In a movie, Tarzan evades his captors by hiding

The approximate volume of the granite monolith known as El Capitan in Yosemite National Park (Fig. 13-47) is about 108 m3. What is its approximate mass?FIGURE 13-47 Problem 1.

What is the approximate mass of air in a living room 5.6 m X 3.8 m X 2.8 m?

If you tried to smuggle gold bricks by filling your backpack, whose dimensions are 56 cm X 28 cm X 22 cm, what would its mass be?

State your mass and then estimate your volume. [Hint: Because you can swim on or just under the surface of the water in a swimming pool, you have a pretty good idea of your density.]

A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid?

If 5.0 L of antifreeze solution (specific gravity = 0.80) is added to 4.0 L of water to make a 9.0-L mixture, what is the specific gravity of the mixture?

The Earth is not a uniform sphere, but has regions of varying density. Consider a simple model of the Earth divided into three regionsinner core, outer core, and mantle. Each region is taken to have a unique constant density (the average density of that region in the real Earth): Region Radius (km) Density (kg/m3) Inner Core 0-1220 13,000 Outer Core 1220-3480 11,100 Mantle 3480-6371 4,400a) Use this model to predict the average density of the entire Earth. (b) The measured radius of the Earth is 6371 km and its mass is 5.98 X 1024kg. Use these data to determine the actual average density of the Earth and compare it (as a percent difference) with the one you determined in (a).

Estimate the pressure needed to raise a column of water to the same height as a 35-m-tall oak tree.

Estimate the pressure exerted on a floor by (a) one pointed rhair lea (66 ka on all four leas'! o f area = 0 090 rm2 anH

What is the difference in blood pressure (mm-Hg) between the top of the head and bottom of the feet of a 1.70-m-tall person standing vertically?

How high would the level be in an alcohol barometer at normal atmospheric pressure?

In a movie, Tarzan evades his captors by hiding underwater for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is -8 5 mm-Hg, calculate the deepest he could have been.

The maximum gauge pressure in a hydraulic lift is 17.0 atm. What is the largest-size vehicle (kg) it can lift if the diameter of the output line is 22.5 cm?

The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a footprint of 220 cm2, estimate the mass of the car.

(a) Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m. (b) What will be the pressure against the side of the pool near the bottom?

A house at the bottom of a hill is fed by a full tank of water 5.0 m deep and connected to the house by a pipe that is 110 m long at an angle of 58 from the horizontal (Fig. 13-48). (a) Determine the water gauge pressure at the house, (b) How high could the water shoot if it came vertically out of a broken pipe in front of the house? FIGURE 13-48 Problem 16.

Water and then oil (which dont mix) are poured into a U-shaped tube, open at both ends. They come to equilibrium as shown in Fig. 13-49. What is the density of the oil? [Hint: Pressures at points a and b are equal. Why?] FIGURE 13-49 Problem 17.

In working out his principle, Pascal showed dramatically how force can be multiplied with fluid pressure. He placed a long, thin tube of radius r = 0.30 cm vertically into a wine barrel of radius R = 21 cm, Fig. 13-50. He found that when the barrel was filled with water and the tube filled to a height of 12 m, the barrel burst. Calculate (a) the mass of water in the tube, and (b) the net force exerted by the water in the barrel on the lid just before rupture.FIGURE 1 3 -5 0

What is the normal pressure of the atmosphere at the summit of Mt. Everest, 8850 m above sea level?

A hydraulic press for compacting powdered samples has a large cylinder which is 10.0 cm in diameter, and a small cylinder with a diameter of 2.0 cm (Fig. 13-51). A lever is attached to the small cylinder as shown. The sample, which is placed on the large cylinder, has an area of 4.0 cm2. What is the pressure on the sample if 350 N is applied to the lever?FIGURE 13-51 Problem 20.

An open-tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is (a) 21.0 cm higher, (b) 5.2 cm lower, than the mercury in the tube connected to the tank?

A beaker of liquid accelerates from rest, on a horizontal surface, with acceleration a to the right, (a) Show that the surface of the liquid makes an angle 6 = tan-1 (a/g) with the horizontal. (b) Which edge of the water surface is higher? (c) How does the pressure vary with depth below the surface?

Water stands at a height h behind a vertical dam of uniform width b. (a) Use integration to show that the total force of the water on the dam is F = jpgh2b. (b) Show that the torque about the base of the dam due to this force can be considered to act with a lever arm equal to h/3. (c) For a freestanding concrete dam of uniform thickness t and height h, what minimum thickness is needed to prevent overturning? Do you need to add in atmospheric pressure for this last part? Explain.

