Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an on-line homework management program such as Wiley PLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 11.1 Mass Density

| 1 | ssm The ice on a lake is 0.010 m thick. The lake is circular, with a radius of 480 m. Find the mass of the ice.

| 2 | One of the concrete pillars that support a house is 2.2 m tall and has a radius of 0.50 m. The density of concrete is about . Find the weight of this pillar in pounds ().

| 3 | The karat is a dimensionless unit that is used to indicate the proportion of gold in a gold-containing alloy. An alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four. What is the volume of gold in a 14.0-karat gold necklace whose weight is 1.27 N?

| 4 | One end of a wire is attached to a ceiling, and a solid brass ball is tied to the lower end. The tension in the wire is 120 N. What is the radius of the brass ball?

| 5 | ssm Accomplished silver workers in India can pound silver into incredibly thin sheets, as thin as (about onehundredth of the thickness of this sheet of paper). Find the area of such a sheet that can be formed from 1.00 kg of silver.

| 6 | A full can of black cherry soda has a mass of 0.416 kg. It contains of liquid. Assuming that the soda has the same density as water, find the volume of aluminum used to make the can.

| 7 | A bar of gold measures . How many gallons of water have the same mass as this bar?

| 8 | A hypothetical spherical planet consists entirely of iron. What is the period of a satellite that orbits this planet just above its surface? Consult Table 11-1 as necessary.

| 9 | ssm www An antifreeze solution is made by mixing ethylene glycol () with water. Suppose the specific gravity of such a solution is 1.0730. Assuming that the total volume of the solution is the sum of its parts, determine the volume percentage of ethylene glycol in the solution.
Section 11.2 Pressure

| 10 | United States currency is printed using intaglio presses that generate a printing pressure of .2 A $20 bill is 6.1 in. by 2.6 in. Calculate the magnitude of the force that the printing press applies to one side of the bill.

| 11 | ssm An airtight box has a removable lid of area and negligible weight. The box is taken up a mountain where the air pressure outside the box is . The inside of the box is completely evacuated. What is the magnitude of the force required to pull the lid off the box?

| 12 | A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is . Assuming that the top and bottom surfaces of the cap each have an area of , obtain the magnitude of the force that the screw thread exerts on the cap in order to keep it on the bottle. The air pressure outside the bottle is one atmosphere.

| 13 | A person who weighs 625 N is riding a 98-N mountain bike. Suppose the entire weight of the rider and bike is supported equally by the two tires. If the gauge pressure in each tire is , what is the area of contact between each tire and the ground?

| 14 | Interactive Solution 11.14 at presents a model for solving this problem. A solid concrete block weighs 169 N and is resting on the ground. Its dimensions are . A number of identical blocks are stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block?

* | 15 | A suitcase () is resting on the floor of an elevator. The part of the suitcase in contact with the floor measures 0.50 m by 0.15 m. The elevator is moving upward, the magnitude of its acceleration being 1.5 m/s2. What pressure (in excess of atmospheric pressure) is applied to the floor beneath the suitcase?

* | 16 | A 58-kg skier is going down a slope oriented 35° above the horizontal. The area of each ski in contact with the snow is 0.13 m2. Determine the pressure that each ski exerts on the snow.

* | 17 | ssm A cylinder (with circular ends) and a hemisphere are solid throughout and made from the same material. They are resting on the ground, the cylinder on one of its ends and the hemisphere on its flat side. The weight of each causes the same pressure to act on the ground. The cylinder is 0.500 m high. What is the radius of the hemisphere?

