What radius needle should be used to inject a volume of

A hydraulic jack has an input piston of area 0.050 m2 and an output piston of area 0.70 m2. How much force on the input piston is required to lift a car weighing 1.2 3 103 N? (a) 42 N (b) 68 N (c) 86 N (d) 110 N (e) 130 N

A 66.0-kg man lies on his back on a bed of nails, with 1 208 of the nails in contact with his body. The end of each nail has area 1.00 3 1026 m2. What average pressure is exerted by one nail on the mans body? (a) 2.21 3 105 Pa (b) 3.09 3 105 Pa (c) 1.65 3 106 Pa (d) 5.35 3 105 Pa (e) 4.11 3 104 Pa

What is the mass of a solid gold rectangular bar that has dimensions of 4.50 cm 3 11.0 cm 3 26.0 cm? (a) 24.8 kg (b) 45.6 kg (c) 11.4 kg (d) 33.2 kg (e) 19.5 kg

A lead bullet is placed in a pool of mercury. What fractional part of the volume of the bullet is submerged? (a) 0.455 (b) 0.622 (c) 0.714 (d) 0.831 (e) 0.930

What is the pressure at the bottom of Loch Ness, which is as much as 754 ft deep? (The surface of the lake is only 15.8 m above sea level; hence, the pressure there can be taken to be 1.013 3 105 Pa.) (a) 1.52 3 105 Pa (b) 2.74 3 105 Pa (c) 2.35 3 106 Pa (d) 7.01 3 105 Pa (e) 3.15 3 105 Pa

A wooden block floats in water, and a solid steel object is attached to the bottom of the block by a string as in Figure MCQ9.6. If the block remains floating, which of the following statements is valid? (Choose all correct statements.) (a) The buoyant force on the steel object is equal to its weight. (b) The buoyant force on the block is equal to its weight. (c) The tension in the string is equal to the weight of the steel object. (d) The tension in the string is less than the weight of the steel object. (e) The buoyant force on the block is equal to the weight of the volume of water it displaces.

A horizontal pipe narrows from a radius of 0.250 m to 0.100 m. If the speed of the water in the pipe is 1.00 m/s in the larger-radius pipe, what is the speed in the smaller pipe? (a) 4.50 m/s (b) 2.50 m/s (c) 3.75 m/s (d) 6.25 m/s (e) 5.13 m/s

A beach ball filled with air is pushed about 1 m below the surface of a swimming pool and released from rest. Which of the following statements is valid, assuming the size of the ball remains the same? (Choose all correct statements.) (a) As the ball rises in the pool, the buoyant force on it increases. (b) When the ball is released, the buoyant force exceeds the gravitational force, and the ball accelerates upwards. (c) The buoyant force on the ball decreases as the ball approaches the surface of the pool. (d) The buoyant force on the ball equals its weight and remains constant as the ball rises. (e) The buoyant force on the ball while it is submerged is equal to the weight of the volume of water the ball displaces.

A boat develops a leak and, after its passengers are rescued, eventually sinks to the bottom of a lake. When the boat is at the bottom, the force of the lake bottom on the boat is (a) greater than the weight of the boat, (b) equal to the weight of the boat, (c) less than the weight of the boat, (d) equal to the weight of the displaced water, or (e) equal to the buoyant force on the boat.

Three vessels of different shapes are filled to the same level with water as in Figure MCQ9.10. The area of the base is the same for all three vessels. Which of the following statements is valid? (a) The pressure at the top surface of vessel A is greatest because it has the largest surface area. (b) The pressure at the bottom of vessel A is greatest because it contains the most water. (c) The pressure at the bottom of each vessel is the same. (d) The force on the bottom of each vessel is not the same. (e) At a given depth below the surface of each vessel, the pressure on the side of vessel A is greatest because of its slope. A B C Figure MCQ9.10

A solid iron sphere and a solid lead sphere of the same size are each suspended by strings and are submerged in a tank of water. (Note that density of lead is greater than that of iron.) Which of the following statements are valid? (Choose all correct statements.) (a) The buoyant force on each is the same. (b) The buoyant force on the lead sphere is greater than the buoyant force on the iron sphere because lead has the greater density. (c) The tension in the string supporting the lead sphere is greater than the tension in the string supporting the iron sphere. (d) The buoyant force on the iron sphere is greater than the buoyant force on the lead sphere because lead displaces more water. (e) None of those statements is true.