Estimate the density of the water 5.4 km deep in the sea. (See Table 12-1 and Section 12-4 regarding bulk modulus.) By what fraction does it differ from the density at the surface?

A cylindrical bucket of liquid (density p) is rotated about its symmetry axis, which is vertical. If the angular velocity is (o, show that the pressure at a distance r from the rotation axis is P = P0 + \ p(o2r2, where P0 is the pressure at r = 0.

What fraction of a piece of iron will be submerged when it floats in mercury?

A geologist finds that a Moon rock whose mass is 9.28 kg has an annarent mass of 6.18 ka when snhmeraed in water.

A crane lifts the 16,000-kg steel hull of a sunken ship out of the water. Determine {a) the tension in the cranes cable when the hull is fully submerged in the water, and (b) the tension when the hull is completely out of the water.

A spherical balloon has a radius of 7.35 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.

A 74-kg person has an apparent mass of 54 kg (because of buoyancy) when standing in water that comes up to the hips. Estimate the mass of each leg. Assume the body has SG = 1.00.

What is the likely identity of a metal (see Table 13-1) if a sample has a mass of 63.5 g when measured in air and an apparent mass of 55.4 g when submerged in water?

Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 3.0000 kg when weighed in air.

Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 230-L steel drum is completely full of gasoline. What total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?

A scuba diver and her gear displace a volume of 65.0 L and have a total mass of 68.0 kg. (a) What is the buoyant force on the diver in seawater? (b) Will the diver sink or float?

The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water?

Archimedes principle can be used not only to determine the specific gravity of a solid using a known liquid (Example 13-10); the reverse can be done as well, (a) As an example, a 3.80-kg aluminum ball has an apparent mass of 2.10 kg when submerged in a particular liquid: calculate the density of the liquid, (b) Derive a formula for determining the density of a liquid using this procedure.

(a) Show that the buoyant force FB on a partially submerged object such as a ship acts at the center of gravity of the fluid before it is displaced. This point is called the center of buoyancy. (b) To ensure that a ship is in stable equilibrium, would it be better if its center of buoyancy was above, below, or at the same point as, its center of gravity? Explain. Fh (See Fig. 13-52.)(a) Show that the buoyant force FB on a partially submerged object such as a ship acts at the center of gravity of the fluid before it is displaced. This point is called the center of buoyancy. (b) To ensure that a ship is in stable equilibrium, would it be better if its center of buoyancy was above, below, or at the same point as, its center of gravity? Explain. Fh (See Fig. 13-52.)

A cube of side length 10.0 cm and made of unknown material floats at the surface between water and oil. The oil has a density of 810 kg/m3. If the cube floats so that it is 72% in the water and 28% in the oil, what is the mass of the cube and what is the buoyant force on the cube

How many helium-filled balloons would it take to lift a person? Assume the person has a mass of 75 kg and that ear.h helium-filled balloon is snherinal with a diameter of

A scuba tank, when fully submerged, displaces 15.7 L of seawater. The tank itself has a mass of 14.0 kg and, when full, contains 3.00 kg of air. Assuming only a weight and buoyant force act, determine the net force (magnitude and direction) on the fully submerged tank at the beginning of a dive (when it is full of air) and at the end of a dive (when it no longer contains any air).

If an object floats in water, its density can be determined by tying a sinker to it so that both the object and the sinker are submerged. Show that the specific gravity is given by w/{wi w2), where w is the weight of the object alone in air, w\ is the apparent weight when a sinker is tied to it and the sinker only is submerged, and w2 is the apparent weight when both the object and the sinker are submerged.

A 3.25-kg piece of wood (SG = 0.50) floats on water. What minimum mass of lead, hung from the wood by a string, will cause it to sink?

A 15-cm-radius air duct is used to replenish the air of a room 8.2 m X 5.0 m X 3.5 m every 12 min. How fast does the air flow in the duct?

Using the data of Example 13-13, calculate the average speed of blood flow in the major arteries of the body which have a total cross-sectional area of about 2.0 cm2.

How fast does water flow from a hole at the bottom of a very wide, 5.3-m-deep storage tank filled with water? Ignore viscosity.

A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 4.0 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?

What gauge pressure in the water mains is necessary if a firehose is to spray water to a height of 18 m?

A -in. (inside) diameter garden hose is used to fill a round swimming pool 6.1 m in diameter. How long will it take to fill the pool to a depth of 1.2 m if water flows from the hose at a speed of 0.40 m/s?

A 180-km/h wind blowing over the flat roof of a house causes the roof to lift off the house. If the house is 6.2 m X 12.4 m in size, estimate the weight of the roof. Assume the roof is not nailed down.

