The Depth of the Atmosphere Evangelista Torricelli

Problem 1P Estimate the weight of the air in your physics classroom.

Problem 2P What weight of water is required to fill a 25-gallon aquarium?

Problem 3CQ Water towers on the roofs of buildings have metal bands wrapped around them for support. The spacing between bands is smaller near the base of a tower than near its top. Explain.

Problem 1CQ Suppose you drink a liquid through a straw. Explain why the liquid moves upward, against gravity, into your mouth.

Referring to Example 15–9 Suppose both h and H are increased by a factor of two. By what factor is the distance D increased?

Problem 2CQ Considering your answer to the previous question, is it possible to sip liquid through a straw on the surface of the Moon? Explain.

Problem 3P You buy a "gold" ring at a pawn shop. The ring has a mass of 0.014 g and a volume of 0.0022 cm3. Is the ring solid gold,?

Problem 4CQ What holds a suction cup in place?

Problem 4P Estimate the weight of a treasure chest filled with gold doubloons.

Suppose a force of 400 N is required to push the top off a wine barrel. In a famous experiment, Blaise Pascal attached a tall,thin tube to the top of a filled wine barrel, as shown in Figure 15–26. Water was slowly added to the tube until the barrel burst. The puzzling result found by Pascal was that the barrel broke when the weight of water in the tube was much less than 400 N. Explain Pascal’s observation.

Problem 5P A cube of metal has a mass of 0347 kg and measures 3.21 cm on a side. Calculate the density and identify the metal.

Why is it more practical to use mercury in the barometer shown in Figure 15–4 than water?

Problem 6P What is the downward force exerted by the atmosphere on a football field, whose dimensions are 360 ft by 160 ft?

Problem 7CQ An object's density can be determined by first weighing it in air, then in water (provided the density of the object is greater than the density of water, so that it is totally submerged when placed in water). Explain how these two measurements can give the desired result.

Problem 7P BIO Bioluminescence Some species of dinoflagellate (a type of unicellular plankton) can produce light as the result of biochemical reactions within the cell. This light is an example of bioluminescence. It is found that bioluminescence in dinofla-gcllates can be triggered by deformation of the cell surface with a pressure as low as one dyne (10?5 N) per square centimeter. What is this pressure in (a) pascals and (b) atmospheres?

Problem 8CQ How does a balloonist control the vertical motion of a hot-air balloon?

Problem 8P A 79-kg person sits on a 3.7-kg chair. Each leg of the chair makes contact with the floor in a circle that is 1.3 cm in diameter. Find the pressure exerted on the floor by each leg of the chair, assuming the weight is evenly distributed.

Problem 9CQ Why is it possible forpeople to float without effort in Utah's Great Salt Lake?

Problem 9P To prevent damage to floors (and to increase friction), a crutch will often have a rubber tip attached to its end. If the end of the crutch is a circle of radius 1.2 cm without the tip, and the tip is a circle of radius 2.5 cm, by what factor does the tip reduce the pressure exerted by the crutch?

Problem 10CQ Physics in the Movies In the movie Voyage to the Bottom of the Sea, the Earth is experiencing a rapid warming. In one scene, large icebergs break up into small, car-size chunks that drop downward through the water and bounce off the hull of the submarine Seaview. Is this an example of good, bad, or ugly physics? Explain.

Problem 10P An inflated basketball has a gauge pressure of 9.9 lb/inz. What is the actual pressure inside the ball?

Problem 11CQ One day, while snorkeling near the surface of a crystal-clear ocean, it occurs to you that you could go considerably deeper by simply lengthening the snorkel tube. Unfortunately, this does not work well at all. Why?

Problem 12CQ Since metal is more dense than water, how is it possible for a metal boat to float?

Problem 11P Suppose that when you ride on your 7.70-kgbike the weight of you and the bike is supported equally by the two tires. If the gauge pressure in the tires is 70.5 1b/in and the area of contact between each tire and the road is 7.13 cm2, what is your weight?

Problem 11P Suppose that when you ride on your 7.70-kg bike the weight of you and the bike is supported equally by the two tires. If the gauge pressure in the tires is 70.5 1b/in2 and the area of contact between each tire and the road is 7.13 cm2, what is your weight?

Problem 13P CE Two drinking glasses, 1 and 2, are filled with water to the same depth. Glass 1 has twice the diameter of glass 2. (a) Is the weight of the water in glass 1 greater than, less than, or equal to the weight of the water in glass 2? (b) Is the pressure at the bottom of glass 1 greater than, less than, or equal to the pressure at the bottom of glass 2?

Problem 14CQ It is a common observation that smoke rises more rapidly through a chimney when there is a wind blowing outside. Explain.

Figure 15–27 shows four containers, each filled with water to the same level. Rank the containers in order of increasing pressure at the depth h. Indicate ties where appropriate.

Problem 15CQ Is it best for an airplane to take off against the wind or with the wind? Explain.