** | 18 | The drawing shows a cylinder fitted with a piston that has a mass m1 of 0.500 kg and a radius of . The top of the piston is open to the atmosphere. The pressure beneath the piston is maintained at a reduced (but constant) value by means of the pump. As shown, a rope of negligible mass is attached to the piston and passes over two massless pulleys. The other end of the rope is attached to a block that has a mass of . The block falls from rest down through a distance of 1.25 m in 3.30 s. Ignoring friction, find the absolute pressure beneath the piston.
Section 11.3 Pressure and Depth in a Static Fluid,
Section 11.4 Pressure Gauges

| 19 | ssm The main water line enters a house on the first floor. The line has a gauge pressure of . (a) A faucet on the second floor, 6.50 m above the first floor, is turned off. What is the gauge pressure at this faucet? (b) How high could a faucet be before no water would flow from it, even if the faucet were open?

| 20 | At a given instant, the blood pressure in the heart is . If an artery in the brain is 0.45 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.

| 21 | The Mariana trench is located in the floor of the Pacific Ocean at a depth of about 11 000 m below the surface of the water. The density of seawater is 1025 kg/m3. (a) If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle’s observation window ()? (b) For comparison, determine the weight of a jetliner whose mass is .

| 22 | Measured along the surface of the water, a rectangular swimming pool has a length of 15 m. Along this length, the flat bottom of the pool slopes downward at an angle of 11° below the horizontal, from one end to the other. By how much does the pressure at the bottom of the deep end exceed the pressure at the bottom of the shallow end?

| 23 | ssm Some researchers believe that the dinosaur Barosaurus held its head erect on a long neck, much as a giraffe does. If so, fossil remains indicate that its heart would have been about 12 m below its brain. Assume that the blood has the density of water, and calculate the amount by which the blood pressure in the heart would have exceeded that in the brain. Size estimates for the single heart needed to withstand such a pressure range up to two tons. Alternatively, Barosaurus may have had a number of smaller hearts.

| 24 | The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is one-twentieth of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1025 kg/m3.

| 25 | Review Conceptual Example 6 as an aid in understanding this problem. Consider the pump on the right side of Figure 11-11, which acts to reduce the air pressure in the pipe. The air pressure outside the pipe is one atmosphere. Find the maximum depth from which this pump can extract water from the well.

| 26 | The vertical surface of a reservoir dam that is in contact with the water is 120 m wide and 12 m high. The air pressure is one atmosphere. Find the magnitude of the total force acting on this surface in a completely filled reservoir. (Hint: The pressure varies linearly with depth, so you must use an average pressure.)

| 27 | ssm A tube is sealed at both ends and contains a 0.0100-m-long portion of liquid. The length of the tube is large compared to 0.0100 m. There is no air in the tube, and the vapor in the space above the liquid may be ignored. The tube is whirled around in a horizontal circle at a constant angular speed. The axis of the rotation passes through one end of the tube, and during the motion, the liquid collects at the other end. The pressure experienced by the liquid is the same as it would experience at the bottom of the tube, if the tube were completely filled with liquid and allowed to hang vertically. Find the angular speed (in rad/s) of the tube.

| 28 | Two identical containers are open at the top and are connected at the bottom via a tube of negligible volume and a valve that is closed. Both containers are filled initially to the same height of 1.00 m, one with water, the other with mercury, as the drawing indicates. The valve is then opened. Water and mercury are immiscible. Determine the fluid level in the left container when equilibrium is reestablished.

| 29 | A 1.00-m-tall container is filled to the brim, partway with mercury and the rest of the way with water. The container is open to the atmosphere. What must be the depth of the mercury so that the absolute pressure on the bottom of the container is twice the atmospheric pressure?

** | 30 | As the drawing illustrates, a pond has the shape of an inverted cone with the tip sliced off and has a depth of 5.00 m. The atmospheric pressure above the pond is . The circular top surface () and circular bottom surface () of the pond are both parallel to the ground. The magnitude of the force acting on the top surface is the same as the magnitude of the force acting on the bottom surface. Obtain (a) R2 and (b) R1.
Section 11.5 Pascal’s Principle

| 31 | ssm The atmospheric pressure above a swimming pool changes from 755 to 765 mm of mercury. The bottom of the pool is a rectangle (). By how much does the force on the bottom of the pool increase?

| 32 | In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 45 N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 8.3. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.

| 33 | Interactive Solution 11.33 at presents a model for solving this problem. Multiple-Concept Example 8 also presents an approach to problems of this kind. The hydraulic oil in a car lift has a density of . The weight of the input piston is negligible. The radii of the input piston and output plunger are and 0.125 m, respectively. What input force F is needed to support the 24 500-N combined weight of a car and the output plunger, when (a) the bottom surfaces of the piston and plunger are at the same level, and (b) the bottom surface of the output plunger is 1.30 m above that of the input piston?

| 34 | A dentist’s chair with a patient in it weighs 2100 N. The output plunger of a hydraulic system begins to lift the chair when the dentist’s foot applies a force of 55 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

* | 35 | The drawing shows a hydraulic chamber in which a spring () is attached to the input piston, and a rock of mass 40.0 kg rests on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed from its unstrained position?