A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPa and 24.0 kPa, respectively. What is the volume rate of flow?

Estimate the air pressure inside a category 5 hurricane, where the wind speed is 300 km/h (Fig. 13-53).

What is the lift (in newtons) due to Bernoullis principle on a wing of area 88 m2 if the air passes over the top and bottom surfaces at speeds of 280 m/s and 150 m/s, respectively?

Show that the power needed to drive a fluid through a pipe with uniform cross-section is equal to the volume rate of flow, Q, times the pressure difference, P\ - P2.

Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.68 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 18 m above (Fig. 13-54), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity.FIGURE 13-54 Problem 54.

In Fig. 13-55, take into account the speed of the top surface of the tank and show that the speed of fluid leaving the opening at the bottom is Vi = 2 gh (1 - A \/A l) where h = y2 yi, and A \ and A 2 are the areas of the opening and of the top surface, respectively. Assume A i <5< A 2 so that the flow remains nearly steady and laminar.FIGURE 13-55 Problems 55,56,58, and 59.

Suppose the top surface of the vessel in Fig. 13-55 is subjected to an external gauge pressure P2. (a) Derive a formula for the speed, V\ , at which the liquid flows from the opening at the bottom into atmospheric pressure, P0. Assume the velocity of the liquid surface, v2, is approximately zero. (b) If P2 = 0.85 atm and y2 ~ y\ = 2.4 m, determine V\ for water.

You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are pointing the hose at the same anale and the distance the water reaches increases hv a

Suppose the opening in the tank of Fig. 13-55 is a height hi above the base and the liquid surface is a height h2 above the base. The tank rests on level ground, (a) At what horizontal distance from the base of the tank will the fluid strike the ground? (b) At what other height, h[, can a hole be placed so that the emerging liquid will have the same range? Assume FIGURE 13-55 (repeated) Problems 55,56,58, and 59.

(a) In Fig. 13-55, show that Bernoullis principle predicts that the level of the liquid, h = y2 - y \, drops at a rate dh _ I 2ghA\ dt V A 2 - A 2 where A 1 and A 2 are the areas of the opening and the top surface, respectively, assuming A t A 2, and viscosity is ignored. (b) Determine h as a function of time by integrating. Let h = ho at t = 0. (c) How long would it take to empty a 10.6-cm-tall cylinder filled with 1.3 L of water if the opening is at the bottom and has a 0.50-cm diameter?

(a) Show that the flow speed measured by a venturi meter (see Fig. 13-32) is given by the relation vi = A 2- 2(fi ~ f 2) p(a 2 a \) (b) A venturi meter is measuring the flow of water; it has a main diameter of 3.0 cm tapering down to a throat diameter of 1.0 cm. If the pressure difference is measured to be 18 mm-Hg, what is the speed of the water entering the venturi throat?

Thrust o f a rocket, (a) Use Bernoullis equation and the equation of continuity to show that the emission speed of the propelling gases of a rocket is v = V t iP - -Po)/p, where p is the density of the gas, P is the pressure of the gas inside the rocket, and Zq is atmospheric pressure just outside the exit orifice. Assume that the gas density stays approximately constant, and that the area of the exit orifice, A 0, is much smaller than the cross-sectional area, A, of the inside of the rocket (take it to be a large cylinder). Assume also that the gas speed is not so high that significant turbulence or nonsteady flow sets in. (b) Show that the thrust force on the rocket due to the emitted gases is F = 2A0{P - P0).

A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.0-cm-diameter hose delivering 450L/min through a 0.75-cm-diameter nozzle?

A viscometer consists of two concentric cylinders, 10.20 cm and 10.60 cm in diameter. A liquid fills the space between them to a depth of 12.0 cm. The outer cylinder is fixed, and a torque of 0.024 m N keeps the inner cylinder turning at a steady rotational speed of 57 rev/min. What is the viscosity of the liquid?

A long vertical hollow tube with an inner diameter of 1.00 cm is filled with SAE 10 motor oil. A 0.900-cm-diameter, 30.0-cm-long 150-g rod is dropped vertically through the oil in the tiihe. What is the maximum sneed attained hv the rod

Engine oil (assume SAE 10, Table 13-3) passes through a fine 1.80-mm-diameter tube that is 8.6 cm long. What pressure difference is needed to maintain a flow rate of 6.2 mL/min?

A gardener feels it is taking too long to water a garden with a |-in.-diameter hose. By what factor will the time be cut using a |-in.-diameter hose instead? Assume nothing else is changed.

