Solved: A blood transfusion is being set up in an

The body of a man whose weight is 690 N contains about (5.5 qt) of blood. (a) Find the bloods weight and (b) express it as a percentage of the body weight.

Suppose that the pressure acting on the back of a swimmers hand is 1.2 105 Pa, a realistic value near the bottom of the diving end of a pool. The surface area of the back of the hand is 8.4 103 m2 . (a) Determine the magnitude of the force that acts on it. (b) Discuss the direction of the force.

As you climb a mountain, your ears pop because of the changes in atmospheric pressure. In which direction, outward or inward, does your eardrum move (a) as you climb up and (b) as you climb down?

A bottle of juice is sealed under partial vacuum, with a lid on which a red dot or button is painted. Around the button the following phrase is printed: Button pops up when seal is broken. Why does the button remain pushed in when the seal is intact? (a) The pressure inside the bottle is greater than the pressure outside the bottle. (b) The pressure inside the bottle is less than the pressure outside the bottle. (c) There is a greater force acting on the interior surface of the seal than acts on the exterior surface.

A method for resealing a partially full bottle of wine under a vacuum uses a specially designed rubber stopper to close the bottle. A simple pump is attached to the stopper, and to remove air from the bottle, the plunger of the pump is pulled up and then released. After about 15 pulland-release cycles the wine is under a partial vacuum. On the fifteenth pull-and-release cycle, does it require (a) more force, (b) less force, or (c) the same force to pull the plunger up than it did on the first cycle?

Lake Mead is the largest wholly artificial reservoir in the United States and was formed after the completion of the Hoover Dam in 1936. As Figure 11.6a suggests, the water in the reservoir backs up behind the dam for a considerable distance (about 200 km or 120 miles). Suppose that all the water were removed, except for a relatively narrow vertical column in contact with the dam. Figure 11.6b shows a side view of this hypothetical situation, in which the water against the dam has the same depth as in Figure 11.6a. How would the dam needed to contain the water in this hypothetical reservoir compare with the Hoover Dam? Would it need to be (a) less massive or (b) equally massive?

Figure 11.7 shows the cross section of a swimming hole. Points A and B are both located at a distance of h 5.50 m below the surface of the water. Find the pressure at each of these two points.

Blood in the arteries is flowing, but as a first approximation, the effects of this flow can be ignored and the blood treated as a static fluid. Estimate the amount by which the blood pressure P2 in the anterior tibial artery at the foot exceeds the blood pressure P1 in the aorta at the heart when a person is (a) reclining horizontally as in Figure 11.9a and (b) standing as in Figure 11.9

Figure 11.10 shows two methods for pumping water from a well. In one method, the pump is submerged in the water at the bottom of the well, while in the other, it is located at ground level. If the well is shallow, either technique can be used. However, if the well is very deep, only one of the methods works. Which pumping method works, (a) the submerged pump or (b) the pump located at ground level?

A scuba diver is swimming under water, and the graph shows a plot of the water pressure acting on the diver as a function of time. In each of the three regions, (a) A B, (b) B C, and (c) C D, does the depth of the diver increase, decrease, or remain constant?

A 15-meter-high tank is closed and completely filled with water. A valve is then opened at the bottom of the tank and water begins to flow out. When the water stops flowing, will the tank be completely empty, or will there still be a noticeable amount of water in it?

Could you use a straw to sip a drink on the moon? (a) Yes. It would be no different than drinking with a straw on earth. (b) No, because there is no air on the moon and, therefore, no air pressure to push the liquid up the straw. (c) Yes, and it is easier on the moon because the acceleration due to gravity on the moon is only of that on the earth.

A scuba diver is below the surface of the water when a storm approaches, dropping the air pressure above the water. Would a sufficiently sensitive pressure gauge attached to his wrist register this drop in air pressure? Assume that the divers wrist does not move as the storm approaches.