* | 36 | The drawing shows a hydraulic system used with disc brakes. The force is applied perpendicularly to the brake pedal. The pedal rotates about the axis shown in the drawing and causes a force to be applied perpendicularly to the input piston () in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (), which are covered with the brake linings. The linings are pressed against both sides of a disc attached to the rotating wheel. Suppose that the magnitude of is 9.00 N. Assume that the input piston and the output plungers are at the same vertical level, and find the force applied to each side of the rotating disc.

| 37 | ssm A dump truck uses a hydraulic cylinder, as the drawing illustrates. When activated by the operator, a pump injects hydraulic oil into the cylinder at an absolute pressure of and drives the output plunger, which has a radius of 0.150 m. Assuming the plunger remains perpendicular to the floor of the load bed, find the torque that the plunger creates about the axis identified in the drawing.
Section 11.6 Archimedes’ Principle

| 38 | A duck is floating on a lake with 25% of its volume beneath the water. What is the average density of the duck?

| 39 | ssm A block is suspended from a wire and is completely under water. What buoyant force acts on the block?

| 40 | The density of ice is 917 kg/m3, and the density of sea water is 1025 kg/m3. A swimming polar bear climbs onto a piece of floating ice that has a volume of 5.2 m3. What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?

| 41 | A paperweight, when weighed in air, has a weight of . When completely immersed in water, however, it has a weight of . Find the volume of the paperweight.

| 42 | An 81-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of and is completely submerged under the water. The volume of the person’s body that is underwater is . What is the density of the life jacket?

| 43 | ssm www A person can change the volume of his body by taking air into his lungs. The amount of change can be determined by weighing the person under water. Suppose that under water a person weighs 20.0 N with partially full lungs and 40.0 N with empty lungs. Find the change in body volume.

| 44 | An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.2 N. When completely submerged in water, its apparent weight is 13.7 N. What is the volume of the object?

| 45 | A hollow cubical box is 0.30 m on an edge. This box is floating in a lake with one-third of its height beneath the surface. The walls of the box have a negligible thickness. Water is poured into the box. What is the depth of the water in the box at the instant the box begins to sink?

| 46 | Refer to Multiple-Concept Example 11 to see a problem similar to this one. What is the smallest number of whole logs () that can be used to build a raft that will carry four people, each of whom has a mass of 80.0 kg?

| 47 | ssm A solid cylinder () has a mass of 7.00 kg. This cylinder is floating in water. Then oil () is poured on top of the water until the situation shown in the drawing results. How much of the height of the cylinder is in the oil?

| 48 | A lighter-than-air balloon and its load of passengers and ballast are floating stationary above the earth. Ballast is weight (of negligible volume) that can be dropped overboard to make the balloon rise. The radius of this balloon is 6.25 m. Assuming a constant value of 1.29 kg/m3 for the density of air, determine how much weight must be dropped overboard to make the balloon rise 1.05 m in 15.0 s.

** | 49 | One kilogram of glass () is shaped into a hollow spherical shell that just barely floats in water. What are the inner and outer radii of the shell? Do not assume the shell is thin. Section 11.8 The Equation of Continuity

| 50 | Oil is flowing with a speed of 1.22 m/s through a pipeline with a radius of 0.305 m. How many gallons of oil () flow in one day?

| 51 | ssm A patient recovering from surgery is being given fluid intravenously. The fluid has a density of 1030 kg/m3, and of it flows into the patient every six hours. Find the mass flow rate in kg/s.

| 52 | Concept Simulation 11.1 at reviews the concept that plays the central role in this problem. (a) The volume flow rate in an artery supplying the brain is . If the radius of the artery is 5.2 mm, determine the average blood speed. (b) Find the average blood speed at a constriction in the artery if the constriction reduces the radius by a factor of 3. Assume that the volume flow rate is the same as that in part (a).

| 53 | A room has a volume of 120 m3. An air-conditioning system is to replace the air in this room every twenty minutes, using ducts that have a square cross section. Assuming that air can be treated as an incompressible fluid, find the length of a side of the square if the air speed within the ducts is (a) 3.0 m/s and (b) 5.0 m/s.