A beach ball is made of thin plastic. It has been inflated with air, but the plastic is not stretched. By swimming with fins on, you manage to take the ball from the surface of a pool to the bottom. Once the ball is completely submerged, what happens to the buoyant force exerted on the beach ball as you take it deeper? (a) It increases. (b) It remains constant. (c) It decreases. (d) It is impossible to determine.

A person in a boat floating in a small pond throws an anchor overboard. What happens to the level of the pond? (a) It rises. (b) It falls. (c) It remains the same.

One of the predicted problems due to global warming is that ice in the polar ice caps will melt and raise sea level everywhere in the world. Is that more of a worry for ice (a) at the north pole, where most of the ice floats on water; (b) at the south pole, where most of the ice sits on land; (c) both at the north and south poles equally; or (d) at neither pole?

Bone has a Youngs modulus of 18 3 109 Pa. Under compression, it can withstand a stress of about 160 3 106 Pa before breaking. Assume that a femur (thigh bone) is 0.50 m long, and calculate the amount of compression this bone can withstand before breaking.

A high-speed lifting mechanism supports an 800-kg object with a steel cable that is 25.0 m long and 4.00 cm2 in cross-sectional area. (a) Determine the elongation of the cable. (b) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 3.0 m/s2? (c) What is the greatest mass that can be accelerated upward at 3.0 m/s2 if the stress in the cable is not to exceed the elastic limit of the cable, which is 2.2 3 108 Pa?

A walkway suspended across a hotel lobby is supported at numerous points along its edges by a vertical cable above each point and a vertical column underneath. The steel cable is 1.27 cm in diameter and is 5.75 m long before loading. The aluminum column is a hollow cylinder with an inside diameter of 16.14 cm, an outside diameter of 16.24 cm, and unloaded length of 3.25 m. When the walkway exerts a load force of 8 500 N on one of the support points, how much does the point move down?

The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately 2.4 cm2. During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of 80 km/h in 5.0 ms. If the arm has an effective mass of 3.0 kg and bone material can withstand a maximum compressional stress of 16 3 107 Pa, is the arm likely to withstand the crash?

Determine the elongation of the rod in Figure P9.19 if it is under a tension of 5.8 3 103 N.

The spring of the pressure gauge shown in Figure P9.20 has a force constant of 1 250 N/m, and the piston has a radius of 1.20 cm. As the gauge is lowered into water, what change in depth causes the piston to move in by 0.750 cm?

(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 27.5 m. Assume the density of the water is 1.00 3 103 kg/m3 and the air above is at a pressure of 101.3 kPa. (b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 35.0 cm?

Mercury is poured into a U-tube as shown in Figure P9.22a on page 324. The left arm of the tube has crosssectional area A1 of 10.0 cm2, and the right arm has a cross-sectional area A2 of 5.00 cm2. One hundred grams of water are then poured into the right arm as shown in Figure P9.22b. (a) Determine the length of the water column in the right arm of the U-tube. (b) Given that the density of mercury is 13.6 g/cm3, what distance h does the mercury rise in the left arm?

A collapsible plastic bag (Figure P9.23) contains a glucose solution. If the average gauge pressure in the vein is 1.33 3 103 Pa, what must be the minimum height h of the bag in order to infuse glucose into the vein? Assume the specific gravity of the solution is 1.02.

The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at the ocean floor is huge, about 1.13 3 108 N/m2. (a) Calculate the change in volume of 1.00 m3 of water carried from the surface to the bottom of the Pacific. (b) The density of water at the surface is 1.03 3 103 kg/m3. Find its density at the bottom. (c) Explain whether or when it is a good approximation to think of water as incompressible.

A container is filled to a depth of 20.0 cm with water. On top of the water floats a 30.0-cm-thick layer of oil with specific gravity 0.700. What is the absolute pressure at the bottom of the container?

