floats, but some water spills out. How does the weight of the object compare with the weight of the water displaced? Weight of object is greater than weight of water displaced. B.Weight of object is less than weight of water displaced. C.Weight of object is equal to weight of water displaced. D.There is not enough information to decide. Flotation CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1049 You place an object in a container that is full to the brim with water on a scale. The object floats, but the water spills out. How does the weight of the object compare with the weight of the water displaced? Weight of object is greater than weight of water displaced. B.Weight of object is less than weight of water displaced. C.Weight of object is equal to weight of water displaced. D.There is not enough information to decide. Flotation CHECK YOUR ANSWER Explanation: This principle is wonderfully illustrated with Scotland’s Falkirk Wheel.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1050 The Falkirk Wheel’s two caisson are brimful of water and the same weight, regardless of whether there are boats in them. This makes rotation and lifting almost effortless. Falkkirk Wheel

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MFMcGrawChap 13d-Liquids - Revised 4-3-1051 Falkkirk Wheel

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MFMcGrawChap 13d-Liquids - Revised 4-3-1052 Archimedes’ Principle Denser fluids will exert a greater buoyant force on a body than less dense fluids of the same volume. Example: Ship will float higher in saltwater (density = 1.03 g/cm 3 ) than in freshwater (density = 1.00 g/cm 3 ).

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MFMcGrawChap 13d-Liquids - Revised 4-3-1053 Archimedes’ Principle Applies in air –The more air an object displaces, the greater the buoyant force on it. –If an object displaces its weight, it hovers at a constant altitude. –If an object displaces less air, it descends.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1054 As you sit in class, is there a buoyant force acting on you? No, as evidenced by an absence of lift B.Yes, due to displacement of air Archimedes’ Principle CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1055 As you sit in class, is there a buoyant force acting on you? No, as evidenced by an absence of lift B.Yes, due to displacement of air Explanation: There is a buoyant force on you due to air displacement, but much less than your weight. Archimedes’ Principle CHECK YOUR ANSWER

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MFMcGrawChap 13d-Liquids - Revised 4-3-1056 What Makes an Object Float or Sink? Whether an object floats or sinks depends upon the volume of the object. volume of the fluid displaced. For an object to float: Weight of object is less than buoyant force of the liquid, i.e., less than the weight of the liquid it displaces. Odd fact - A chuck of iron (7.86 gm/cm 3 ) will float in mercury (13.6 gm/cm 3 ).

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MFMcGrawChap 13d-Liquids - Revised 4-3-1057 What Makes an Object Float or Sink? Three rules: 1.An object more dense than the fluid in which it is immersed will sink. 2.An object less dense than the fluid in which it is immersed will float. 3.An object having a density equal to the density of the fluid in which it is immersed will neither sink nor float.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1058 Artesian Diver

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MFMcGrawChap 13d-Liquids - Revised 4-3-1059 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? On the lead block B.On the aluminum block C.Same on both blocks D.There is not enough information to decide. What Makes an Object Float or Sink? CHECK YOUR NEIGHBOR

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MFMcGrawChap 13d-Liquids - Revised 4-3-1060 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? On the lead block B.On the aluminum block C.Same on both blocks D.There is not enough information to decide. What Makes an Object Float or Sink? CHECK YOUR ANSWER Explanation: The buoyant force depends upon the volume of the block that is submerged. Since both submerged blocks are the same size, they displace the same volume of water. So they have the same buoyant force.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1061 Pascal’s Principle A change in pressure at any point in a confined fluid is transmitted everywhere throughout the fluid. (This is useful in making a hydraulic lift.) The pressure transmitted throughout a confined liquid is pressure over and above that already in the liquid.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1062 Pascal’s Principle Pressure applied to one portion of a confined liquid is transferred through out the liquid.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1063 Pascal’s Principle Pressing on the “wrong” side of the hydraulic lift doesn’t take advantage of Pascal’s Principle In a real hydraulic lift thesmaller force is applied using an air compressor.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1064 Apply a force F 1 here to a piston of cross-sectional area A 1. The applied force is transmitted to the piston of cross-sectional area A 2 here. Pascal’s Principle

