Several teenagers swim toward a rectangular, wooden raft

If the gauge pressure is doubled, the absolute pressure will be (a) halved, (b) doubled, (c) unchanged, (d) increased by a factor greater than 2, (e) increased by a factor less than 2.

Two spherical objects differ in size and mass. Object A has a mass that is eight times the mass of object B. The radius of object A is twice the radius of object B. How do their densities compare? (a) (b) (c) (d) Not enough information is given to compare their densities.

Two objects differ in density and mass. Object A has a mass that is eight times the mass of object B. The density of object A is four times the density of object B. How do their volumes compare? (a) (b) (c) (d) Not enough information is given to compare their volumes.

A sphere is constructed by gluing together two hemispheres. The density of each hemisphere is uniform, but the density of one is greater than the density of the other. True or false: The average density of the sphere is the numerical average of the two different densities. Clearly explain your reasoning.

BIOLOGICAL APPLICATION, CONTEXT-RICH In several jungle adventure movies, the hero and heroine escape the bad guys by hiding underwater for extended periods of time. To do this, they breathe through long vertical hollow reeds. Imagine that in one movie, the water is so clear that to be safely hidden, the two are at a depth of 15 m. As a science consultant to the movie producers, you tell them that this depth is not realistic and the knowledgeable viewer will laugh during this scene. Explain why this is so.

Two objects are balanced as in Figure 13-28. The objects have identical volumes but different masses. Assume all the objects in the figure are denser than water and thus none will float. Will the equilibrium be disturbed if the entire system is completely immersed in water? Explain your reasoning.

A solid 200-g block of lead and a solid 200-g block of copper are completely submerged in a aquarium filled with water. Each block is suspended just above the bottom of the aquarium by a thread. Which of the following is true? (a) The buoyant force on the lead block is greater than the buoyant force on the copper block. (b) The buoyant force on the copper block is greater than the buoyant force on the lead block. (c) The buoyant force is the same on both blocks. (d) More information is needed to choose the correct answer.

A block of lead and a block of copper are completely submerged in an aquarium filled with water. Each is suspended just above the bottom of the aquarium by a thread. Which of the following is true? (a) The buoyant force on the lead block is greater than the buoyant force on the copper block. (b) The buoyant force on the copper block is greater than the buoyant force on the lead block. (c) The buoyant force is the same on both blocks. (d) More information is needed to choose the correct answer.

Two bricks are completely submerged in water. Brick 1 is made of lead and has rectangular dimensions of Brick 2 is made of wood and has rectangular dimensions of True or false: The buoyant force on brick 2 is larger than the buoyant force on brick 1.

Figure 13-29 shows an object called a Cartesian diver. The diver consists of a small tube, open at the bottom, with an air bubble at the top, inside a closed plastic soda bottle that is partly filled with water. The diver normally floats, but sinks when the bottle is squeezed hard. (a) Explain why this happens. (b) Explain the physics behind how a submarine can silently sink vertically simply by allowing water to flow into empty tanks near its keel. (c) Explain why a person floating in water will oscillate up and down on the waters surface as he or she breathes in and out.

A certain object has a density just slightly less than that of water so that it floats almost completely submerged. However, the object is more compressible than water. What happens if the floating object is given a slight downward push? Explain.

In Example 13-11, the fluid is accelerated to a greater speed as it enters the narrow part of the pipe. Identify the forces that act on the fluid at the entrance to the narrow region to produce this acceleration.

An upright glass of water is accelerating to the right along a flat, horizontal surface. What is the origin of the force that produces the acceleration on a small element of water in the middle of the glass? Explain by using a diagram. Hint: The water surface will not remain level as long as the glass of water is accelerating. Draw a freebody diagram of the small element of water.

You are sitting in a boat floating on a very small pond. You take the anchor out of the boat and drop it into the water. Does the water level in the pond rise, fall, or remain the same? Explain your answer.

A horizontal pipe narrows from a diameter of 10 cm at location A to 5.0 cm at location B. For a nonviscous incompressible fluid flowing without turbulence from location Ato location B, how do the flow speeds compare at the two locations? (a) (b) (c) (d) (e)

Ahorizontal pipe narrows from a diameter of 10 cm at location A to 5.0 cm at location B. For a nonviscous incompressible fluid flowing without turbulence from location Ato location B, how do the pressures compare at the two locations? (a) (b) (c) (d) (e) (f) There is not enough information to compare the pressures quantitatively.