Blaise Pascal duplicated Torricellis barometer using a red Bordeaux wine, of density 984 kg/m3 as the working liquid (Fig. P9.26). (a) What was the height h of the wine column for normal atmospheric pressure? (b) Would you expect the vacuum above the column to be as good as for mercury?

Figure P9.27 shows the essential parts of a hydraulic brake system. The area of the piston in the master cylinder is 1.8 cm2 and that of the piston in the brake cylinder is 6.4 cm2. The coefficient of friction between shoe and wheel drum is 0.50. If the wheel has a radius of 34 cm, determine the frictional torque about the axle when a force of 44 N is exerted on the brake pedal.

Piston _ in Figure P9.28 has a diameter of 0.25 in.; piston _ has a diameter of 1.5 in. In the absence of friction, determine the force F S necessary to support the 500-lb weight.

A table-tennis ball has a diameter of 3.80 cm and average density of 0.084 0 g/cm3. What force is required to hold it completely submerged under water?

The average human has a density of 945 kg/m3 after inhaling and 1 020 kg/m3 after exhaling. (a) Without making any swimming movements, what percentage of the human body would be above the surface in the Dead Sea (a body of water with a density of about 1 230 kg/m3) in each of these cases? (b) Given that bone and muscle are denser than fat, what physical characteristics differentiate sinkers (those who tend to sink in water) from floaters (those who readily float)?

A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into the river. What is the weight of the truck?

A 62.0-kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 m 3 2.00 m 3 0.090 0 m. The bottom 0.024 m of the raft is submerged. (a) Draw a force diagram of the system consisting of the survivor and raft. (b) Write Newtons second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and wr for the weight of the raft. (Set a 5 0.) (c) Calculate the numeric value for the buoyancy, B. (Seawater has density 1 025 kg/m3.) (d) Using the value of B and the weight w of the survivor, calculate the weight wr of the Styrofoam. (e) What is the density of the Styrofoam? (f) What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface? (g) What total mass of survivors can the raft support?

A wooden block of volume 5.24 3 1024 m3 floats in water, and a small steel object of mass m is placed on top of the block. When m 5 0.310 kg, the system is in equilibrium, and the top of the wooden block is at the level of the water. (a) What is the density of the wood? (b) What happens to the block when the steel object is replaced by a second steel object with a mass less than 0.310 kg? What happens to the block when the steel object is replaced by yet another steel object with a mass greater than 0.310 kg?

A large balloon of mass 226 kg is filled with helium gas until its volume is 325 m3. Assume the density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3. (a) Draw a force diagram for the balloon. (b) Calculate the buoyant force acting on the balloon. (c) Find the net force on the balloon and determine whether the balloon will rise or fall after it is released. (d) What maximum additional mass can the balloon support in equilibrium? (e) What happens to the balloon if the mass of the load is less than the value calculated in part (d)? (f) What limits the height to which the balloon can rise?

A spherical weather balloon is filled with hydrogen until its radius is 3.00 m. Its total mass including the instruments it carries is 15.0 kg. (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3. (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) Why does the radius of the balloon tend to increase as it rises to higher altitude?

A man of mass m 5 70.0 kg and having a density of r 5 1 050 kg/m3 (while holding his breath) is completely submerged in water. (a) Write Newtons second law for this situation in terms of the mans mass m, the density of water rw, his volume V, and g. Neglect any viscous drag of the water. (b) Substitute m 5 rV into Newtons second law and solve for the acceleration a, canceling common factors. (c) Calculate the numeric value of the mans acceleration. (d) How long does it take the man to sink 8.00 m to the bottom of the lake?

On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of 3.35 km (11 000 ft) powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about 0.50 m and an estimated mass of 0.30 kg. (a) Estimate the total buoyant force on the 600 balloons. (b) Estimate the net upward force on all 600 balloons. (c) Ashpole parachuted to Earth after the balloons began to burst at the high altitude and the system lost buoyancy. Why did the balloons burst?

The gravitational force exerted on a solid object is 5.00 N as measured when the object is suspended from a spring scale as in Figure P9.38a. When the suspended object is submerged in water, the scale reads 3.50 N (Figure P9.38b). Find the density of the object.