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MFMcGrawChap 13d-Liquids - Revised 4-3-1065 Mathematically, Here we simplify the problem by ignoring the contribution of the difference in the fluid column heights. Pascal’s Principle

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MFMcGrawChap 13d-Liquids - Revised 4-3-1066 Example: Assume that a force of 500 N (about 110 lbs) is applied to the smaller piston in the previous figure. For each case, compute the force on the larger piston if the ratio of the piston areas (A 2 /A 1 ) are 1, 10, and 100. 50,000 N100 5000 N10 500 N1 F2F2 Using Pascal’s Principle: Pascal’s Principle

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MFMcGrawChap 13d-Liquids - Revised 4-3-1067 Surface Tension & Capillarity In the next chapter on gases we’ll think of atoms as rigid balls that ricochet off one another. Here we think of atoms as sticky balls which demonstrate the property of capillarity. An interesting example of capillarity (not in the text) involves the tallness of trees. The cohesive forces of water explains the transport of water from roots to the top of tall trees. When a single water molecule evaporates from the cell membrane inside a leaf, it is replaced by the one immediately next to it due to the cohesive forces between water molecules. A pull is created on the column of water which is continuous from leaves to roots. Water can be lifted far higher than the 10.2 m that atmospheric pressure would serve—even to 100 m in this way, the height of the largest trees.

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Quick Questions

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MFMcGrawChap 13d-Liquids - Revised 4-3-1069 Consider a boat loaded with scrap iron in a swimming pool. If the iron is thrown overboard into the pool, will the water level at the edge of the pool rise, fall, or remain unchanged? 1. Rise 2. Fall 3. Remain unchanged

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MFMcGrawChap 13d-Liquids - Revised 4-3-1070 1. Rise 2. Fall 3. Remain unchanged Consider a boat loaded with scrap iron in a swimming pool. If the iron is thrown overboard into the pool, will the water level at the edge of the pool rise, fall, or remain unchanged?

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MFMcGrawChap 13d-Liquids - Revised 4-3-1071

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MFMcGrawChap 13d-Liquids - Revised 4-3-1072 In the presence of air, the small iron ball and large plastic ball balance each other. When air is evacuated from the container, the larger ball 1. rises. 2. falls. 3. remains in place.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1073

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MFMcGrawChap 13d-Liquids - Revised 4-3-1074 The weight of the stand and suspended solid iron ball is equal to the weight of the container of water as shown above. When the ball is lowered into the water the balance is upset. The amount of weight that must be added to the left side to restore balance, compared to the weight of water displaced by the ball, would be 1. half.2. the same. 3. twice.4. more than twice.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1075

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MFMcGrawChap 13d-Liquids - Revised 4-3-1076 A pair of identical balloons are inflated with air and suspended on the ends of a stick that is horizontally balanced. When the balloon on the left is punctured, the balance of the stick is 1. upset and the stick rotates clockwise. 2. upset and the stick rotates counter-clockwise. 3. unchanged.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1077

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MFMcGrawChap 13d-Liquids - Revised 4-3-1078 Consider an air-filled balloon weighted so that it is on the verge of sinking—that is, its overall density just equals that of water. Now if you push it beneath the surface, it will 1. sink. 2. return to the surface. 3. stay at the depth to which it is pushed.

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MFMcGrawChap 13d-Liquids - Revised 4-3-1079

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MFMcGrawChap 13d-Liquids - Revised 4-3-1080 Summary Pressure Pressure in a Liquid Buoyancy in a Liquid Archimedes’ Principle What Makes an Object Sink or Float Flotation Pascal’s Principle Surface Tension & Capillarity

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Extras

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MFMcGrawChap 13d-Liquids - Revised 4-3-1082 Densities of Common Substances

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MFMcGrawChap 13d-Liquids - Revised 4-3-1083 The density of the block of wood floating in water is 1. greater than the density of water. 2. equal to the density of water. 3. less than half that of water. 4. more than half the density of water. 5. … not enough information is given.

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