Problem 16CQ If you have a hair dryer and a Ping Pong ball at home, try this demonstration. Direct the air from the dryer in a direction just above horizontal. Next, place the Ping Pong ball in the stream of air. If done just right, the ball will remain suspended in midair. Use the Bernoulli effect to explain this behavior.

Problem 15P Water in the lake behind Hoover Dam is 221 m deep. What is the water pressure at the base of the dam?

Problem 16P In a classroom demonstration, the pressure inside a soft drink can is suddenly reduced to essentially zero. Assuming the can to be a cylinder with a height of 12 cm and a diameter of 6.5 cm, find the net inward force exerted on the vertical sides of the can due to atmospheric pressure.

Problem 17CQ Suppose a pitcher wants to throw a baseball so that it rises as it approaches the batter. How should the ball be spinning to accomplish this feat? Explain.

Problem 17P As a storm front moves in, you notice that the column of mercury in a barometer rises to only 736 mm. (a) What is the air pressure? (b) If the mercury in this barometer is replaced with water, to what height does the column of water rise? Assume the same air pressure found in part (a).

A circular wine barrel \(75 \mathrm{~cm}\) in diameter will burst if the net upward force exerted on the top of the barrel is 643 N. A tube \(1.0 \mathrm{~cm}\) in diameter extends into the barrel through a hole in the top, as indicated in Figure 15–26. Initially, the barrel is filled to the top and the tube is empty above that level. What weight of water must be poured into the tube in order to burst the barrel? Equation Transcription: Text Transcription: 75 cm 1.0 cm

In the hydraulic system shown in Figure 15–28, the piston on the left has a diameter of \(4.4 \mathrm{~cm}\) and a mass of \(1.8 \mathrm{~kg}\). The piston on the right has a diameter of \(12 \mathrm{~cm}\) and a mass of 3.2 kg. If the density of the fluid is \(750 \mathrm{~kg} / \mathrm{m}^{3}\) what is the height difference h between the two pistons? Equation Transcription: Text Transcription: 4.4 cm 1.8 kg 12 cm 750 kg/m3

Problem 20P A cylindrical container with a cross-sectional area of 65.2 cm2 holds a fluid of density 806 kg/m3. At the bottom of the container the pressure is 116 kPa. (a) What is the depth of the fluid? (b) Find the pressure at the bottom of the container after an additional 2.05 × 10?3 m3 of this fluid is added to the container. Assume that no fluid spills out of the container.

Problem 21P IP Tourist Submarine A submarine called the Deep View 66 is currently being developed to take 66 tourists at a time on sightseeing trips to tropical coral reefs. According to guidelines of the AmericanSociety of Mechanical Engineers (ASME), to be safe for human occupancy the Deep View 66 must be able to withstand a pressure of 10.0 N per square millimeter, (a) To what depth can the Deep View 66 safely descend in seawater? (b) If the submarine is used in freshwater instead, is its maximum safe depth greater than, less than, or the same as in seawater? Explain.

A water storage tower, like the one shown in the accompanying photo, is filled with freshwater to a depth of 6.4 m. What is the pressure at (a) 4.5 m and (b) 5.5 m below the surface of the water? (c) Why are the metal bands on such towers more closely spaced near the base of the tower?

Problem 23P IP You step into an elevator holding a glass of water filled to a depth of 6.9 cm. After a moment, the elevator moves upward with constant acceleration, increasing its speed from 0 to 2.4 m/s in 3.2 s. (a) During the period of acceleration, is the pressure exerted on the bottom of the glass greater than, less than, or the same as before the elevator began to move? Explain, (b) Find the change in the pressure exerted on the bottom of the glass as the elevator accelerates.

Problem 25P Referring to Example 15%, suppose that some vegetable oil has been added to both sides of the U tube. On the right side of the tube, the depth of oil is 5.00 cm, as before. On the left side of the tube, the depth of the oil is 3.00 cm. Find the difference in fluid level between the two sides of the tube.

Problem 24P Suppose you pour water into a container until it reaches a depth of 12 cm. Next, you carefully pour i na 7,2-cm thickness of olive oil so that it floats on top of the water. What is the pressure at the bottom of the container?

Problem 26P P As a stunt, you want to sip some water through a very long, vertical straw, (a) First, explain why the liquid moves upward, against gravity, into your mouth when you sip. (b) What is the tallest straw that you could, in principle, drink from in this way?

The patient in Figure 15–29 is to receive an intravenous injection of medication. In order to work properly, the pressure of fluid containing the medication must be 109 kPa at the injection point. (a) If the fluid has a density of \(1020 \mathrm{~kg} / \mathrm{m}^{3}\) find the height at which the bag of fluid must be suspended above the patient. Assume that the pressure inside the bag is one atmosphere. (b) If a less dense fluid is used instead, must the height of suspension be increased or decreased? Explain. Equation Transcription: Text Transcription: 1020 kg/m3

Problem 28P Acylindrical container 1.0 m tall contains mercury to a certain depth, d. The rest of the cylinder is filled with water, If the pressure at the bottom of the cylinder is two atmospheres, what is the depth d?