A cube of wood having an edge dimension of 20.0 cm and a density of 650 kg/m3 floats on water. (a) What is the distance from the horizontal top surface of the cube to the water level? (b) What mass of lead should be placed on the cube so that the top of the cube will be just level with the water surface?

A light spring of force constant k 5 160 N/m rests vertically on the bottom of a large beaker of water (Fig. P9.40a). A 5.00-kg block of wood (density 5 650 kg/m3) is connected to the spring, and the blockspring system is allowed to come to static equilibrium (Fig. P9.40b). What is the elongation DL of the spring?

A sample of an unknown material appears to weigh 300 N in air and 200 N when immersed in alcohol of specific gravity 0.700. What are (a) the volume and (b) the density of the material?

An object weighing 300 N in air is immersed in water after being tied to a string connected to a balance. The scale now reads 265 N. Immersed in oil, the object appears to weigh 275 N. Find (a) the density of the object and (b) the density of the oil.

A 1.00-kg beaker containing 2.00 kg of oil (density 5 916 kg/m3) rests on a scale. A 2.00-kg block of iron is suspended from a spring scale and is completely submerged in the oil (Fig. P9.43). Find the equilibrium readings of both scales.

Water flowing through a garden hose of diameter 2.74 cm fills a 25.0-L bucket in 1.50 min. (a) What is the speed of the water leaving the end of the hose? (b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle?

(a) Calculate the mass flow rate (in grams per second) of blood (r 5 1.0 g/cm3) in an aorta with a cross-sectional area of 2.0 cm2 if the flow speed is 40 cm/s. (b) Assume that the aorta branches to form a large number of capillaries with a combined crosssectional area of 3.0 3 103 cm2. What is the flow speed in the capillaries?

A liquid (r 5 1.65 g/cm3) flows through a horizontal pipe of varying cross section as in Figure P9.46. In the first section, the cross-sectional area is 10.0 cm2, the flow speed is 275 cm/s, and the pressure is 1.20 3 105 Pa. In the second section, the cross- sectional area is 2.50 cm2. Calculate the smaller sections (a) flow speed and (b) pressure.

A hypodermic syringe contains a medicine with the density of water (Fig. P9.47). The barrel of the syringe has a cross-sectional area of 2.50 3 1025 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F S of magnitude 2.00 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicines flow speed through the needle. Assume the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal.

When a person inhales, air moves down the bronchus (windpipe) at 15 cm/s. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction.

A jet airplane in level flight has a mass of 8.66 3 104 kg, and the two wings have an estimated total area of 90.0 m2. (a) What is the pressure difference between the lower and upper surfaces of the wings? (b) If the speed of air under the wings is 225 m/s, what is the speed of the air over the wings? Assume air has a density of 1.29 kg/m3. (c) Explain why all aircraft have a ceiling, a maximum operational altitude.

An airplane has a mass M, and the two wings have a total area A. During level flight, the pressure on the lower wing surface is P1. Determine the pressure P2 on the upper wing surface.

In a water pistol, a piston drives water through a larger tube of radius 1.00 cm into a smaller tube of radius 1.00 mm as in Figure P9.51. (a) If the pistol is fired horizontally at a height of 1.50 m, use ballistics to determine the time it takes water to travel from the nozzle to the ground. (Neglect air resistance and assume atmospheric pressure is 1.00 atm.) (b) If the range of the stream is to be 8.00 m, with what speed must the stream leave the nozzle? (c) Given the areas of the nozzle and cylinder, use the equation of continuity to calculate the speed at which the plunger must be moved. (d) What is the pressure at the nozzle? (e) Use Bernoullis equation to find the pressure needed in the larger cylinder. Can gravity terms be neglected? (f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.)

Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in Figure P9.52, the pressure is 1.75 3 105 Pa and the pipe radius is 3.00 cm. At the higher point located at y 5 2.50 m, the pressure is 1.20 3 105 Pa and the pipe radius is 1.50 cm. Find the speed of flow (a) in the lower section and (b) in the upper section. (c) Find the volume flow rate through the pipe.