In the hydraulic car lift shown in Figure 11.14b, the input piston on the left has a radius of r1 0.0120 m and a negligible weight. The output plunger on the right has a radius of r2 0.150 m. The combined weight of the car and the plunger is 20 500 N. Since the output force has a magnitude of F2 20 500 N, it supports the car. Suppose that the bottom surfaces of the piston and plunger are at the same level, so that h 0 m in Figure 11.14b. What is the magnitude F1 of the input force needed so that F2 20 500 N? Reas

The data are the same as in Example 7. Suppose now, however, that the bottom surfaces of the piston and plunger are at different levels, such that h 1.10 m in Figure 11.14b. The car lift uses hydraulic oil that has a density of 8.00 102 kg/m3 . What is the magnitude F1 of the input force that is now needed to produce an output force having a magnitude of F2 20 500 N? Re

A solid, square pinewood raft measures 4.0 m on a side and is 0.30 m thick. (a) Determine whether the raft floats in water, and (b) if so, how much of the raft is beneath the surface (see the distance h in Figure 11.18)

A ship floating in the ocean is a familiar sight. But is all that water really necessary? Can an ocean vessel float in the amount of water that a swimming pool contains, for instance?

Normally, a Goodyear airship, such as the one in Figure 11.21, contains about 5.40 103 m3 of helium (He), whose density is 0.179 kg/m3 . Find the weight WL of the load that the airship can carry in equilibrium at an altitude where the density of air is 1.20 kg/m3

A glass is filled to the brim with water and has an ice cube floating in it. When the ice cube melts, what happens? (a) Water spills out of the glass. (b) The water level in the glass drops. (c) The water level in the glass does not change

A steel beam is suspended completely under water by a cable that is attached to one end of the beam, so it hangs vertically. Another identical beam is also suspended completely under water, but by a cable that is attached to the center of the beam, so it hangs horizontally. Which beam, if either, experiences the greater buoyant force? Neglect any change in water density with depth

A glass beaker, filled to the brim with water, is resting on a scale. A solid block is then placed in the water, causing some of it to spill over. The water that spills is wiped away, and the beaker is still filled to the brim. How do the initial and final readings on the scale compare if the block is made from (a) wood (whose density is less than that of water) and (b) iron (whose density is greater than that of water)?

On a distant planet the acceleration due to gravity is less than it is on earth. Would you float more easily in water on this planet than on earth?

As a person dives toward the bottom of a swimming pool, the pressure increases noticeably. Does the buoyant force acting on her also increase? Neglect any change in water density with depth.

A pot is partially filled with water, in which a plastic cup is floating. Inside the floating cup is a small block of lead. When the lead block is removed from the cup and placed into the water, it sinks to the bottom. When this happens, does the water level in the pot (a) rise, (b) fall, or (c) remain the same?

In steady flow, the velocity of a fluid particle at any point is constant in time. On the other hand, the fluid in a pipe accelerates when it moves from a larger-diameter section of the pipe into a smaller-diameter section, so the velocity is increasing during the transition. Does the condition of steady flow rule out such an acceleration?

A garden hose has an unobstructed opening with a cross-sectional area of 2.85 104 m2 , from which water fills a bucket in 30.0 s. The volume of the bucket is 8.00 103 m3 (about two gallons). Find the speed of the water that leaves the hose through (a) the unobstructed opening and (b) an obstructed opening with half as much area. R

In the condition known as atherosclerosis, a deposit, or atheroma, forms on the arterial wall and reduces the opening through which blood can flow. In the carotid artery in the neck, blood flows three times faster through a partially blocked region than it does through an unobstructed region. Determine the ratio of the effective radii of the artery at the two places.

Water flows from left to right through the five sections (A, B, C, D, E) of the pipe shown in the drawing. In which section(s) does the water speed increase, decrease, and remain constant? Treat the water as an incompressible fluid.

See Concept Simulation 11.1 at www.wiley.com/college/cutnell. In case A, water falls downward from a faucet. In case B, water shoots upward, as in a fountain. In each case, as the water moves downward or upward, it has a cross-sectional area that (a) does not change, (b) becomes larger in A and smaller in B, (c) becomes smaller in A and larger in B, (d) becomes larger in both cases, (e) becomes smaller in both cases.

A tarpaulin is a piece of canvas that is used to cover a cargo, like that pulled by the truck in Figure 11.30. Whenever the truck stops, the tarpaulin lies flat. Why does it bulge outward whenever the truck is speeding down the highway? (a) The air rushing over the outside surface of the canvas creates a higher pressure than does the stationary air inside the cargo area. (b) The air rushing over the outside surface of the canvas creates a lower pressure than does the stationary air inside the cargo area. (c) The air inside the cargo area heats up, thus increasing the pressure on the tarp and pushing it outward.