Problem 31P CE A fish canying a pebble in its mouth swims with a small, constant velocity in a small bowl. When the fish drops the pebble to the bottom of the bowl, does the water level rise, fall, or stay the same?

Problem 30P CE Lead is more dense than aluminum, (a) Is the buoyant force on a solid lead sphere greater than, less than, or equal to the buoyant force on a solid aluminum sphere of the same diameter? (b) Does your answer to part (a) depend on the fluid that is causing the buoyant force?

Problem 29P CE Predict/Explain Beebe and Barton On Wednesday, August 15,1934, William Beebe and Otis Barton made history by descending in the Bathysphere—basically a steel sphere 4.75 ft in diameter—3028 ft below the surface of the ocean, deeper than anyone had been before, (a) As the Bathysphere was lowered, was the buoyant force exerted on it at a depth of 10 ft greater than, less than, or equal to the buoyant force exerted on it at a depth of 50 ft? (b) Choose the best explanation from among the following: I. The buoyant force depends on the density of the water, which is essentially the same at 10 ft and 50 ft. II. The pressure increases with depth, and this increases the buoyant force. III. The buoyant force decreases as an object sinks below the surface of the water.

Problem 33P To walk on water, all you need is a pair of water-walking boots shaped like boats. If each boot is 27 cm high and 34 cm wide, how long must they be to support a 75-kg person?

Problem 32P A raft is 4.2 m wide and 6.5 m long. When a horse is loaded fonto the raft, it sinks 2,7 cm deeper into the water. What is the weight of the horse?

Problem 34P A3.2-kg balloon is filled with helium (density = 0.179 kg/m3). If the balloon is a sphere with a radius of 4.9 m, what is the maximum weight it can lift?

Problem 35P A hot-air balloon plus cargo has a mass of 1890 kg and a volume of 11,430 m3. The balloon is floating at a constant height of 6.25 m above the ground, What is the density of the hot air in the balloon?

Problem 36P In the lab you place a beaker that is half full of water (density pw)on a scale. You now use a high t string to suspend a piece of metal of volume v in the water, The metal is completely submerged, and none of the water spills out of the beaker. Give a symbolic expression for the change in reading of the scale.

Problem 37P · CE Predict/Explain A block of wood has a steel ball glued one surface. The block can be Floated with the ball "high dry" on its top surface, (a) When the block is inverted, and th ball is immersed in water, does the volume of wood that is submerged increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. When the block is inverted the ball pulls it downward causing more of the block to be submerged. II. The same amount of mass is supported in either case, there fore the amount of the block that is submerged is the same III. When the block is inverted the ball experiences a buoyant force, which reduces the buoyant force that must be provided by the wood.

Problem 41P CE On a planet in a different solar system the acceleration of gravity is greater than it is on Earth. Tf you float in a pool of water on this planet, do you float higher than, lower than, or at the same level as when you float in water on Earth?

Measuring Density with a Hydrometer A hydrometer, a device for measuring fluid density, is constructed as shown in Figure 15–30. If the hydrometer samples fluid 1, the small float inside the tube is submerged to level 1. When fluid 2 is sampled, the float is submerged to level 2. Is the density of fluid 1 greater than, less than, or equal to the density of fluid 2? (This is how mechanics test your antifreeze level. Since antifreeze [ethylene glycol] is more dense than water, the higher the density of coolant in your radiator the more antifreeze protection you have.)

Problem 38P · CE Predict/Explain In the preceding problem, suppose the block of wood with the ball "high and dry" is floating in a tank of water, (a) When the block is inverted, does the water level in the tank increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. Inverting the block makes the block float higher in the water, which lowers the water level in the tank. II. The same mass is supported by the water in either case, and therefore the amount of displaced water is the same. III. The inverted block floats lower in the water, which displaces more water and raises the level in the tank.

Problem 42P An air mattress is 2.3 m long, 0,66 m wide, and 14 cm deep. If the air mattress itself has a mass of 0.22 kg, what is the maximum mass it can support in freshwater?

Problem 43P A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is completely immersed in water, the scale reads 17.7 N. What are (a) the volume and (b) the density of the block?

Problem 44P As in the previous problem, a solid block is suspended from a spring scale. If the reading on the scale when the block is completely immersed in water is 25.0 N, and the reading when it is completely immersed in alcohol of density 806 kg/m3 is 25.7 N, what are (a) the block's volume and (b) its density?

Problem 45P BIO A person weighs 756 N in air and has a body-fat percentage of 28.1%. (a) What is the overall density of this person's body? (b) What is the volume of this person's body? (c) Find the apparent weight of this person when completely submerged in water.