A jet of water squirts out horizontally from a hole near the bottom of the tank shown in Figure P9.53. If the hole has a diameter of 3.50 mm, what is the height h of the water level in the tank?

A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of flow from the leak is 2.50 3 1023 m3/min, determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

The inside diameters of the larger portions of the horizontal pipe depicted in Figure P9.55 are 2.50 cm. Water flows to the right at a rate of 1.80 3 1024 m3/s. Determine the inside diameter of the constriction.

Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564 m elevation and the village is at 2 096 m. (a) At what minimum pressure must the water be pumped to arrive at the village? (b) If 4 500 m3 are pumped per day, what is the speed of the water in the pipe? (c) What additional pressure is necessary to deliver this flow? Note: You may assume the free-fall acceleration and the density of air are constant over the given range of elevations.

Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals, and the height of the fountain reaches 40.0 m (Fig. P9.57). (a) Consider the rising stream as a series of separate drops. Analyze the free-fall motion of one of the drops to determine the speed at which the water leaves the ground. (b) Treat the rising stream as an ideal fluid in streamline flow. Use Bernoullis equation to determine the speed of the water as it leaves ground level. (c) What is the pressure (above atmospheric pressure) in the heated underground chamber 175 m below the vent? You may assume the chamber is large compared with the geyser vent.

The Venturi tube shown in Figure P9.58 may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline (r 5 7.00 3 102 kg/m3) through a hose having an outlet radius of 1.20 cm. If the difference in pressure is measured to be P1 2 P2 5 1.20 kPa and the radius of the inlet tube to the meter is 2.40 cm, find (a) the speed of the gasoline as it leaves the hose and (b) the fluid flow rate in cubic meters per second.

A square metal sheet 3.0 cm on a side and of negligible thickness is attached to a balance and inserted into a container of fluid. The contact angle is found to be zero, as shown in Figure P9.59a, and the balance to which the metal sheet is attached reads 0.40 N. A thin veneer of oil is then spread over the sheet, and the contact angle becomes 180, as shown in Figure P9.59b. The balance now reads 0.39 N. What is the surface tension of the fluid?

To lift a wire ring of radius 1.75 cm from the surface of a container of blood plasma, a vertical force of 1.61 3 1022 N greater than the weight of the ring is required. Calculate the surface tension of blood plasma from this information.

A certain fluid has a density of 1 080 kg/m3 and is observed to rise to a height of 2.1 cm in a 1.0-mmdiameter tube. The contact angle between the wall and the fluid is zero. Calculate the surface tension of the fluid.

Whole blood has a surface tension of 0.058 N/m and a density of 1 050 kg/m3. To what height can whole blood rise in a capillary blood vessel that has a radius of 2.0 3 1026 m if the contact angle is zero?

The block of ice (temperature 0C) shown in Figure P9.63 is drawn over a level surface lubricated by a layer of water 0.10 mm thick. Determine the magnitude of the force F S needed to pull the block with a constant speed of 0.50 m/s. At 0C, the viscosity of water has the value h 5 1.79 3 1023 N ? s/m2. 0.800 m 0.10 m 1.20 m F S Figure P9.63

A thin 1.5-mm coating of glycerine has been placed between two microscope slides of width 1.0 cm and length 4.0 cm. Find the force required to pull one of the microscope slides at a constant speed of 0.30 m/s relative to the other slide.

A straight horizontal pipe with a diameter of 1.0 cm and a length of 50 m carries oil with a coefficient of viscosity of 0.12 N ? s/m2. At the output of the pipe, the flow rate is 8.6 3 1025 m3/s and the pressure is 1.0 atm. Find the gauge pressure at the pipe input.

The pulmonary artery, which connects the heart to the lungs, has an inner radius of 2.6 mm and is 8.4 cm long. If the pressure drop between the heart and lungs is 400 Pa, what is the average speed of blood in the pulmonary artery?

Spherical particles of a protein of density 1.8 g/cm3 are shaken up in a solution of 20C water. The solution is allowed to stand for 1.0 h. If the depth of water in the tube is 5.0 cm, find the radius of the largest particles that remain in solution at the end of the hour.

