A rectangular air mattress is 2.0 m long, 0.50 m wide, and

If the elastic limit of steel is 5.0  108 Pa, determine the minimum diameter a steel wire can have if it is to support a 70-kg circus performer without its elastic limit being exceeded.

If the shear stress in steel exceeds about 4.00  108 N/m2, the steel ruptures. Determine the shearing force necessary to (a) shear a steel bolt 1.00 cm in diameter and (b) punch a 1.00-cm-diameter hole in a steel plate 0.500 cm thick.

The heels on a pair of womens shoes have radii of 0.50 cm at the bottom. If 30% of the weight of a woman weighing 480 N is supported by each heel, nd the stress on each heel.

When water freezes, it expands about 9.00%. What would be the pressure increase inside your automobile engine block if the water in it froze? The bulk modulus of ice is 2.00  109 N/m2.

For safety in climbing, a mountaineer uses a nylon rope that is 50 m long and 1.0 cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6 m. Find its Youngs modulus.

A stainless-steel orthodontic wire is applied to a tooth, as in Figure P9.6. The wire has an unstretched length of 3.1 cm and a diameter of 0.22 mm. If the wire is stretched 0.10 mm, nd the magnitude and direction of the force on the tooth. Disregard the width of the tooth, and assume that Youngs modulus for stainless steel is 18  1010 Pa.

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

The distortion of the Earths crustal plates is an example of shear on a large scale. A particular crustal rock has a shear modulus of 1.5  1010 Pa. What shear stress is involved when a 10-km layer of this rock is sheared through a distance of 5.0 m?

A child slides across a oor in a pair of rubber-soled shoes. The friction force acting on each foot is 20 N, the footprint area of each foot is 14 cm2, and the thickness of the soles is 5.0 mm. Find the horizontal distance traveled by the sheared face of the sole. The shear modulus of the rubber is 3.0  106 Pa.

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 upwards at a rate of 3.0 m/s2? (c) What is the greatest mass that can be accelerated upwards 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  108 Pa?

Determine the elongation of the rod in Figure P9.11 if it is under a tension of 5.8  103 N.

The total cross-sectional area of the load-bearing calcied 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  107 Pa, is the arm likely to withstand the crash?

A 50.0-kg ballet dancer stands on her toes during a performance with four square inches (26.0 cm2) in contact with the oor. What is the pressure exerted by the oor over the area of contact (a) if the dancer is stationary and (b) if the dancer is leaping upwards with an acceleration of 4.00 m/s2?

The four tires of an automobile are inated to a gauge pressure of 2.0  105 Pa. Each tire has an area of 0.024 m2 in contact with the ground. Determine the weight of the automobile.

Air is trapped above liquid ethyl alcohol in a rigid container, as shown in Figure P9.15. If the air pressure above the liquid is 1.10 atm, determine the pressure inside a bubble 4.0 m below the surface of the liquid.

A 70-kg man in a 5.0-kg chair tilts back so that all the weight is balanced on two legs of the chair. Assume that each leg makes contact with the oor over a circular area with a radius of 1.0 cm, and nd the pressure exerted by each leg on the oor.

If 1.0 m3 of concrete weighs 5.0  104 N, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? The compression strength of concrete (the maximum pressure that can be exerted on the base of the structure) is 1.7  107 Pa.

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

A collapsible plastic bag (Figure P9.19) contains a glucose solution. If the average gauge pressure in the vein is 1.33  103 Pa, what must be the minimum height h of the bag in order to infuse glucose into the vein? Assume that the specic gravity of the solution is 1.02.

(a) A very powerful vacuum cleaner has a hose 2.86 cm in diameter. With no nozzle on the hose, what is the weight of the heaviest brick it can lift? (b) A very powerful octopus uses one sucker, of diameter 2.86 cm, on each of the two shells of a clam, in an attempt to pull the shells apart. Find the greatest force the octopus can exert in salt water 32.3 m deep.

For the cellar of a new house, a hole is dug in the ground, with vertical sides going down 2.40 m. A concrete foundation wall is built all the way across the 9.60-m width of the excavation. The foundation wall is 0.183 m away from the front of the cellar hole. During a rainstorm, drainage from the street lls up the space in front of the concrete wall, but not the cellar behind the wall. The water does not soak into the clay soil. Find the force the water foundation wall. For comparison, the weight of the water is 2.40 m  9.60 m  0.183 m  1 000 kg/m3  9.80 m/s2  41.3 kN.

Blaise Pascal duplicated Torricellis barometer using a red Bordeaux wine of density 984 kg/m3 as the working liquid (Fig. P9.22). What was the height h of the wine column for normal atmospheric pressure? Would you expect the vacuum above the column to be as good as for mercury?