Problem 46P IP A log floats in a river with one-fourth of its volume above the water, (a) What is the density of the log? (b) If the river carries the log into the ocean, does the portion of the log above the water increase, decrease, or stay the same? Explain.

Problem 47P A person with a mass of 81 kg and a volume of 0.089 m3 floats quietly in water, (a) What is the volume of the person that is above water? (b) If an upward force F is applied to the person by a friend, the volume of the person above water increases by 0.0018 m3. Find the force F.

Problem 49P A piece of lead has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.5 cm. If the puck is placed in a mercury bath, it floats. How deep below the surface of the mercury is the bottom of the lead puck?

A block of wood floats on water. A layer of oil is now poured on top of the water to a depth that more than covers the block, as shown in Figure 15–31. (a) Is the volume of wood submerged in water greater than, less than, or the same as before? (b) If \(90 \%\) of the wood is submerged in water before the oil is added, find the fraction submerged when oil with a density of \(875 \mathrm{~kg} / \mathrm{m}^{3}\) covers the block. Equation Transcription: Text Transcription: 90% 875 kg/m3

Problem 51P To water the yard, you use a hose with a diameter of 3.4 cm. water flows from the hose with a speed of 1.1 rn/s. If you partially block the end of the hose so the effective diameter is now 0-57 cm, with what speed does water spray from the hose?

Problem 50P lead weight with a volume of 0.82 × 10?5 m3 is lowered on a fishing line into a lake to a depth of 1.0 m. (a) What tension is required in the fishing line to give the weight an upward acceleration of 2.1 m/s2? (b) If the initial depth of the weight is increased to 2.0 m, does the tension found in part (a) increase, decrease, or stay the same? Explain, (c) What acceleration will the weight have if the tension in the fishing line is 1.2 N? Give both direction and magnitude.

Problem 53P To fill a child's inflatable wading pool, you use a garden hose with a diameter of 2.9 cm. Water flows from this hose with a speed of 1.3 m/s. How long will it take to fill the pool to a depth of 26 cm if the pool is circular and has a diameter of 2.0 m?

Problem 52P Water flows through a pipe with a speed of 2.1 m/s. Find the flow rate in kg/s if the diameter of the pipe is 3.8 cm.

Problem 54P BIO Heart Pump Rate When at rest, your heart pumps blood at the rate of 5.00 liters per minute (L/min). What are the volume and mass of blood pumped by your heart in one day?

Problem 55P BIO Blood Speed in an Arteriole A typical arteriole has a diameter of 0.030 mm and carries blood at the rate of 5.5 × 10?6 cm3/s. (a) What is the speed of the blood in an arteriole? (b) Suppose an arteriole branches into 340 capillaries, each with a diameter of 4.0 × 10?6 m. What is the blood speed in the capillaries? (The low speed in capillaries is beneficial; it promotes the diffusion of materials to and from the blood.)

Problem 56P IP Water flows at the rate of 3.11 kg/s through a hose with a diameter of 3.22 cm. (a) What is the speed of water in this hose? (b) If the hose is attached to a nozzle with a diameter of 0.732 cm, what is the speed of water in the nozzle? (c) Is the number of kilograms per second flowing through the nozzle greater than, less than, or equal to 3.11 kg/s? Explain.

Problem 57P A river narrows at a rapids from a width of 12 m to a width of only 5.8 m. The depth of the river before the rapids is 2.7 m; the depth in the rapids is 0.85 m. Find the speed of water flowing in the rapids, given that its speed before the rapids is 1.2 m/s. Assume the river has a rectangular cross section.

Problem 58P BIO How Many Capillaries? The aorta has an inside diameter of approximately 2,1 cm, compared to that of a capillary, which is about 1.0 × 10?5 m (10 ?m). In addition, the average speed of How is approximately 1.0 m/s in the aorta and 1.0 cm/s in a capillary. Assuming that all the blood that flows through the aorta also flows through the capillaries, how many capillaries does the circulatory system have?

Problem 59P BIO Plaque in an Artery The buildup of plaque on the walls of an artery may decrease its diameter from 1.1 cm to 0.75 cm. If the speed of blood flow was 15 cm/s before reaching the region of plaque buildup, find (a) the speed of blood flow and (b) the pressure drop within the plaque region.

Problem 60P A horizontal pipe contains water at a pressure of 110 kPa flowing with a speed of 1.6 m/s. When the pipe narrows to one-half its original diameter, what are (a) the speed and (b) the pressure of the water?

A Blowhard Tests of lung capacity show that adults are able to exhale 1.5 liters of air through their mouths in as little as 1.0 second. (a) If a person blows air at this rate through a drinking straw with a diameter of 0.60 cm, what is the speed of air in the straw? (b) If the air from the straw in part (a) is directed horizontally across the upper end of a second straw that is vertical, as shown in Figure 15–32, to what height does water rise in the vertical straw?