A hypodermic needle is 3.0 cm in length and 0.30 mm in diameter. What pressure difference between the input and output of the needle is required so that the flow rate of water through it will be 1 g/s? (Use 1.0 3 1023 Pa ? s as the viscosity of water.)

What radius needle should be used to inject a volume of of a solution into a patient in 30 min? Assume the length of the needle is 2.5 cm and the solution is elevated 1.0 m above the point of injection. Further, assume the viscosity and density of the solution are those of pure water, and that the pressure inside the vein is atmospheric.

Water is forced out of a fire extinguisher by air pressure, as shown in Figure P9.70. What gauge air pressure in the tank (above atmospheric pressure) is required for the water to have a jet speed of 30.0 m/s when the water level in the tank is 0.500 m below the nozzle?

The aorta in humans has a diameter of about 2.0 cm, and at certain times the blood speed through it is about 55 cm/s. Is the blood flow turbulent? The density of whole blood is 1 050 kg/m3, and its coefficient of viscosity is 2.7 3 1023 N ? s/m2.

A pipe carrying 20C water has a diameter of 2.5 cm. Estimate the maximum flow speed if the flow must be streamline.

Sucrose is allowed to diffuse along a 10-cm length of tubing filled with water. The tube is 6.0 cm2 in cross-sectional area. The diffusion coefficient is equal to 5.0 3 10210 m2/s, and 8.0 3 10214 kg is transported along the tube in 15 s. What is the difference in the concentration levels of sucrose at the two ends of the tube?

Glycerin in water diffuses along a horizontal column that has a cross-sectional area of 2.0 cm2. The concentration gradient is 3.0 3 1022 kg/m4, and the diffusion rate is found to be 5.7 3 10215 kg/s. Determine the diffusion coefficient.

The viscous force on an oil drop is measured to be equal to 3.0 3 10213 N when the drop is falling through air with a speed of 4.5 3 1024 m/s. If the radius of the drop is 2.5 3 1026 m, what is the viscosity of air?

Small spheres of diameter 1.00 mm fall through 20C water with a terminal speed of 1.10 cm/s. Calculate the density of the spheres.

An iron block of volume 0.20 m3 is suspended from a spring scale and immersed in a flask of water. Then the iron block is removed, and an aluminum block of the same volume replaces it. (a) In which case is the buoyant force the greatest, for the iron block or the aluminum block? (b) In which case does the spring scale read the largest value? (c) Use the known densities of these materials to calculate the quantities requested in parts (a) and (b). Are your calculations consistent with your previous answers to parts (a) and (b)?

The true weight of an object can be measured in a vacuum, where buoyant forces are absent. A measure- ment in air, however, is disturbed by buoyant forces. An object of volume V is weighed in air on an equal-arm balance with the use of counterweights of density r. Representing the density of air as rair and the balance reading as Fg9, show that the true weight Fg is Fg 5 Fgr 1 aV 2 Fgr rg brairg

As a first approximation, Earths continents may be thought of as granite blocks floating in a denser rock (called peridotite) in the same way that ice floats in water. (a) Show that a formula describing this phenomenon is rgt 5 rpd where rg is the density of granite (2.8 3 103 kg/m3), rp is the density of peridotite (3.3 3 103 kg/m3), t is the thickness of a continent, and d is the depth to which a continent floats in the peridotite. (b) If a continent sinks 5.0 km into the peridotite layer (this surface may be thought of as the ocean floor), what is the thickness of the continent?

Take the density of blood to be r and the distance between the feet and the heart to be hH. Ignore the flow of blood. (a) Show that the difference in blood pressure between the feet and the heart is given by PF 2 PH 5 rghH. (b) Take the density of blood to be 1.05 3 103 kg/m3 and the distance between the heart and the feet to be 1.20 m. Find the difference in blood pressure between these two points. This problem indicates that pumping blood from the extremities is very difficult for the heart. The veins in the legs have valves in them that open when blood is pumped toward the heart and close when blood flows away from the heart. Also, pumping action produced by physical activities such as walking and breathing assists the heart.