An aneurysm is an abnormal enlargement of a blood vessel such as the aorta. Because of an aneurysm, the normal cross-sectional area A1 of the aorta increases to a value of A2 1.7 A1. The speed of the blood ( 1060 kg/m3 ) through a normal portion of the aorta is v1 0.40 m/s. Assuming that the aorta is horizontal (the person is lying down), determine the amount by which the pressure P2 in the enlarged region exceeds the pressure P1 in the normal region. R

The tank in Figure 11.34a is open to the atmosphere at the top. Find an expression for the speed of the liquid leaving the pipe at the bottom.

Fluid is flowing from left to right through a pipe (see the drawing). Points A and B are at the same elevation, but the cross-sectional areas of the pipe are different. Points B and C are at different elevations, but the cross-sectional areas are the same. Rank the pressures at the three points, highest to lowest: (a) A and B (a tie), C (b) C, A and B (a tie) (c) B, C, A (d) C, B, A (e) A, B, C

Have you ever had a large truck (traveling in your direction) pass you from behind? You probably noticed that your car was pulled toward the truck as it passed. How does the speed of the air (and, hence, its pressure) between your car and the truck compare to the speed of the air on the opposite side of your car? The speed of the air between the two vehicles is (a) less and produces a smaller air pressure (b) less and produces a greater air pressure (c) greater and produces a smaller air pressure (d) greater and produces a greater air pressure

Hold two sheets of paper by adjacent corners, so that they hang downward. The sheets should be parallel and slightly separated, so that you can see the floor through the gap between them. Blow air strongly down through the gap. What happens to the sheets? (a) Nothing (b) The sheets move further apart. (c) The sheets come closer together

Suppose that you are a right-handed batter in a baseball game, so the ball is moving from your left to your right. You are caught unprepared, looking directly at the ball as it passes by for a strike. If the ball curves upward on its way to the plate, which way is it spinning? (a) Clockwise (b) Counterclockwise

You are sitting on a stationary train next to an open window, and the pressure of the air in your inner ear is equal to the pressure outside your ear. The train starts up, and as it accelerates to a high speed, your ears pop. Your eardrums respond to a decrease or increase in the air pressure by popping outward or inward, respectively. Assume that the air pressure in your inner ear has not had time to change, so it remains the same as when the train was stationary. Do your eardrums pop (a) outward or (b) inward?

Sometimes the weather conditions at an airport give rise to air that has an unusually low density. What effect does such a low-density condition have on a planes ability to generate the required lift force for takeoff? (a) It has no effect. (b) It makes it easier. (c) It makes it harder.

A hypodermic syringe is filled with a solution whose viscosity is 1.5 103 Pa s. As Figure 11.39 shows, the plunger area of the syringe is 8.0 105 m2 , and the length of the needle is 0.025 m. The internal radius of the needle is 4.0 104 m. The gauge pressure in the vein that is injected is 1900 Pa (14 mm of mercury). What force must be applied to the plunger, so that 1.0 106 m3 of solution can be injected in 3.0 s? Reas

Figure 11.40a shows a rear view of a loaded two-wheeled wheelbarrow on a horizontal surface. It has balloon tires and a weight of W 684 N, which is uniformly distributed. The left tire has a contact area with the ground of AL 6.6 104 m2 , whereas the right tire is underinflated and has a contact area of AR 9.9 104 m2 . Find the force and the pressure that each tire applies to the ground. c11F

Force is a vector. Therefore, both a direction and a magnitude are needed to specify it. Are both a direction and a magnitude needed to specify a pressure?

The problem asks for the force that each tire applies to the ground. How is this force related to the force that the ground applies to each tire?

Do the left and right tires apply the same force to the ground?

Do the left and right tires apply the same pressure to the ground?

A father (weight W 830 N) and his daughter (weight W 340 N) are spending the day at the lake. They are each sitting on a beach ball that is just submerged beneath the water (see Figure 11.41). Ignoring the weight of the air within the balls and the volumes of their legs that are under water, find the radius of each ball.

Each beach ball is in equilibrium, being stationary and having no acceleration. Thus, the net force acting on each ball is zero. What balances the downward-acting weight in each case?

In which case is the buoyant force greater?

In the situation described, what determines the magnitude of the buoyant force?

Which beach ball has the larger radius?

The drawing shows three containers filled to the same height with the same fluid. In which container, if any, is the pressure at the bottom greatest? (a) Container A, because its bottom has the greatest surface area. (b) All three containers have the same pressure at the bottom. (c) Container A, because it has the greatest volume of fluid. (d) Container B, because it has the least volume of fluid. (e) Container C, because its bottom has the least surface area.