Problem 62P IP Water flows through a horizontal tube of diameter 2.8 cm that is joined to a second horizontal tube of diameter 1.6 cm. The pressure difference between the tubes is 7.5 kPa. (a) Which tube has the higher pressure? (b) Which tube has the higher speed of flow? (c) Find the speed of flow in the first tube.

Problem 63P A garden hose is attached to a water faucet on one end and a spray nozzle on the other end. The water faucet is turned on, but the nozzle is turned off so that no water flows through the hose. The hose lies horizontally on the ground, and a stream of water sprays vertically out of a small leak to a height of 0.68 m. What is the pressure inside the hose?

Problem 64P A water tank springs a leak. Find the speed of water emerging from the hole if the leak is 2.7 m below the surface of the water, which is open to the atmosphere.

Problem 67P IP During a thunderstorm, winds with a speed of 47.7 m/s blow across a flat roof with an area of 668 m2. (a) Find the magnitude of the force exerted on the roof as a result of this wind. (b) Is the force exerted on the roof in the upward or downward direction? Explain.

Problem 65P (a) Find the pressure difference on an airplane wing if air flows over the upper surface with a speed of 115 m/s, and along the bottom surface with a speed of 105 m/s. (b) If the area of the wing is 32 m2, what is the net upward force exerted on the wing?

Problem 66P On a vacation flight, you look out the window of the jet and wonder about the forces exerted on the window. Suppose the air outside the window moves with a speed of approximately 170 m/s shortly after takeoff, and that the air inside the plane is at atmospheric pressure, (a) Find the pressure difference between the inside and outside of the window, (b) If the window is 25 cm by 42 cm, find the force exerted on the window by air pressure.

Problem 68P A garden hose with a diameter of 0.63 in. has water flowing in it with a speed of 0.78 m/s and a pressure of 1.2 atmospheres. At the end of the hose is a nozzle with a diameter of 0.25 in. Find (a) the speed of water in the nozzle and (b) the pressure in the nozzle.

Problem 69P IP Water flows in a cylindrical, horizontal pipe. As the pipe narrows to half its initial diameter, the pressure in the pipe changes, (a) Is the pressure in the narrow region greater than, less than, or the same as the initial pressure? Explain, (b) Calculate the change in pressure between the wide and narrow regions of the pipe. Give your answer symbolically in terms of the density of the water, p, and its initial speed v.

Problem 70P BIO Vasodilation When the body requires an increased blood flow rate in a particular organ or muscle, it can accomplish this by increasing the diameter of arterioles in that area. This is referred to as vasodilation. What percentage increase in the diameter of an arteriole is required to double the volume flow rate of blood, all other factors remaining the same?

(a) Find the volume of blood that flows per second through the pulmonary artery described in Example 15–10. (b) If the radius of the artery is reduced by 18%, by what factor is the blood flow rate reduced? Assume that all other properties of the artery remain unchanged.

Problem 73P IP Water at 20 "C flows through a horizontal garden hose at the rate of 5.0 × 10?4 m3/s. The diameter of the garden hose is 2.5 cm. (a) What is the water speed in the hose? (b) What is the pressure drop across a 15-m length of hose? Suppose the cross-sectional area of the hose is halved, but the length and pressure drop remain the same, (c) By what factor does the water speed| change? (d) By what factor does the volume flow rate change? Explain,

Problem 72P · BIO An Occlusion in an Artery Suppose an occlusion in an artery reduces its diameter by 15%, but the volume flow rate of blood in the artery remains the same. By what factor has th pressure drop across the length of this artery increased?

Reading a Weather Glass A weather glass, as shown in Figure 15–33, is used to give an indication of a change in the weather. Does the water level in the neck of the weather glass move up or move down when a low-pressure system approaches?

Problem 75GP CE A helium-filled balloon for a birthday party is being brought home in a car. The balloon is connected to a string, and the passenger holds the lower end of the string in her lap. When the car i s a t res t a t a stop sign the string is vertical. As the car accelerates away from the light, does the string going to the balloon lean forward, lean backward, or remain vertical?

Problem 76GP ·CE Predict/Explain A person floats in a boat in a small backyard swimming pool. Inside the boat with the person are some bricks, (a) If the person drops the bricks overboard to the bottom of the pool, does the water level in the pool increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. When the bricks sink they displace less water than when they were floating in the boat; hence, the water level decreases. II. The same mass (boat + bricks + person) is in the pool in either case, and therefore the water level remains the same. III. The bricks displace more water when they sink to the bottom than they did when they were above the water in the boat; therefore the water level increases.

Problem 77GP CE A person floats in a boat in a small backyard swimming pool. Inside the boat with the person are several blocks of wood. Suppose the person now throws the blocks of wood into the pool, where they float, (a) Does the boat float higher, lower, or at the same level relative to the water? (b) Does the water level in the pool increase, decrease, or stay the same?

Problem 80GP CE In the system described in the previous problem, suppose the temperature is lowered below the freezing point of water as the turntable continues to rotate. The water is now a solid block of ice. If a marble is placed on the surface of the ice and released from rest, will it move toward the axis of rotation, move away from the axis of rotation, or stay where it is released?