BIOLOGICAL APPLICATION Figure 13-30 is a diagram of a prairie dog tunnel. The geometry of the two entrances are such that entrance 1 is surrounded by a mound and entrance 2 is surrounded by flat ground. Explain how the tunnel remains ventilated, and indicate in which direction air will flow through the tunnel. SSM

Your undergraduate research project involves atmospheric sampling. The sampling device has a mass of 25.0 kg. Estimate the diameter of a helium-filled balloon required to lift the device off the ground. Neglect the mass of the balloon skin and the small buoyancy force on the device itself.

CONTEXT-RICH Your friend wants to start a business giving hot-air balloon rides. The empty balloon, the basket and the occupants have a total maximum mass of 1000 kg. If the balloon has a diameter of 22.0 m when fully inflated with hot air, estimate the required density of the hot air. Neglect the buoyancy force on the basket and people.

Find the mass of a solid lead sphere with a radius equal to 2.00 cm.

Consider a room measuring Under normal atmospheric conditions at Earths surface, what would be the mass of the air in the room?

An average neutron star has approximately the same mass as the Sun, but is compressed into a sphere of radius roughly 10 km. What would be the approximate mass of a teaspoonful of matter that dense?

A 50.0-g ball consists of a plastic spherical shell and a water-filled core. The shell has an outside diameter equal to 50.0 mm and an inside diameter equal to 20.0 mm. What is the density of the plastic?

A 60.0-mL flask is filled with mercury at (Figure 13-31). When the temperature increases to of mercury spills out of the flask. Assuming that the volume of the flask stays constant, find the change in the density of mercury at if its density at 0C is 13645 kg>m3. 80C 80C, 1.47 g 0C SSM 4.0 m _ 5.0 m _ 4.0 m.

One sphere is made of gold and has a radius and another sphere is made of copper and has a radius If the spheres have equal mass, what is the ratio of the radii,

Since 1983, the U.S. Mint has coined pennies that are made out of zinc with a copper cladding. The mass of this type of penny is 2.50 g. Model the penny as a uniform cylinder of height 1.23 mm and radius 9.50 mm. Assume the copper cladding is uniformly thick on all surfaces. If the density of zinc is and that of copper is what is the thickness of the copper cladding?

Barometer readings are commonly given in inches of mercury (inHg). Find the pressure in inches of mercury equal to

The pressure on the surface of a lake is (a) At what depth is the pressure (b) If the pressure at the top of a deep pool of mercury is at what depth is the pressure

BIOLOGICAL APPLICATION When at cruising altitude, a typical airplane cabin will have an air pressure equivalent to an altitude of about 2400 m. During the flight, ears often equilibrate, so that the air pressure inside the inner ear equalizes with the air pressure outside the plane. The Eustachian tubes allow for this equalization, but can become clogged. If an Eustachian tube is clogged, pressure equalization may not occur on descent and the air pressure inside an inner ear may remain equal to the pressure at 2400 m. In that case, by the time the plane lands and the cabin is repressurized to sea-level air pressure, what is the net force on one ear drum due to this pressure difference, assuming the ear drum has an area of

The axis of a cylindrical container is vertical. The container is filled with equal masses of water and oil. The oil floats on top of the water, and the open surface of the oil is at a height above the bottom of the container. What is the height, if the pressure at the bottom of the water is greater than the pressure at the top of the oil? Assume the oil density is

ENGINEERING APPLICATION A hydraulic lift is used to raise a 1500-kg automobile. The radius of the shaft of the lift is 8.00 cm and the radius of the compressors piston is 1.00 cm. How much force must be applied to the piston to raise the automobile? Hint: The shaft of the lift is the other piston.

A 1500-kg car rests on four tires, each of which is inflated to a gauge pressure of If the four tires support the car’s weight equally, what is the area of contact of each tire with the road?

What pressure increase is required to compress the volume of 1.00 kg of water from 1.00 L to 0.99 L ? Could this compression occur in the ocean, where the maximum depth is about 11 km? Explain.

When a woman in high-heeled shoes takes a step, she momentarily places her entire weight on one heel of her shoe. If her mass is 56.0 kg and if the area of the heel is what is the pressure exerted on the floor by the heel? Compare your answer to the pressure exerted by one foot of an elephant on a flat floor. Assume the elephants mass is 5000 kg, that he has all four feet equally distributed on the floor, and that each foot has an area of 400 cm2.