Two liquids, 1 and 2, are in equilibrium in a U-tube that is open at both ends, as in the drawing. The liquids do not mix, and liquid 1 rests on top of liquid 2. How is the density 1 of liquid 1 related to the density 2 of liquid 2? (a) 1 is equal to 2 because the liquids are in equilibrium. (b) 1 is greater than 2. (c) 1 is less than 2. (d) There is not enough information to tell which liquid has the greater density. Sectio

A beaker is filled to the brim with water. A solid object of mass 3.00 kg is lowered into the beaker so that the object is fully submerged in the water (see the drawing). During this process, 2.00 kg of water flows over the rim and out of the beaker. What is the buoyant force that acts on the submerged object, and, when released, does the object rise, sink, or remain in place? (a) 29.4 N; the object rises. (b) 29.4 N; the object sinks. (c) 19.6 N; the object rises. (d) 19.6 N; the object sinks. (e) 19.6 N; the object remains in place.

Three solid objects are floating in a liquid, as in the drawing. They have different weights and volumes, but have the same thickness (the dimension perpendicular to the page). Rank the objects according to their density, largest first. (a) A, B, C (b) A, C, B (c) B, A, C (d) B, C, A (e) C, A, B

A hollow pipe is submerged in a stream of water so that the length of the pipe is parallel to the velocity of the water. If the water speed doubles and the cross-sectional area of the pipe triples, what happens to the volume flow rate of the water passing through the pipe? (a) The volume flow rate does not change. (b) The volume flow rate increases by a factor of 2. (c) The volume flow rate increases by a factor of 3. (d) The volume flow rate increases by a factor of 4. (e) The volume flow rate increases by a factor of 6.

In the drawing, water flows from a wide section of a pipe to a narrow section. In which part of the pipe is the volume flow rate the greatest? (a) The wide section (b) The narrow section (c) The volume flow rate is the same in both sections of the pipe.

Blood flows through a section of a horizontal artery that is partially blocked by a deposit along the artery wall. A hemoglobin molecule moves from the narrow region into the wider region. What happens to the pressure acting on the molecule? (a) The pressure increases. (b) The pressure decreases. (c) There is no change in the pressure.

Water is flowing down through the pipe shown in the drawing. Point A is at a higher elevation than B and C are. The crosssectional areas are the same at A and B but are wider at C. Rank the pressures at the three points, largest first. (a) PA, PB, PC (b) PC, PB, PA (c) PB, PC, PA

A viscous fluid is flowing through two horizontal pipes. The pressure difference P2P1 between the ends of each pipe is the same. The pipes have the same radius, although one is twice as long as the other. How does the volume flow rate QB in the longer pipe compare with the rate QA in the shorter pipe? (a) QB is the same as QA. (b) QB is twice as large as QA. (c) QB is four times as large as QA. (d) QB is one-half as large as QA. (e) QB is one-fourth as large as QA.

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 2.2 103 kg/m3 . Find the weight of this pillar in pounds (1 N 0.2248 lb).

A cylindrical storage tank has a radius of 1.22 m. When filled to a height of 3.71 m, it holds 14 300 kg of a liquid industrial solvent. What is the density of the solvent?

Accomplished silver workers in India can pound silver into incredibly thin sheets, as thin as 3.00 107 m (about one-hundredth 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.

Neutron stars consist only of neutrons and have unbelievably high densities. A typical mass and radius for a neutron star might be 2.7 1028 kg and 1.2 103 m. (a) Find the density of such a star. (b) If a dime (V  2.0 107 m3) were made from this material, how much would it weigh (in pounds)? 5.

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?

Planners of an experiment are evaluating the design of a sphere of radius R that is to be filled with helium (0 C, 1 atm pressure). Ultrathin silver foil of thickness T will be used to make the sphere, and the designers claim that the mass of helium in the sphere will equal the mass of silver used. Assuming that T is much less than R, calculate the ratio T/R for such a sphere.

A bar of gold measures 0.15 m 0.050 m 0.050 m. How many gallons of water have the same mass as this bar? *

A full can of black cherry soda has a mass of 0.416 kg. It contains 3.54 104 m3 of liquid. Assuming that the soda has the same density as water, find the volume of aluminum used to make the can. *

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.

An antifreeze solution is made by mixing ethylene glycol (  1116 kg/m3 ) with water. Suppose that 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.