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

Piston  in Figure P9.24 has a diameter of 0.25 in.; piston
has a diameter of 1.5 in. In the absence of friction, determine the force necessary to support the 500-lb weight.

Figure P9.25 shows the essential parts of a hydraulic brake system. The area of the piston in the master cylinder is 6.4 cm2, and that of the piston in the brake cylinder is 1.8 cm2. The coefcient 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

A frog in a hemispherical pod nds that he just oats without sinking in a uid of density 1.35 g/cm3. If the pod has a radius of 6.00 cm and negligible mass, what is the mass of the frog? (See Fig. P9.26.)

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?

The density of ice is 920 kg/m3, and that of sea water is 1 030 kg/m3. What fraction of the total volume of an iceberg is exposed?

As a rst approximation, the Earths continents may be thought of as granite blocks oating in a denser rock (called peridotite) in the same way that ice oats in water. (a) Show that a formula describing this phenomenon is where  g is the density of granite (2.8  103 kg/m3),  p is the density of peridotite (3.3  103 kg/m3), t is the thickness of a continent, and d is the depth to which a continent oats in the peridotite. (b) If a continent sinks 5.0 km into the peridotite layer (this surface may be thought of as the ocean oor), what is the thickness of the continent?

A 10.0-kg block of metal is suspended from a scale and immersed in water, as in Figure P9.30. The dimensions of the block are 12.0 cm  10.0 cm  10.0 cm. The 12.0-cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. (a) What are the forces exerted by the water on the top and bottom of the block? (Take P0  1.013 0  105 N/m2.) (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.

A bathysphere used for deep sea exploration has a radius of 1.50 m and a mass of 1.20  104 kg. In order to dive, the sphere takes on mass in the form of sea water. Determine the mass the bathysphere must take on so that it can descend at a constant speed of 1.20 m/s when the resistive force on it is 1 100 N upward. The density of sea water is 1.03  103 kg/m3.

The United States possesses the eight largest warships in the worldaircraft carriers of the Nimitz classand is building one more. Suppose that, at a location where g  9.78 m/s2, one of the ships bobs up to float 11.0 cm higher in the water when 50 fighters take off from it in 25 minutes. Bristling with bombs and missiles, each plane has an average mass of 29 000 kg. Find the horizontal area enclosed by the waterline of the $4-billion ship. By comparison, its flight deck has area of 18 000 m2. Below decks are passageways hundreds of meters long, so narrow that two large men cannot pass each other.

An empty rubber balloon has a mass of 0.012 0 kg. The balloon is lled with helium at a density of 0.181 kg/m3. At this density, the balloon has a radius of 0.500 m. If the lled balloon is fastened to a vertical line, what is the tension in the line?

A light spring of force constant k  160 N/m rests vertically on the bottom of a large beaker of water (Fig. P9.34a). A 5.00-kg block of wood (density  650 kg/m3) is connected to the spring, and the blockspring system is allowed to come to static equilibrium (Fig. P9.34b). What is the elongation L of the spring?

A sample of an unknown material appears to weigh 300 N in air and 200 N when immersed in alcohol of specic 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 thin spherical shell of mass 0.400 kg and diameter 0.200 m is lled with alcohol (   806 kg/m3). It is then released from rest at the bottom of a pool of water. Find the acceleration of the alcohol-lled shell as it starts to rise toward the surface of the water.

A rectangular air mattress is 2.0 m long, 0.50 m wide, and 0.08 m thick. If it has a mass of 2.0 kg, what additional mass can it support in water?

A 1.00-kg beaker containing 2.00 kg of oil (density  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. P9.39). Find the equilibrium readings of both scales.

Water is pumped into a storage tank from a well delivering 20.0 gallons of water in 30.0 seconds through a pipe of 1.00-in.2 cross-sectional area. What is the average velocity of the water in the pipe as the water is pumped from the well?

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

A liquid (   1.65 g/cm3) ows through two horizontal sections of tubing joined end to end. In the rst section, the cross-sectional area is 10.0 cm2, the ow speed is 275 cm/s, and the pressure is 1.20  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. P9.43). The barrel of the syringe has a cross-sectional area of 2.50  105 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force of magnitude 2.00 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicines ow speed through the needle. Assume that 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 ow speed of the air doubles through a constriction in the bronchus. Assuming incompressible ow, determine the pressure drop in the constriction.