* | 54 | The aorta carries blood away from the heart at a speed of about 40 cm/s and has a radius of approximately 1.1 cm. The aorta branches eventually into a large number of tiny capillaries that distribute the blood to the various body organs. In a capillary, the blood speed is approximately 0.07 cm/s, and the radius is about . Treat the blood as an incompressible fluid, and use these data to determine the approximate number of capillaries in the human body.

* | 55 | ssm A water line with an internal radius of is connected to a shower head that has 12 holes. The speed of the water in the line is 1.2 m/s. (a) What is the volume flow rate in the line? (b) At what speed does the water leave one of the holes () in the head?
Section 11.9 Bernoulli’s Equation,
Section 11.10 Applications of Bernoulli’s Equation

| 56 | Prairie dogs are burrowing rodents. They do not suffocate in their burrows, because the effect of air speed on pressure creates sufficient air circulation. The animals maintain a difference in the shapes of two entrances to the burrow, and because of this difference, the air () blows past the openings at different speeds, as the drawing indicates. Assuming that the openings are at the same vertical level, find the difference in air pressure between the openings and indicate which way the air circulates.

| 57 | ssm Review Conceptual Example 14 as an aid in understanding this problem. Suppose that a 15-m/s wind is blowing across the roof of your house. The density of air is 1.29 kg/m3. (a) Determine the reduction in pressure (below atmospheric pressure of stationary air) that accompanies this wind. (b) Explain why some roofs are “blown outward” during high winds.

| 58 | See Multiple-Concept Example 15 to review the concepts that are pertinent to this problem. The blood speed in a normal segment of a horizontal artery is 0.11 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to one-fourth the normal cross-sectional area. What is the difference in blood pressures between the normal and constricted segments of the artery?

| 59 | ssm An airplane wing is designed so that the speed of the air across the top of the wing is 251 m/s when the speed of the air below the wing is 225 m/s. The density of the air is 1.29 kg/m3. What is the lifting force on a wing of area 24.0 m2?

| 60 | Water is circulating through a closed system of pipes in a two-floor apartment. On the first floor, the water has a gauge pressure of and a speed of 2.1 m/s. However, on the second floor, which is 4.0 m higher, the speed of the water is 3.7 m/s. The speeds are different because the pipe diameters are different. What is the gauge pressure of the water on the second floor?

| 61 | Interactive LearningWare 11.2 at reviews the approach taken in problems such as this one. A small crack occurs at the base of a 15.0-m-high dam. The effective crack area through which water leaves is . (a) Ignoring viscous losses, what is the speed of water flowing through the crack? (b) How many cubic meters of water per second leave the dam?

| 62 | A fountain sends a stream of water straight up into the air to a maximum height of 5.00 m. The effective cross-sectional area of the pipe feeding the fountain is . Neglecting air resistance and any viscous effects, determine how many gallons per minute are being used by the fountain. ()

| 63 | ssm A Venturi meter is a device that is used for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at speed v2 through a horizontal section of pipe whose cross-sectional area is . The gas has a density of . The Venturi meter has a cross-sectional area of and has been substituted for a section of the larger pipe. The pressure difference between the two sections is . Find (a) the speed v2 of the gas in the larger original pipe and (b) the volume flow rate Q of the gas.

| 64 | A pump and its horizontal intake pipe are located 12 m beneath the surface of a reservoir. The speed of the water in the intake pipe causes the pressure there to decrease, in accord with Bernoulli’s principle. Assuming nonviscous flow, what is the maximum speed with which water can flow through the intake pipe?