An airtight box has a removable lid of area 1.3 102 m2 and negligible weight. The box is taken up a mountain where the air pressure outside the box is 0.85 105 Pa. 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 person who weighs 625 N is riding a 98-N mountain bike. Suppose that the entire weight of the rider and bike is supported equally by the two tires. If the pressure in each tire is 7.60 105 Pa, what is the area of contact between each tire and the ground?

A solid concrete block weighs 169 N and is resting on the ground. Its dimensions are 0.400 m 0.200 m 0.100 m. 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? 1

United States currency is printed using intaglio presses that generate a printing pressure of 8.0 104 lb/in.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.

A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.80 105 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 4.10 104 m2 , 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. * 1

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.

A suitcase (mass m  16 kg) is resting on the floor of an elevator. The part of the suitcase in contact with the floor measures 0.50 m 0.15 m. The elevator is moving upward with an acceleration of magnitude 1.5 m/s2 . What pressure (in excess of atmospheric pressure) is applied to the floor beneath the suitcase?

A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3600 N/m. The piston has a negligible mass and a radius of 0.024 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring?

As the initially empty urinary bladder fills with urine and expands, its internal pressure increases by 3300 Pa, which triggers the micturition reflex (the feeling of the need to urinate). The drawing shows a horizontal, square section of the bladder wall with an edge length of 0.010 m. Because the bladder is stretched, four tension forces of equal magnitude T act on the square section, one at each edge, and each force is directed at an angle below the horizontal. What is the magnitude T of the tension force acting on one edge of the section when the internal bladder pressure is 3300 Pa and each of the four tension forces is directed 5.0 below the horizontal?

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 vehicles observation window (radius  0.10 m)? (b) For comparison, determine the weight of a jetliner whose mass is 1.2 105 kg.

Review Conceptual Example 6 as an aid in understanding this problem. Consider the pump on the right side of Figure 11.10, 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.

A meat baster consists of a squeeze bulb attached to a plastic tube. When the bulb is squeezed and released, with the open end of the tube under the surface of the basting sauce, the sauce rises in the tube to a distance h, as the drawing shows. Using 1.013 105 Pa for the atmospheric pressure and 1200 kg/m3 for the density of the sauce, find the absolute pressure in the bulb when the distance h is (a) 0.15 m and (b) 0.10 m.

The main water line enters a house on the first floor. The line has a gauge pressure of 1.90 105 Pa. (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?

The drawing shows an intravenous feeding. With the distance shown, nutrient solution ( 1030 kg/m3 ) can just barely enter the blood in the vein. What is the gauge pressure of the venous blood? Express your answer in millimeters of mercury. 2

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

At a given instant, the blood pressure in the heart is 1.6 104 Pa. 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.

A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 5.25 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes.

A mercury barometer reads 747.0 mm on the roof of a building and 760.0 mm on the ground. Assuming a constant value of 1.29 kg/m3 for the density of air, determine the height of the building.

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?

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.

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.)

A house has a roof with the dimensions shown in the drawing. Determine the magnitude and direction of the net force that the atmosphere applies to the roof when the outside pressure drops suddenly by 75.0 mm of mercury before the air pressure in the attic can adjust. Express your answer in (a) newtons and (b) pounds.

The atmospheric pressure above a swimming pool changes from 755 to 765 mm of mercury. The bottom of the pool is a rectangle (12 m 24 m). By how much does the force on the bottom of the pool increase?

A barbers chair with a person in it weighs 2100 N. The output plunger of a hydraulic system begins to lift the chair when the barbers 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?

Multiple-Concept Example 8 presents an approach to problems of this kind. The hydraulic oil in a car lift has a density of 8.30 102 kg/m3 . The weight of the input piston is negligible. The radii of the input piston and output plunger are 7.70 103 m 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? 3

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.

The drawing shows a hydraulic chamber with a spring (spring constant 1600 N/m) attached to the input piston and a rock of mass 40.0 kg resting 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?

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 (radius 9.50 103 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii 1.90 102 m), 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. Se

The density of ice is 917 kg/m3 , and the density of seawater 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?