In the seventeenth century, Blaise Pascal performed the experiment shown in Figure 13-32. A wine barrel filled with water was coupled to a long tube. Water was added to the tube until the barrel burst. The radius of the barrels lid was 20 cm and the height of the water in the tube was 12 m. (a) Calculate the force exerted on the lid due to the pressure increase. (b) If the tube had an inner radius of 3.0 mm, what mass of water in the tube caused the pressure that burst the barrel?

BIOLOGICAL APPLICATION Blood plasma flows from a bag through a tube into a patients vein, where the blood pressure is 12 mmHg. The specific gravity of blood plasma at is 1.03. What is the minimum elevation of the bag so that the plasma flows into the vein?

BIOLOGICAL APPLICATION Many people have imagined that if they were to float the top of a flexible snorkel tube out of the water, they would be able to breathe through it while walking underwater (Figure 13-33). However, they generally do not take into account just how much water pressure opposes the expansion of the chest and the inflation of the lungs. Suppose you can just breathe while lying on the floor with a 400-N (90-lb) weight on your chest. How far below the surface of the water could your chest be for you still to be able to breathe, assuming your chest has a frontal area of 0.090 m2? 37C

ENGINEERING APPLICATION In Example 13-3, a 150-N force is applied to a small piston to lift a car that weighs 15 000 N. Demonstrate that this does not violate the law of conservation of energy by showing that, when the car is lifted some distance the work done by the 150-N force acting on the small piston equals the work done on the car by the large piston.

A 5.00-kg lead sinker is accidentally dropped overboard by fishermen in a boat directly above the deepest portion of the Marianas trench, near the Philippines. By what percentage does the volume of the sinker change, by the time it settles on the trench bottom, which is 10.9 km below the surface?

The volume of a cone of height and base radius is Ajar in the shape of a cone of height 25 cm has a base with a radius equal to 15 cm. The jar is filled with water. Then its lid (the base of the cone) is screwed on and the jar is turned over so its lid is horizontal. (a) Find the volume and weight of the water in the jar. (b) Assuming the pressure inside the jar at the top of the cone is equal to 1 atm, find the excess force exerted by the water on the base of the jar, where by excess force we mean the force minus the force exerted by air pressure on the outside of the base of the jar. Explain how this force can be greater than the weight of the water in the jar.

A 500-g piece of copper, with specific gravity of 8.96, is suspended from a spring scale and is submerged in water (Figure 13-34). What force does the spring scale read?

When a certain rock is suspended from a spring scale, the scale-display reads 60 N. However, when the suspended stone is submerged in water, the display reads 40 N. What is the density of the rock?

A block of an unknown material weighs 5.00 N in air and 4.55 N when submerged in water. (a) What is the density of the material? (b) From what material is the block likely to have been made?

A solid piece of metal weighs 90.0 N in air and 56.6 N when submerged in water. What is the density of this metal?

A homogeneous solid object floats on water, with 80.0 percent of its volume below the surface. When placed in a second liquid, the same object floats on that liquid with 72.0 percent of its volume below the surface. Determine the density of the object and the specific gravity of the liquid.

A 5.00-kg iron block is suspended from a spring scale and is submerged in a fluid of unknown density. The spring scale reads 6.16 N. What is the density of the fluid?

A large piece of cork weighs 0.285 N in air. When held submerged underwater by a spring scale, as shown in Figure 13-35, the spring scale reads 0.855 N. Find the density of the cork.

A helium balloon lifts a basket and cargo with a total weight of 2000 N under standard conditions, at which the density of air is and the density of helium is What is the minimum volume of the balloon?

An object has neutral buoyancy when its density equals that of the liquid in which it is submerged, which means that it neither floats nor sinks. If the average density of an 85-kg diver is what mass of lead should the dive master suggest be added to give the diver neutral buoyancy? SSM

A 1.00-kg beaker containing 2.00 kg of water rests on a scale. A 2.00-kg block of aluminum suspended from a spring scale is submerged in the water, as in Figure 13-36. Find the readings of both scales.

ENGINEERING APPLICATION When cracks form at the base of a dam, the water seeping into the cracks exerts a buoyant force that tends to lift the dam. As a result, the dam can topple. Estimate the buoyant force exerted on a 2.0-m-thick by 5.0-m-long dam wall by water seeping into cracks at its base. The water level in the lake is 5.0 m above the cracks.