A jet of water squirts out horizontally from a hole near the bottom of the tank shown in Figure P9.45. 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 lled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of ow from the leak is 2.50  103 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 P9.47 are 2.50 cm. Water ows to the right at a rate of 1.80  104 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 ow? [Note: You may assume that the freefall 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. (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 uid in streamline ow. 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 that the chamber is large compared with the geyser vent.

An airplane is cruising at an altitude of 10 km. The pressure outside the craft is 0.287 atm; within the passenger compartment, the pressure is 1.00 atm and the temperature is 20C. The density of air is 1.20 kg/m3 at 20C and 1 atm of pressure. A small leak forms in one of the window seals in the passenger compartment. Model the air as an ideal uid to nd the speed of the stream of air owing through the leak.

A siphon is a device that allows a uid to seemingly defy gravity (Fig. P9.51). The ow must be initiated by a partial vacuum in the tube, as in a drinking straw. (a) Show that the speed at which the water emerges from the siphon is given by . (b) For what values of y will the siphon work?

In order 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  102 N greater than the weight of the ring is required. Calculate the surface tension of blood plasma from this information.

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 uid. The contact angle is found to be zero, as shown in Figure P9.53a, 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 P9.53b. The balance now reads 0.39 N. What is the surface tension of the uid?

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  106 m if the contact angle is zero?

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

A staining solution used in a microbiology laboratory has a surface tension of 0.088 N/m and a density 1.035 times the density of water. What must be the diameter of a capillary tube so that this solution will rise to a height of 5 cm? (Assume a contact angle of zero.)

The block of ice (temperature 0C) shown in Figure P9.57 is drawn over a level surface lubricated by a layer of water 0.10 mm thick. Determine the magnitude of the force needed to pull the block with a constant speed of 0.50 m/s. At 0C, the viscosity of water has the value 

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 coefcient of viscosity of 0.12 Ns/m2. At the output of the pipe, the ow rate is 8.6  105 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, nd 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 excess pressure is required along the needle so that the ow rate of water through it will be 1 g/s? (Use 1.0  103 Pas as the viscosity of water.)

What diameter needle should be used to inject a volume of 500 cm3 of a solution into a patient in 30 min? Assume that the length of the needle is 2.5 cm and that the solution is elevated 1.0 m above the point of injection. Furthermore, assume the viscosity and density of the solution are those of pure water, and assume that the pressure inside the vein is atmospheric.

Water is forced out of a re extinguisher by air pressure, as shown in Figure P9.64. 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 ow turbulent? The density of whole blood is 1 050 kg/m3, and its coefcient of viscosity is 2.7  103 Ns/m2.

A pipe carrying 20C water has a diameter of 2.5 cm. Estimate the maximum ow speed if the ow 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 crosssectional area. The diffusion coefficient is equal to 5.0  1010 m2/s, and 8.0  1014 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  102 kg/m4, and the diffusion rate is found to be 5.7  1015 kg/s. Determine the diffusion coefcient.

The viscous force on an oil drop is measured to be 3.0  1013 N when the drop is falling through air with a speed of 4.5  104 m/s. If the radius of the drop is 2.5  106 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 ask 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 part (a) and (b)?

Take the density of blood to be  and the distance between the feet and the heart to be hH. Ignore the ow of blood. (a) Show that the difference in blood pressure between the feet and the heart is given by PF  PH   ghH. (b) Take the density of blood to be 1.05  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 difcult 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 ows 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  m. The approximate average blood ow 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 ows through the capillaries, estimate the number of capillaries in the circulatory system.

Superman attempts to drink water through a very long vertical straw. 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 uid. The uid 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 uids, including the cerebrospinal uid, typically have nearly the same density as water. The pressure of the cerebrospinal uid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height to which the uid rises is observed, as shown in Figure P9.75. If the uid 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 ow of cerebrospinal uid 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 ow of cerebrospinal uid. 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 uid. What should be the normal effect on the height of the uid in the spinal tap? (c) Suppose that compressing the veins had no effect on the level of the uid. What might account for this phenomenon?

Determining the density of a uid has many important applications. A car battery contains sulfuric acid, and the battery will not function properly if the acid density is too low. Similarly, the effectiveness of antifreeze in your cars engine coolant depends on the density of the mixture (usually ethylene glycol and water). When you donate blood to a blood bank, its screening includes a determination of the density of the blood, since higher density correlates with higher hemoglobin content. A hydrometer is an instrument used to determine the density of a liquid. A simple one is sketched in Figure P9.76. 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  0, oats partially immersed in the liquid of density  . A length h of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by

A 600-kg weather balloon is designed to lift a 4 000-kg package. What volume should the balloon have after being inated with helium at standard temperature and pressure (see Table 9.3) in order that the total load can be lifted?