A 0.10-m 0.20-m 0.30-m block is suspended from a wire and is completely under water. What buoyant force acts on the block? 4

A hydrometer is a device used to measure the density of a liquid. It is a cylindrical tube weighted at one end, so that it floats with the heavier end downward. The tube is contained inside a large medicine dropper, into which the liquid is drawn using the squeeze bulb (see the drawing). For use with your car, marks are put on the tube so that the level at which it floats indicates whether the liquid is battery acid (more dense) or antifreeze (less dense). The hydrometer has a weight of W 5.88 102 N and a cross-sectional area of A 7.85 105 m2 . How far from the bottom of the tube should the mark be put that denotes (a) battery acid ( 1280 kg/m3 ) and (b) antifreeze ( 1073 kg/m3)? 43. A d

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

A paperweight, when weighed in air, has a weight of W 6.9 N. When completely immersed in water, however, it has a weight of Win water 4.3 N. Find the volume of the paperweight. 4

An 81-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of 3.1 102 m3 and is completely submerged under the water. The volume of the persons body that is under water is 6.2 102 m3 . What is the density of the life jacket? 4

A lost shipping container is found resting on the ocean floor and completely submerged. The container is 6.1 m long, 2.4 m wide, and 2.6 m high. Salvage experts attach a spherical balloon to the top of the container and inflate it with air pumped down from the surface. When the balloons radius is 1.5 m, the shipping container just begins to rise toward the surface. What is the mass of the container? Ignore the mass of the balloon and the air within it. Do not neglect the buoyant force exerted on the shipping container by the water. The density of seawater is 1025 kg/m3

Refer to Multiple-Concept Example 11 to see a problem similar to this one. What is the smallest number of whole logs ( 725 kg/m3 , radius 0.0800 m, length 3.00 m) that can be used to build a raft that will carry four people, each of whom has a mass of 80.0 kg? F

A hot-air balloon is accelerating upward under the influence of two forces, its weight and the buoyant force. For simplicity, consider the weight to be only that of the hot air within the balloon, thus ignoring the balloon fabric and the basket. The hot air inside the balloon has a density of hot air 0.93 kg/m3 , and the density of the cool air outside is cool air 1.29 kg/m3 . What is the acceleration of the rising balloon? * 4

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 from a hose is poured into the open top of the box. What is the depth of the water in the box just at the instant that water from the lake begins to pour into the box from the lake?

To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 5.0 103 kg/m3 . What fraction of the specimens apparent volume is solid?

A solid cylinder (radius 0.150 m, height 0.120 m) has a mass of 7.00 kg. This cylinder is floating in water. Then oil ( 725 kg/m3 ) 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? **

A spring is attached to the bottom of an empty swimming pool, with the axis of the spring oriented vertically. An 8.00-kg block of wood ( 840 kg/m3 ) is fixed to the top of the spring and compresses it. Then the pool is filled with water, completely covering the block. The spring is now observed to be stretched twice as much as it had been compressed. Determine the percentage of the blocks total volume that is hollow. Ignore any air in the hollow space.

One kilogram of glass ( 2.60 103 kg/m3 ) 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 that the shell is thin. Se

A fuel pump sends gasoline from a cars fuel tank to the engine at a rate of 5.88 102 kg/s. The density of the gasoline is 735 kg/m3 , and the radius of the fuel line is 3.18 103 m. What is the speed at which the gasoline moves through the fuel line? 5

A patient recovering from surgery is being given fluid intravenously. The fluid has a density of 1030 kg/m3 , and 9.5 104 m3 of it flows into the patient every six hours. Find the mass flow rate in kg/s.

(a) The volume flow rate in an artery supplying the brain is 3.6 106 m3 /s. 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).

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.

Water flows straight down from an open faucet. The crosssectional area of the faucet is 1.8 104 m2 , and the speed of the water is 0.85 m/s as it leaves the faucet. Ignoring air resistance, find the cross-sectional area of the water stream at a point 0.10 m below the faucet.

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 6 104 cm. Treat the blood as an incompressible fluid, and use these data to determine the approximate number of capillaries in the human body.

Three fire hoses are connected to a fire hydrant. Each hose has a radius of 0.020 m. Water enters the hydrant through an underground pipe of radius 0.080 m. In this pipe the water has a speed of 3.0 m/s. (a) How many kilograms of water are poured onto a fire in one hour by all three hoses? (b) Find the water speed in each hose.

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 ( 1.29 kg/m3 ) 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. 62

Review Conceptual Example 14 before attempting this problem. The truck in that example is traveling at 27 m/s. The density of air is 1.29 kg/m3 . By how much does the pressure inside the cargo area beneath the tarpaulin exceed the outside pressure?

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 ?