ENGINEERING APPLICATION, CONTEXT-RICH Your team is in charge of launching a large helium weather balloon that is spherical in shape, and whose radius is 2.5 m and total mass is 15 kg (balloon plus helium plus equipment). (a) What is the initial upward acceleration of the balloon when it is released from sea level? (b) If the drag force on the balloon is given by where is the balloon radius, is the density of air, and the balloons ascension speed, calculate the terminal velocity of the ascending balloon.

ENGINEERING APPLICATION A ship sails from seawater (specific gravity 1.025) into freshwater, and therefore sinks slightly. When its 600,000-kg load is removed, it returns to its original level. Assuming that the sides of the ship are vertical at the water line, find the mass of the ship before it was unloaded.

Water flows at through a 3.0-cm-diameter hose that terminates in a 0.30-cm-diameter nozzle. Assume laminar nonviscous steady-state flow. (a) At what speed does the water pass through the nozzle? (b) If the pump at one end of the hose and the nozzle at the other end are at the same height, and if the pressure at the nozzle is what is the pressure at the pump outlet?

Water is flowing at in a horizontal pipe under a pressure of The pipe narrows to half its original diameter. (a) What is the speed of flow in the narrow section? (b) What is the pressure in the narrow section? (c) How do the volume flow rates in the two sections compare?

The pressure in a section of horizontal pipe with a diameter of 2.00 cm is Water flows through the pipe at If the pressure at a certain point is to be reduced to by constricting a section of the pipe, what should the diameter of the constricted section be?

BIOLOGICAL APPLICATION Blood flows at in an aorta of radius 9.0 mm. (a) Calculate the volume flow rate in liters per minute. (b) Although the cross-sectional area of a capillary is much smaller than that of the aorta, there are many capillaries, so their total cross-sectional area is much larger. If all the blood from the aorta flows into the capillaries and the speed of flow through the capillaries is calculate the total cross-sectional area of the capillaries. Assume laminar nonviscous steady-state flow.

Water flows through a 1.0-m-long conical section of pipe that joins a cylindrical pipe of radius 0.45 m, on the left, to a cylindrical pipe of radius 0.25 m, on the right. If the water flows into the 0.45-m pipe with a speed of and if we assume laminar nonviscous steady-state flow, (a) what is the speed of flow in the 0.25-m pipe? (b) What is the speed of flow at a position in the conical section, if is the distance measured from the left-hand end of the conical section of pipe?

ENGINEERING APPLICATION The $8-billion, 800-mile-long Alaskan Pipeline has a maximum volume flow rate of of oil per day. Most of the pipeline has a radius of 60.0 cm. Find the pressure at a point where the pipe has a 30.0-cm radius. Take the pressure in the 60.0-cm-radius sections to be and the density of oil to be Assume laminar nonviscous steady-state flow.

Water flows through a Venturi meter like that in Example 13-11 with a pipe diameter of 9.50 cm and a constriction diameter of 5.60 cm. The U-tube manometer is partially filled with mercury. Find the volume flow rate of the water if the difference in the mercury level in the U-tube is 2.40 cm.

ENGINEERING APPLICATION, CONTEXT-RICH Horizontal flexible tubing for carrying cooling water extends through a large electromagnet used in your physics experiment at Fermi National Accelerator Laboratory. Aminimum volume flow rate of through the tubing is necessary to keep your magnet cool. Within the magnet volume, the tubing has a circular cross section of radius 0.500 cm. In regions outside the magnet, the tubing widens to a radius of 1.25 cm. You have attached pressure sensors to measure differences in pressure between the 0.500- and 1.25-cm sections. The lab technicians tell you that if the flow rate in the system drops below the magnet is in danger of overheating and that you should install an alarm to sound a warning when the flow rate drops below that level. What is the critical pressure difference at which you should program the sensors to send the alarm signal (and is this a minimum, or maximum, pressure difference)? Assume laminar nonviscous steady-state flow.

Figure 13-37 shows a Pitot-static tube, a device used for measuring the speed of a gas. The inner pipe faces the incoming fluid, while the ring of holes in the outer tube is parallel to the gas flow. Show that the speed of the gas is given by where is the density of the liquid used in the manometer and is the density of the gas.

Derive the Bernoulli equation in more generality than is done in the text, that is, allow for the fluid to change elevation during its movement. Using the work-energy theorem, show that when changes in elevation are allowed, Equation 13-16 becomes (Equation 13-17).

A large keg of height and cross-sectional area is filled with root beer. The top is open to the atmosphere. There is a spigot opening of area which is much smaller than at the bottom of the keg. (a) Show that when the height of the root beer is the speed of the root beer leaving the spigot is approximately (b) Show that if the rate of change of the height of the root beer is given by (c) Find as a function of time if at (d) Find the total time needed to drain the keg if and Assume laminar nonviscous flow.