Problem 79GP CE A pan half-filled with water is placed near the run of a rotating turntable. Is the normal to the surface of the water in the pan tilted outward away from the axis of rotation, tilted inward toward the axis of rotation, or is the water surface level and the normal vertical? (Refer to Problem 68 in Chapter 6 for a similar situation.) . Chapter 6 Problem 68 • CE BIO Gravitropism As plants grow, they tend to align their stems and roots along the direction of the gravitational field. This tendency, which is related to differential concentrations of plant hormones known as auxins, is referred to as gravitropism. As an illustration of gravitropism, experiments show that seedlings placed in pots on the rim of a rotating turntable do not grow in the vertical direction. Do you expect their stems to tilt inward—toward the axis of rotation—or outward—away from the axis of rotation?

The three identical containers in Figure 15–34 are open to the air and filled with water to the same level. A block of wood floats in container A; an identical block of wood floats in container B, supporting a small lead weight; container C holds only water. (a) Rank the three containers in order of increasing weight of water they contain. Indicate ties where appropriate. (b) Rank the three containers in order of increasing weight of the container plus its contents. Indicate ties where appropriate.

Problem 81GP CE BIO Sphygmomanometer" When a person's blood pressure is taken with a device known as a sphygmomanometer, it is measured on the arm, at approximately the same level as the heart. If the measurement were to be taken on the patient's leg instead, would the reading on the sphygmomanometer be greater than, less than, or the same as when the measurement is made on the arm?

Problem 83GP Su ersonic Erosion In waterjet cutting, a stream of supersonic water is used to slice through materials ranging from sheets of paper to solid steel plates. The water is held in a reservoir at 59,5OÜ psi and allowed to exit through a small orifice at high speed. Find the exit speed of the water, and compare with the speed of sound.

Problem 82GP At what depth below the ocean surface is the pressure equal to two atmospheres?

Problem 84GP A water main broke on Lake Shore Drive in Chicago on November 8, 2002, shooting water straight upward to a height of 8.0 ft. What was the pressure in the pipe?

Measuring Pain Threshold A useful instrument for evaluating fibromyalgia and trigger-point tenderness is the doloriometer or algorimeter. This device consists of a force meter attached to a circular probe that is pressed against the skin until pain is experienced. If the reading of the force meter is \(3.25 \mathrm{lb}\), and the diameter of the circular probe is \(1.39 \mathrm{~cm}\), what is the pressure applied to the skin? Give your answer in pascals. Equation Transcription: Text Transcription: 3.25 lb 1.39 cm

Problem 86GP BIO Power Output of the Heart The power output of the heart is given by the product of the average blood pressure, 1.33 N/cm2, and the flow rate, 105 cm3/s. (a) Find the power of the heart. Give your answer in watts, (b) How much energy does the heart expend in a day? (c) Suppose the energy found in part (b) is used to lift a 72-kg person vertically to a height h Find h, in meters.

Problem 87GP An above-ground backyard swimming pool is shaped like a large hockey puck, with a circular bottom and a vertical wall forming its perimeter. The diameter of the pool is 4.8 m and its depth is 1.8 m. Find the total outward force exerted on the vertical wall of the pool by the water, assuming the pool is completely filled.

Problem 88GP A solid block is suspended from a spring scale. When the block is in air, the scale reads 35.0 N, when immersed in water the scale reads 31.1 N, and when immersed in oil the scale reads 31.8 N. (a) What is the density of the block? (b) What is the density of the oil?

Problem 89GP A wooden block with a density of 710 kg/m3 and a volume of 0.012 m3 is attached to the top of a vertical spring whose force constant is k = 540 N/m. Find the amount by which the spring is stretched or compressed if it and the wooden block are (a) in air or (b) completely immersed in water. [The density of air may be neglected in part (a).]

Problem 90GP IP Floating a Ball and Block A 1.25-kg wooden block has an iron ball of radius 1.22 cm glued to one side, (a) If the block floats in water with the iron ball "high and dry," what is the volume of wood that is submerged? (b) If the block is now inverted, so that the iron ball is completely immersed, does the volume of wood that is submerged in water increase, decrease, or remain the same? Explain, (c) Calculate the volume of wood that is submerged when the block is in the inverted position.

Problem 91GP On a bet, you try to remove water from a glass by blowing across the top of a vertical straw immersed in the water. What is the minimum speed you must give the air at the top of the straw to draw water upward through a height of 1.6 cm?

Problem 92GP The Depth of the Atmosphere Evangelista Torricelli (1608-1647) was the first to put forward the idea that we live at the bottom of an ocean of air. (a) Given the value of atmospheric pressure at the surface of the Earth, and the fact that there is zero pressure in the vacuum of space, determine the depth of the atmosphere, assuming that the density of air and the acceleration of gravity are constant, (b) According to this model, what is the atmospheric pressure at the summit of Mt. Everest, 29,035 ft above sea level. (In fact, the density of air and the acceleration of gravity decrease with altitude, so the result obtained here is less than the actual depth of the atmosphere. Still this is a reasonable first estimate.)