Consult Multiple-Concept Example 15 to review the concepts on which this problem depends. Water flowing out of a horizontal pipe emerges through a nozzle. The radius of the pipe is 1.9 cm, and the radius of the nozzle is 0.48 cm. The speed of the water in the pipe is 0.62 m/s. Treat the water as an ideal fluid, and determine the absolute pressure of the water in the pipe.

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?

A small crack occurs at the base of a 15.0-m-high dam. The effective crack area through which water leaves is 1.30 103 m2 . (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?

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 3.4 105 Pa 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?

A ship is floating on a lake. Its hold is the interior space beneath its deck; the hold is empty and is open to the atmosphere. The hull has a hole in it, which is below the water line, so water leaks into the hold. The effective area of the hole is and is located 2.0 m beneath the surface of the lake. What volume of water per second leaks into the ship?

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 A2 0.0700 m2 . The gas has a density of 1.30 kg/m3 . The Venturi meter has a cross-sectional area of A1 0.0500 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2  P1 120 Pa. Find (a) the speed v2 of the gas in the larger, original pipe and (b) the volume flow rate Q of the gas. 8.0

A hand-pumped water gun is held level at a height of above the ground and fired. The water stream from the gun hits the ground a horizontal distance of from the muzzle. Find the gauge pressure of the water guns reservoir at the instant when the gun is fired. Assume that the speed of the water in the reservoir is zero and that the water flow is steady. Ignore both air resistance and the height difference between the reservoir and the muzzle.

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?

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?

The construction of a flat rectangular roof (5.0 m 6.3 m) 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?

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

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?

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

Poiseuilles law remains valid as long as the fluid flow is laminar. For sufficiently high speed, however, the flow becomes turbulent, even if the fluid is moving through a smooth pipe with no restrictions. It is found experimentally that the flow is laminar as long as the Reynolds number Re is less than about 2000: Re Here , , and  are, respectively, the average speed, density, and viscosity of the fluid, and R is the radius of the pipe. Calculate the highest average speed that blood ( 1060 kg/m3 ,  4.0 103 Pa s) could have and still remain in laminar flow when it flows through the aorta (R m). 78.

A pipe is horizontal and carries oil that has a viscosity of 0.14 Pa s. The volume flow rate of the oil is 5.3 105 m3 /s. The length of the pipe is 37 m, and its radius is 0.60 cm. At the output end of the pipe the pressure is atmospheric pressure. What is the absolute pressure at the input end?

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.

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 4.0 103 Pa s. 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 4.5 108 m3 /s. What is the distance h above the victims 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.) 8

A pressure difference of 1.8 103 Pa is needed to drive water ( 1.0 103 Pa s) through a pipe whose radius is 5.1 103 m. The volume flow rate of the water is 2.8 104 m3 /s. What is the length of the pipe? 82.

A cylindrical air duct in an air conditioning system has a length of 5.5 m and a radius of 7.2 102 m. A fan forces air ( 1.8 105 Pa s) through the duct, so that the air in a room (volume 280 m3 ) is replenished every ten minutes. Determine the difference in pressure between the ends of the air duct. *

Two hoses are connected to the same outlet using a Y-connector, as the drawing shows. The hoses A and B have the same length, but hose B has the larger radius. Each is open to the atmosphere at the end where the water exits. Water flows through both hoses as a viscous fluid, and Poiseuilles law [Q R4(P2  P1)/(8L)] applies to each. In this law, P2 is the pressure upstream, P1 is the pressure downstream, and Q is the volume flow rate. The ratio of the radius of hose B to the radius of hose A is RB/RA 1.50. Find the ratio of the speed of the water in hose B to the speed in hose A. *

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, F 6Rv, where  is the viscosity of the fluid. (a) What is the viscous force on a sphere of radius R 5.0 104 m that is falling through water ( 1.00 103 Pa s) 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 1.0 105 kg, what is its terminal speed?  F

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?

One way to administer an inoculation is with a gun that shoots the vaccine through a narrow opening. No needle is necessary, for the vaccine emerges with sufficient speed to pass directly into the tissue beneath the skin. The speed is high, because the vaccine ( 1100 kg/m3 ) is held in a reservoir where a high pressure pushes it ouout. The pressure on the surface of the vaccine in one gun is 4.1 106 Pa above the atmospheric pressure outside the narrow opening. The dosage is small enough that the vaccines surface in the reservoir is nearly stationary during an inoculation. The vertical height between the vaccines surface in the reservoir and the opening can be ignored. Find the speed at which the vaccine emerges.