The approximate inside diameter of the aorta is 0.50 cm; that of a capillary is 10 mm. The approximate average blood flow speed is 1.0 m/s in the aorta and 1.0 cm/s in the capillaries. If all the blood in the aorta eventually flows through the capillaries, estimate the number of capillaries in the circulatory system.

Superman attempts to drink water through a very long vertical straw as in Figure P9.82. With his great strength, he achieves maximum possible suction. The walls of the straw dont collapse. (a) Find the maximum height through which he can lift the water. (b) Still thirsty, the Man of Steel repeats his attempt on the Moon, which has no atmosphere. Find the difference between the water levels inside and outside the straw.

The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to 200 mm of H2O above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of mm of H2O because body fluids, including the cerebrospinal fluid, typically have nearly the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height to which the fluid rises is observed, as shown in Figure P9.83. If the fluid rises to a height of 160 mm, we write its gauge pressure as 160 mm H2O. (a) Express this pressure in pascals, in atmospheres, and in millimeters of mercury. (b) Sometimes it is necessary to determine whether an accident victim has suffered a crushed vertebra that is blocking the flow of cerebrospinal fluid in the spinal column. In other cases, a physician may suspect that a tumor or other growth is blocking the spinal column and inhibiting the flow of cerebrospinal fluid. Such conditions can be investigated by means of the Queckensted test. In this procedure the veins in the patients neck are compressed, to make the blood pressure rise in the brain. The increase in pressure in the blood vessels is transmitted to the cerebrospinal fluid. What should be the normal effect on the height of the fluid in the spinal tap? (c) Suppose compressing the veins had no effect on the level of the fluid. What might account for this phenomenon?

A hydrometer is an instrument used to determine liquid density. A simple one is sketched in Figure P9.84. The bulb of a syringe is squeezed and released to lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. (Assume the rod is cylindrical.) The rod, of length L and average density r0, floats partially immersed in the liquid of density r. A length h of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by

Figure P9.85 (page 330) shows a water tank with a valve. If the valve is opened, what is the maximum height attained by the stream of water coming out of the right side of the tank? Assume h 5 10.0 m, L 5 2.00 m, and u 5 30.0, and that the cross-sectional area at A is very large compared with that at B.

A helium-filled balloon, whose envelope has a mass of 0.25 kg, is tied to a 2.0-m-long, 0.050-kg string. The balloon is spherical with a radius of 0.40 m. When released, it lifts a length h of the string and then remains in equilibrium, as in Figure P9.86. Determine the value of h. Hint: Only that part of the string above the floor contributes to the load being supported by the balloon.

A light spring of constant k 5 90.0 N/m is attached vertically to a table (Fig. P9.87a). A 2.00-g balloon is filled with helium (density 5 0.179 kg/m3) to a volume of 5.00 m3 and is then connected to the spring, causing the spring to stretch as shown in Figure P89.87b. Determine the extension distance L when the balloon is in equilibrium.

A U-tube open at both ends is partially filled with water (Fig. P9.88a). Oil (r 5 750 kg/m3) is then poured into the right arm and forms a column L 5 5.00 cm high (Fig. P9.88b). (a) Determine the difference h in the heights of the two liquid surfaces. (b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Fig. P9.88c). Determine the speed of the air being blown across the left arm. Assume the density of air is 1.29 kg/m3.

In about 1657, Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P9.89). Two teams of eight horses each could pull the hemispheres apart only on some trials and then with greatest difficulty, with the resulting sound likened to a cannon firing. Find the force F required to pull the thin-walled evacuated hemispheres apart in terms of R, the radius of the hemispheres, P the pressure inside the hemispheres, and atmospheric pressure P0.

Oil having a density of 930 kg/m3 floats on water. A rectangular block of wood 4.00 cm high and with a density of 960 kg/m3 floats partly in the oil and partly in the water. The oil completely covers the block. How far below the interface between the two liquids is the bottom of the block?

A water tank open to the atmosphere at the top has two small holes punched in its side, one above the other. The holes are 5.00 cm and 12.0 cm above the floor. How high does water stand in the tank if the two streams of water hit the floor at the same place?