The Hydrostatic Paradox I Consider the lightweight containers shown in Figure 15–35. Both containers have bases of area \(A_{\text {base }}=24 \mathrm{~cm}^{2}\) and depths of water equal to \(18 \mathrm{~cm}\). As a result, the downward force on the base of container 1 is equal to the downward force on container 2, even though the containers clearly hold different weights of water. This is referred to as the hydrostatic paradox. (a) Given that container 2 has an annular (ring-shaped) region of area \(A_{\text {ring }}=72 \mathrm{~cm}^{2}\) determine the net downward force exerted on the container by the water. (b) Show that your result from part (a) is equal to the weight of the water in container 2. Equation Transcription: Text Transcription: Abase=24 cm2 18 cm Aring=72 cm2

The Hydrostatic Paradox II Consider the two lightweight containers shown in Figure 15–36. As in the previous problem, these containers have equal forces on their bases but contain different weights of water. This is another version of the hydrostatic paradox. (a) Determine the net downward force exerted by the water on container 2. Note that the bases of the containers have an area \(A_{\text {base }}=24 \mathrm{~cm}^{2}\), the annular region has an area \(A_{\text {ring }}=18 \mathrm{~cm}^{2}\), and the depth of the water is \(18 \mathrm{~cm}\). (b) Show that your result from part (a) is equal to the weight of the water in container 2. (c) If a hole is poked in the annular region of container 2, how fast will water exit the hole? (d) How high above the hole will the stream of water rise? Equation Transcription: Text Transcription: Abase=24 cm2 Aring=18 cm2 18 cm

Problem 95GP IP A backyard swimming pool is circular in shape and contains water to a uniform depth of 38 cm. It is 2.3 m in diameter and is not completely filled, (a) What is the pressure at the bottom of the pool? (b) If a person gets into the pool and floats peacefully, does the pressure at the bottom of the pool increase, decrease, or stay the same? (c) Calculate the pressure at the bottom of the pool if the floating person has a mass of 72 kg.

Problem 96GP A prospector finds a solid rock composed of granite (p = 2650 kg/m3) and gold. If the volume of the rock is 3.55 × 10?4 m3, and its mass is 3.81 kg, (a) what mass of gold is contained in the rock? What percentage of the rock is gold by (b) volume and (c) mass?

Problem 97GP The Maximum Depth of the Earth's Crust Consider the crustal rocks of the Earth to be a fluid of density 3.0 × 103 kg/m3. Under this assumption, the pressure at a depth h within the crust is P = Pat + pgh. If the greatest pressure crustal rock can sustain before crumbling is 1.2 × 103Pa, find the maximum depth of the Earth's crust. (Below this depth the crust changes from a solid to a plasticlike material.)

Problem 98GP IP (a) If the tension in the string in Active Example 15-1 is 0.89 N, what is the volume of the wood? Assume that everything else remains the same, (b) If the string breaks and the wood floats on the surface, does the water level in the flask rise, drop, or stay the same? Explain, (c) Assuming the flask is cylindrical with a cross-sectional area of 62 cm2, find the change in water level after the string breaks.

Problem 100GP A tin can is filled with water to a depth of 39 on. Ahole 11 cm above the bottom of the can produces a stream of water that directed at an angle of 36° above the horizontal. Find (a) the range and (b) the maximum height of this stream of water

Problem 101GP BOA person weighs 685 N in air but only 497 N when standing in water up to the hips. Find (a) the volume of each of the person's legs and (b) the mass of each leg, assuming they have a density that is "1.05 times the density of water

Problem 102GP A horizontal pipe carries oil whose coefficient of viscosity is 0.00012 N · s/m2. The diameter of the pipe is 5.2 cm, and its length is 55 m. (a) What pressure difference is required between the ends of this pipe if the oil is to flow with an average speed of 1.2 m/s? (b) What is the volume flow rate in this case?

A Siphon for Irrigation A siphon is a device that allows water to flow from one level to another. The siphon shown in Figure 15–37 delivers water from an irrigation canal to a field of crops. To operate the siphon, water is first drawn through the length of the tube. After the flow is started in this way it continues on its own. (a) Using points 1 and 3 in Figure 15–37, find the speed of the water leaving the siphon at its lower end. Give a symbolic answer. (b) Is the speed of the water at point 2 greater than, less than, or the same as its speed at point 3? Explain.

Problem 103GP BIO A patient is given an injection with a hypodermic needle 3.3 cm long and 0.26 mm in diameter. Assuming the solution being injected has the same density and viscosity as water at 20°C, find the pressure difference needed to inject the solution at the rate of 1.5 g/s.