Multiple-Concept Example 11 reviews the concepts that are important in this problem. What is the radius of a hydrogen-filled balloon that would carry a load of 5750 N (in addition to the weight of the hydrogen) when the density of air is 1.29 kg/m3 ?

If a scuba diver descends too quickly into the sea, the internal pressure on each eardrum remains at atmospheric pressure, while the external pressure increases due to the increased water depth. At sufficient depths, the difference between the external and internal pressures can rupture an eardrum. Eardrums can rupture when the pressure difference is as little as 35 kPa. What is the depth at which this pressure difference could occur? The density of seawater is 1025 kg/m3

A water bed for sale has dimensions of 1.83 m 2.13 m 0.229 m. The floor of the bedroom will tolerate an additional weight of no more than 6660 N. Find the weight of the water in the bed and determine whether the bed should be purchased.

An underground pump initially forces water through a horizontal pipe at a flow rate of 740 gallons per minute. After several years of operation, corrosion and mineral deposits have reduced the inner radius of the pipe to 0.19 m from 0.24 m, but the pressure difference between the ends of the pipe is the same as it was initially. Find the final flow rate in the pipe in gallons per minute. Treat water as a viscous fluid.

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?

A volume of 7.2 m3 of glycerol ( 0.934 Pa s) is pumped through a 15-m length of pipe in 55 minutes. The pressure at the input end of the pipe is 8.6 105 Pa, and the pressure at the output end is atmospheric pressure. What is the pipes radius? 9

As background for this problem, review Conceptual Example 6. A submersible pump is put under the water at the bottom of a well and is used to push water up through a pipe. What minimum output gauge pressure must the pump generate to make the water reach the nozzle at ground level, 71 m above the pump?

(a) The mass and the radius of the sun are, respectively, 1.99 1030 kg and 6.96 108 m. What is its density? (b) If a solid object is made from a material that has the same density as the sun, would it sink or float in water? Why? (c) Would a solid object sink or float in water if it were made from a material whose density was the same as that of the planet Saturn (mass 5.7 1026 kg, radius 6.0 107 m)? Provide a reason for your answer. * 95

A water line with an internal radius of 6.5 103 m 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 (effective hole radius 4.6 104 m) in the head? *

A log splitter uses a pump with hydraulic oil to push a piston, which is attached to a chisel. The pump can generate a pressure of 2.0 107 Pa in the hydraulic oil, and the piston has a radius of 0.050 m. In a stroke lasting 25 s, the piston moves 0.60 m. What is the power needed to operate the log splitters pump?

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?

Mercury is poured into a tall glass. Ethyl alcohol (which does not mix with mercury) is then poured on top of the mercury until the height of the ethyl alcohol itself is 110 cm. The air pressure at the top of the ethyl alcohol is one atmosphere. What is the absolute pressure at a point that is 7.10 cm below the ethyl alcoholmercury interface?

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 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.

A gold prospector finds a solid rock that is composed solely of quartz and gold. The mass and volume of the rock are, respectively, 12.0 kg and 4.00 103 m3 . Find the mass of the gold in the rock.

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 5.00 104 m2 . Neglecting air resistance and any viscous effects, determine how many gallons per minute are being used by the fountain. (Note: 1 gal 3.79 103 m3 .)

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 1.01 105 Pa. The circular top surface (radius R2) and circular bottom surface (radius R1) 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. **

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 105 m in 15.0 s.

A siphon tube is useful for removing liquid from a tank. The siphon tube is first filled with liquid, and then one end is inserted into the tank. Liquid then drains out the other end, as the drawing illustrates. (a) Using reasoning similar to that employed in obtaining Torricellis theorem (see Example 16), derive an expression for the speed v of the fluid emerging from the tube. This expression should give v in terms of the vertical height y and the acceleration due to gravity g. (Note that this speed does not depend on the depth d of the tube below the surface of the liquid.) (b) At what value of the vertical distance y will the siphon stop working? (c) Derive an expression for the absolute pressure at the highest point in the siphon (point A) in terms of the atmospheric pressure P0, the fluid density , g, and the heights h and y. (Note that the fluid speed at point A is the same as the speed of the fluid emerging from the tube, because the cross-sectional area of the tube is the same everywhere.)

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 3.54 106 Pa and drives the output plunger, which has a radius of 0.150 m. Assuming that 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.