A siphon is a device for transferring a liquid from one container to another. The tube shown in Figure 13-38 must be filled to start the siphon, but once this has been done, fluid will flow through the tube until the liquid surfaces in the containers are at the same level. (a) Using Bernoullis equation, show that the speed of water in the tube is (b) What is the pressure at the highest part of the tube?

Afountain designed to spray a column of water 12 m into the air has a 1.0-cm-diameter nozzle at ground level. The water pump is 3.0 m below the ground. The pipe to the nozzle has a diameter of 2.0 cm. Find the pump pressure necessary if the fountain is to operate as designed. (Assume laminar nonviscous steady-state flow.)

Water at exits a circular tap moving straight down with a flow rate of (a) If the diameter of the tap is 1.20 cm, what is the speed of the water? (b) As the fluid falls from the tap, the stream of water narrows. What is the new diameter of the stream at a point 7.50 cm below the tap? Assume that the stream still has a circular cross section and neglect any effects of drag forces acting on the water. (c) If turbulent flows are characterized by Reynolds numbers above 2300 or so, how far does the water have to fall before it becomes turbulent? Does this match your everyday observations?

ENGINEERING APPLICATION, CONTEXT-RICH To better fight fires in your seaside community, the local fire brigade has asked you to construct a pump system to draw seawater from the ocean to the top of the steep cliff adjacent to the water where most of the homes are. If the cliff is 12.0 m high, and the pump is capable of producing a gauge pressure of how much water can be pumped using a hose with a radius of 4.00 cm?

MULTISTEP In Figure 13-39, is the depth of the liquid and is the distance from the surface of the liquid to the pipe inserted in the tanks side. (a) Find the distance at which the water strikes the ground after exiting the pipe as a function of and (b) Show that, for a given value of H, there are two values of h

Water flows through a horizontal 25.0-cm-long tube with an inside diameter of 1.20 mm at Find the pressure difference required to drive this flow if the viscosity of water is Assume laminar flow.

Find the diameter of a tube that would give double the flow rate for the pressure difference in Problem 70.

BIOLOGICAL APPLICATION Blood takes about 1.00 s to pass through a 1.00-mm-long capillary in the human circulatory system. If the diameter of the capillary is 7.00 and the pressure drop is find the viscosity of blood. Assume laminar flow.

An abrupt transition occurs at Reynolds numbers of about where the drag on a sphere moving through a fluid abruptly decreases. Estimate the speed at which this transition occurs for a baseball, and comment on whether it should play a role in the physics of the game.

A horizontal pipe of radius 1.5 cm and length 25 m is connected to the output that can sustain an output gauge pressure of 10 kPa . What is the speed of \(20^\circ \mathrm C\) water flowing through the pipe? If the temperature of the water is \(60^\circ \mathrm C\), what is the speed of the water in the pipe.

A very large tank is filled to a depth of 250 cm with oil that has a density of and a viscosity of If the container walls are 5.00 cm thick, and a cylindrical hole of radius 0.750 cm is bored through the base of the container, what is the initial volume flow rate (in ) of the oil through the hole?

The drag force on a moving sphere at a very low Reynolds number is given by where is the viscosity of the surrounding fluid and is the radius of the sphere. (This relation is called Stokes law.) Using this information, find the terminal speed of ascent for a spherical 1.0-mm-diameter carbon dioxide bubble rising in a carbonated beverage ( and ). How long should it take for this bubble to rise 20 cm (the height of the drinking glass)? Is this length of time consistent with your observations?

Several teenagers swim toward a rectangular, wooden raft that is 3.00 m wide and 2.00 m long. If the raft is 9.00 cm thick, how many 75.0-kg teenage boys can stand on top of the raft without the raft becoming submerged? Assume the wood density is

Athread attaches a 2.7-g Ping-Pong ball to the bottom of a beaker. When the beaker is filled with water so that the ball is totally submerged, the tension in the thread is Determine the diameter of the ball.

Seawater has a bulk modulus of Find the difference in density of seawater at a depth where the pressure is as compared to the density at the surface which is Neglect any effects due to changes in either temperature or salinity.

A solid cube with 0.60-m edge length is suspended from a spring balance. When the cube is submerged in water, the spring balance reads 80 percent of the reading for when the cube is in air. Determine the density of the cube.