A helium-lled balloon 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 P9.78. Determine the value of h. When deated, the balloon has a mass of 0.25 kg. [Hint: Only that part of the string above the oor contributes to the load being held up by the balloon.]

A block of wood weighs 50.0 N in air. A sinker is attached to the block, and the weight of the woodsinker combination is 200 N when the sinker alone is immersed in water. Finally, the woodsinker combination is completely immersed, and the weight is measured to be 140 N. Find the density of the block.

A U-tube open at both ends is partially lled with water (Fig. P9.80a). Oil (   750 kg/m3) is then poured into the right arm and forms a column L  5.00 cm high (Fig. P9.80b). (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. 9.80c). Determine the speed of the air being blown across the left arm. Assume that the density of air is 1.29 kg/m3.

Figure P9.81 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 that h  10.0 m, L  2.00 m, and   30.0. Assume also that the cross-sectional area at A is very large compared with that at B.

A solid copper ball with a diameter of 3.00 m at sea level is placed on the bottom of the ocean, at a depth of 10.0 km. If the density of sea water is 1 030 kg/m3, how much does the diameter of the ball decrease when it reaches bottom?

A 1.0-kg hollow ball with a radius of 0.10 m and lled with air is released from rest at the bottom of a 2.0-m-deep pool of water. How high above the water does the ball shoot upward? Neglect all frictional effects, and neglect changes in the balls motion when it is only partially submerged.

In about 1657, Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P9.84). Two teams of eight horses each could pull the hemispheres apart only on some trials and even then with the greatest difculty. (a) Show that the force required to pull the evacuated hemispheres apart is  R2(P0  P), where R is the radius of the hemispheres and P is the pressure inside the sphere, which is much less than atmospheric pressure P0. (b) Determine the required force if P  0.10 P0 and R  0.30 m.

A 2.0-cm-thick bar of soap is floating on a water surface so that 1.5 cm of the bar is under water. Bath oil of specic gravity 0.60 is poured into the water and floats on top of it. What is the depth of the oil layer when the top of the soap is just level with the upper surface of the oil?

A cube of ice whose edge is 20.0 mm is oating in a glass of ice-cold water with one of its faces parallel to the waters surface. (a) How far below the water surface is the bottom face of the block? (b) Ice-cold ethyl alcohol is gently poured onto the water surface to form a layer 5.00 mm thick above the water. When the ice cube attains hydrostatic equilibrium again, what will be the distance from the top of the water to the bottom face of the block? (c) Additional cold ethyl alcohol is poured onto the water surface until the top surface of the alcohol coincides with the top surface of the ice cube (in hydrostatic equilibrium). How thick is the required layer of ethyl alcohol?

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 oor. How high does water stand in the tank if the two streams of water hit the oor at the same place?

Oil having a density of 930 kg/m3 oats on water. A rectangular block of wood 4.00 cm high and with a density of 960 kg/m3 oats 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 hollow object with an average density of 900 kg/m3 oats in a pan containing 500 cm3 of water. Ethanol is added to the water and mixed into it until the object is just on the verge of sinking. What volume of ethanol has been added? (Disregard the loss of volume caused by mixing.)

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 an unloaded length of 3.25 m. When the walkway exerts a load force of 8 500 N on one of the support points, through what distance does the point move down?

You will need a large spring scale, a clear container partially lled with water, and a few cylinders of the same size, but made of different materials. Your instructor may be able to supply these items. Measure the volume of each cylinder. Hang a cylinder on the scale, record the reading, and start lowering the cylinder into the water. What happens to the reading on the scale as more of the cylinder is submerged? Why does the reading behave as it does? Is the effect independent of the type of material used for the cylinder? Record the reading for a cylinder when it is not submerged and when it is completely immersed. How can you use these two readings to verify Archimedess principle?

Place an egg at the bottom of a container of fresh water. Now use a funnel to slowly add a salt solution to the water. You will observe that the egg begins to rise to the surface. Use Archimedess principle to explain your observation.

Suppose you have the following collection of objects: a pencil, a coin, an empty plastic box for a tape cassette with its edges taped shut, a needle, an unopened can of soft drink, and an empty can of soft drink. Which of these objects do you expect will oat and which will sink in water? Will it make a difference if you carefully place the object with its largest surface on the surface of the water? In which cases? Explain your reasoning. After you have writ ten your answer, perform the experiments and compare the results with your predictions. (Activity 3 is courtesy of Edward F. Redish. For more problems of this type, see http://www.physics.umd.edu/perg/.)