* | 65 | Interactive Solution 11.65 at presents one method for modeling this problem. The construction of a flat rectangular roof () allows it to withstand a maximum net outward force that is 22 000 N. The density of the air is 1.29 kg/m3. At what wind speed will this roof blow outward?

* | 66 | The concepts that play roles in this problem are similar to those in Multiple-Concept Example 15, except that the fluid here moves upward rather than remaining horizontal. A liquid is flowing through a horizontal pipe whose radius is 0.0200 m. The pipe bends straight upward through a height of 10.0 m and joins another horizontal pipe whose radius is 0.0400 m. What volume flow rate will keep the pressures in the two horizontal pipes the same?

* | 67 | An airplane has an effective wing surface area of 16 m2 that is generating the lift force. In level flight the air speed over the top of the wings is 62.0 m/s, while the air speed beneath the wings is 54.0 m/s. What is the weight of the plane?

** | 68 | Two circular holes, one larger than the other, are cut in the side of a large water tank whose top is open to the atmosphere. The center of one of these holes is located twice as far beneath the surface of the water as the other. The volume flow rate of the water coming out of the holes is the same. (a) Decide which hole is located nearest the surface of the water. (b) Calculate the ratio of the radius of the larger hole to the radius of the smaller hole.

** | 69 | ssm A uniform rectangular plate is hanging vertically downward from a hinge that passes along its left edge. By blowing air at 11.0 m/s over the top of the plate only, it is possible to keep the plate in a horizontal position, as illustrated in part a of the drawing. To what value should the air speed be reduced so that the plate is kept at a 30.0° angle with respect to the vertical, as in part b of the drawing? (Hint: Apply Bernoulli’s equation in the form of Equation 11.12.)
Section 11.11 Viscous Flow

| 70 | In the human body, blood vessels can dilate, or increase their radii, in response to various stimuli, so that the volume flow rate of the blood increases. Assume that the pressure at either end of a blood vessel, the length of the vessel, and the viscosity of the blood remain the same, and determine the factor Rdilated/Rnormal by which the radius of a vessel must change in order to double the volume flow rate of the blood through the vessel.

| 71 | ssm www A 1.3-m length of horizontal pipe has a radius of . Water within the pipe flows with a volume flow rate of out of the right end of the pipe and into the air. What is the pressure in the flowing water at the left end of the pipe if the water behaves as (a) an ideal fluid and (b) a viscous fluid ()?

| 72 | A cylindrical air duct in an air conditioning system has a length of 5.5 m and a radius of . A fan forces air () through the duct, such that the air in a room () is replenished every ten minutes. Determine the difference in pressure between the ends of the air duct.

| 73 | Interactive Solution 11.73 at illustrates a model for solving this problem. A pressure difference of is needed to drive water () through a pipe whose radius is . The volume flow rate of the water is . What is the length of the pipe?

| 74 | A blood transfusion is being set up in an emergency room for an accident victim. Blood has a density of 1060 kg/m3 and a viscosity of . The needle being used has a length of 3.0 cm and an inner radius of 0.25 mm. The doctor wishes to use a volume flow rate through the needle of . What is the distance h above the victim’s arm where the level of the blood in the transfusion bottle should be located? As an approximation, assume that the level of the blood in the transfusion bottle and the point where the needle enters the vein in the arm have the same pressure of one atmosphere. (In reality, the pressure in the vein is slightly above atmospheric pressure.)

| 75 | ssm When an object moves through a fluid, the fluid exerts a viscous force on the object that tends to slow it down. For a small sphere of radius R, moving slowly with a speed v, the magnitude of the viscous force is given by Stokes’ law, , where is the viscosity of the fluid. (a) What is the viscous force on a sphere of radius falling through water () when the sphere has a speed of 3.0 m/s? (b) The speed of the falling sphere increases until the viscous force balances the weight of the sphere. Thereafter, no net force acts on the sphere, and it falls with a constant speed called the “terminal speed.” If the sphere has a mass of , what is its terminal speed?

* | 76 | Water () is flowing through a horizontal pipe with a volume flow rate of 0.014 m3/s. As the drawing shows, there are two vertical tubes that project from the pipe. From the data in the drawing, find the radius of the horizontal pipe.

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