A1.5-kg block of wood floats on water with 68 percent of its volume submerged. A lead block is placed on the wood, fully submerging the wood to a depth where the lead remains entirely out of the water. Find the mass of the lead block.

A Styrofoam cube, 25 cm on an edge, is placed on one pan of a balance. The balance is in equilibrium when a 20-g mass of brass is placed on the other pan. Find the mass of the Styrofoam cube. Neglect the buoyant force of the brass mass, but do not neglect the buoyant force of the air on the Styrofoam cube.

A spherical shell of copper with an outer diameter of 12.0 cm floats on water with half its volume above the waters surface. Determine the inner diameter of the shell. The cavity inside the spherical shell is empty.

A200-mL beaker that is half-filled with water is on the left pan of a balance, and a sufficient amount of sand is placed on the right pan to bring the balance to equilibrium. A cube 4.0 cm on an edge that is attached to a string is then lowered into the water until the cube is completely submerged, but not touching the bottom of the beaker. Apiece of brass of mass is then added to the right pan to restore equilibrium. What is

ENGINEERING APPLICATION, CONTEXT-RICH Crude oil has a viscosity of about 0.800 Pa s at normal temperature. You are the chief design engineer in charge of constructing a 50.0-km horizontal pipeline that connects an oil field to a tanker terminal. The pipeline is to deliver oil at the terminal at a rate of and the flow through the pipeline is to be laminar. Assuming that the density of crude oil is estimate the diameter of the pipeline that should be used.

Water flows through the pipe in Figure 13-40 and exits to the atmosphere at the right end of section C. The diameter of the pipe is 2.00 cm at A, 1.00 cm at B, and 0.800 cm at C. The gauge pressure in the pipe at the center of section A is and the flow rate is The vertical pipes are open to the air. Find the level (above the flow midline as shown) of the liquid-air interfaces in the two vertical pipes. Assume laminar nonviscous flow.

ENGINEERING APPLICATION, CONTEXT-RICH You are employed as a tanker truck driver for the summer. Heating oil is delivered to customers for winter usage by your large tanker truck. The delivery hose has a 1.00-cm radius. The specific gravity of the oil is 0.875, and its coefficient of viscosity is What is the minimum time it will take you to fill a customers 55-gal oil drum, if laminar flow through the hose must be maintained?

AU-tube is filled with water until the liquid level reaches 28 cm above the bottom of the tube (Figure 13-41a). Oil, which has a specific gravity of 0.78, is now poured into one arm of the U-tube until the level of the water in the other arm of the tube reaches 34 cm above the bottom of the tube (Figure 13-41b). Find the levels of the oilwater and oilair interfaces in the other arm of the tube. SSM

A helium balloon can just lift a load that weighs 750 N and has a negligible volume. The skin of the balloon has a mass of 1.5 kg. (a) What is the volume of the balloon? (b) If the volume of the balloon were twice that found in Part (a), what would be the initial acceleration of the balloon when released at sea level carrying a load weighing 900 N?

A hollow sphere has an inner radius and an outer radius It is made of material of density and is floating in a liquid of density The interior is now completely filled with material of density such that the sphere just floats completely submerged. Find

According to the law of atmospheres, the fractional decrease in atmospheric pressure is proportional to the change in altitude. This law can be expressed as the differential equation where is a positive constant. (a) Show that where is the pressure at is a solution of the differential equation. (b) Given that the pressure above sea level is half that at sea level, find the constant

ENGINEERING APPLICATION Asubmarine has a total mass of including crew and equipment. The vessel consists of two parts, the pressure hull, which has a volume of and the ballast tanks, which have a volume of When the boat cruises on the surface, the ballast tanks are filled with air at atmospheric pressure; to cruise below the surface, seawater must be admitted into the tanks. (a) What fraction of the submarines volume is above the water surface when the tanks are filled with air? (b) How much water must be admitted into the tanks to give the submarine neutral buoyancy? Neglect the mass of any air in the tanks and use 1.025 as the specific gravity of seawater.

BIOLOGICAL APPLICATION Most species of fish have expandable sacs, commonly known as swim bladders, that enable fish to rise in the water by filling the bladders with oxygen collected by their gills and to sink by emptying the bladders into the surrounding water. A freshwater fish has an average density equal to when its swim bladder is empty. How large must the volume of oxygen in the fishs swim bladder be if the fish is to have neutral buoyancy? The fish has a mass of 0.825 kg. Assume the density of oxygen in the bladder is equal to air density at standard temperature and pressure.