Problem 104GP An Airburst over Pennsylvania On the evening of July 23, 2001, a meteor streaked across the skies of Pennsylvania, creating a spectacular fireball before exploding in the atmosphere with an energy release of 3 kilotons of TNT. The pressure wave from the airburst caused an increase in pressure of 0.50 kPa, enough to shatter some windows. Find the force that this"overpressure" would exert on a 34-in. × 46-in. window. Give your answer in newtons and pounds.

Problem 105GP Going Over Like a Mythbuster Lead Balloon On one episode of Mythbusters, Jamie and Adam try to make a lead balloon that will float when filled with helium. The balloon they constructed was approximately cubical in shape, and 10 feet on a side. They used a thin lead foil, which gave the finished balloon a mass of 11 kg. (a) What was the thickness of the foil? (b) Would the lead balloon float if filled with helium? (c) If the balloon does float, what would be the most mass it could lift in addition to its own mass?

Problem 107GP A wooden block of cross-sectional area A, height H and density floats in fluid density . If the block is displaced downward and then released, it will oscillate with simple harmonic motion. Find the period of its motion

Problem 106GP IP A pan half-filled with water is placed in the back of an SUV. (a) When the SUV is driving on the freeway with a constant velocity, is the surface of the water in the pan level, tilted forward, or tilted backward? Explain, (b) Suppose the SUV accelerates in the forward direction with a constant acceleration a. Is the surface of the water tilted forward, or tilted backward? Ex-plain. (c) Show that the angle of tilt, 0, in part (b) has a magnitude given by tan 6 = a/g, where g is the acceleration of gravity.

Problem 110GP A geode is a hollow rock with a solid shell and an air-filled interior. Suppose a particular geode weighs twice as much in air as it does when completely submerged in water. If the density of the solid part of the geode is 2500 kg/m3, what fraction of the geode's volume is hollow?

Problem 108GP A round wooden log with a diameter of 73 cm floats with one-half of its radius out of the water. What is the log’s density?

A tank of water filled to a depth d has a hole in its side a height h above the table on which it rests. Show that water emerging from the hole hits the table at a horizontal distance of \(2 \sqrt{(d-h) h}\) from the base of the tank. Equation Transcription: Text Transcription: 2 \sqrt{(d-h) h}

The hollow, spherical glass shell shown in Figure 15–38 has an inner radius R and an outer radius 1.2R. The density of the glass is \(\rho_{g}\). What fraction of the shell is submerged when it floats in a liquid of density \(\rho=1.5 \rho_{g}\)? (Assume the interior of the shell is a vacuum.) Equation Transcription: Text Transcription: \rho_{g} \rho=1.5 \rho_{g}

The water tank in Figure 15–39 is open to the atmosphere and has two holes in it, one 0.80 m and one 3.6 m above the floor on which the tank rests. If the two streams of water strike the floor in the same place, what is the depth of water in the tank?

Problem 113GP A hollow cubical box, 0.29 m on a side, with walls of negligible thickness floats with 35% of its volume submerged. What mass of water can be added to the box before it sinks?

Assuming the doughnut has a cylindrical shape of height H and diameter D, and that the height of the white stripe is 0.22H, what is the density of the doughnut? A. \(260 \mathrm{~kg} / \mathrm{m}^{3}\) B. \(360 \mathrm{~kg} / \mathrm{m}^{3}\) C. \(720 \mathrm{~kg} / \mathrm{m}^{3}\) D. \(820 \mathrm{~kg} / \mathrm{m}^{3}\) Equation Transcription: Text Transcription: 260 kg/m3 360 kg/m3 720 kg/m3 820 kg/m3

A new doughnut is being planned whose density will be \(330 \mathrm{~kg} / \mathrm{m}^{3}\). If the height of the doughnut is H, what will be the height of the white stripe? A. 0.14H B. 0.24H C. 0.28H D. 0.64H Equation Transcription: Text Transcription: 330 kg/m3

Problem 118IP · · IP Referring to Example 15-4 Suppose we use a different vegetable oil that has a higher density than the one in Example 15-4. (a) If everything else remains the same, will the height difference, h, increase, decrease, or remain the same? Explain, (b) Find the height difference for an oil that has a density of 9.60 × 102 kg/m3.

Problem 119IP Referring to Example 15-4 Find the height difference, h, if the depth of the oil is increased to 7.50 cm. Assume everything else in the problem remains the same.

Problem 120IP Referring to Example 15-9 (a) Find the height H required to make D = 0.655 m. Assume everything else in the problem remains the same, (b) Find the depth h required to make D = 0.455 in. Assume everything else in the problem remains the same.

Problem 12P IP The weight of your 1420-kg car is supported equally by its four tires, each inflated to a gauge pressure of 35.0 lb/in2. (a) What is the area of contact each tire makes with the road? (b) If the gauge pressure is increased, does the area of contact increase, decrease, or stay the same? (c) What gauge pressure is required to give an area of contact of 116 cm2 for each tire?