What diameter must a 15.5-m-long air duct have if the ventilation and heating system is to replenish the air in a room 8.0 m X 14.0 m X 4.0 m every 12.0 min? Assume the pump can exert a gauge pressure of 0.710 X 10-3 atm.

What must be the pressure difference between the two ends of a 1.9-km section of pipe, 29 cm in diameter, if it is to transport oil (p = 950 kg/m3, 17 = 0.20 Pa s) at a rate of 650 cm3/s?

Poiseuilles equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, Re, exceeds approximately 2000. Re is defined as 2 vrp Re = V where v is the average speed of the fluid, p is its density, rj is its viscosity, and r is the radius of the tube in which the fluid is flowing, (a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta (r = 0.80 cm) during the resting part of the hearts cycle is about 35 cm/s. (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent

Assuming a constant pressure gradient, if blood flow is reduced by 85%, by what factor is the radius of a blood vessel decreased?

A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein (Fig. 13-56). The inside diameter of the 25-mm-long needle is 0.80 mm, and the required flow rate is 2.0 cm3 of blood per minute. How high h should the bottle be placed above the needle? Obtain p and 7) from the Tables. Assume the blood pressure is 78 torr above atmospheric pressure.FIGURE 13-56 Problems 71 and 79.

If the force F needed to move the wire in Fig. 13-35 is 3.4 X 10_3N, calculate the surface tension y of the enclosed fluid. Assume I = 0.070 m.

Calculate the force needed to move the wire in Fig. 13-35 if it is immersed in a soapy solution and the wire is 24.5 cm long.

The surface tension of a liquid can be determined by measuring the force F needed to just lift a circular platinum ring of radius r from the surface of the liquid, (a) Find a formula for y in terms of F and r. (b) At 30 C, if F = 5.80 X 10-3 N and r = 2.8 cm, calculate y for the tested liquid.

Rstimate the diameter o f a steel needle that can iust

Show that inside a soap bubble, there must be a pressure AP in excess of that outside equal to AP = 4y/r, where r is the radius of the bubble and y is the surface tension. [Hint. Think of the bubble as two hemispheres in contact with each other; and remember that there are two surfaces to the bubble. Note that this result applies to any kind of membrane, where 2y is the tension per unit length in that membrane.

A common effect of surface tension is the ability of a liquid to rise up a narrow tube due to what is called capillary action. Show that for a narrow tube of radius r placed in a liquid of density p and surface tension y, the liquid in the tube will reach a height h = 2y/pgr above the level of the liquid outside the tube, where g is the gravitational acceleration. Assume that the liquid wets the capillary (the liquid surface is vertical at the contact with the inside of the tube).

A 2.8-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle 0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 75 mm-Hg? Answer for the instant just before the fluid starts to move.

Intravenous infusions are often made under gravity, as shown in Fig. 13-56. Assuming the fluid has a density of 1.00 g/cm3, at what height h should the bottle be placed so the liquid pressure is (a) 55 mm-Hg, and (b) 650 mm-H20 ? (c) If the blood pressure is 78 mm-Hg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein?

A beaker of water rests on an electronic balance that reads 998.0 g. A 2.6-cm-diameter solid copper ball attached to a string is submerged in the water, but does not touch the bottom. What are the tension in the string and the new balance reading?

Estimate the difference in air pressure between the top and the bottom of the Empire State building in New York City? It is 380 m tall and is located at sea level. Express as a fraction of atmospheric pressure at sea level.

A hydraulic lift is used to jack a 920-kg car 42 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 350 N. (a) What is the area of the input piston? (b) What is the work done in lifting the car 42 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up 42 cm? (e) Show that energy is conserved.

When you ascend or descend a great deal when driving in a car, your ears pop, which means that the pressure behind the eardrum is being equalized to that outside. If this did not happen, what would be the approximate force on an eardrum of area 0.20 cm2 if a change in altitude of 950 m takes place?

Giraffes are a wonder of cardiovascular engineering. Calculate the difference in pressure (in atmospheres) that the blood vessels in a giraffes head must accommodate as the head is lowered from a full upright position to ground level for a drink. The height of an average giraffe is about 6 m.

Suppose a person can reduce the pressure in his lungs to -7 5 mm-Hg gauge pressure. How high can water then be sucked up a straw?

Airlines are allowed to maintain a minimum air pressure within the passenger cabin equivalent to that at an altitude of 8000 ft (2400 m) to avoid adverse health effects among nassenpers due to oxvaen denrivation. Estimate this

A simple model (Fig. 13-57) considers a continent as a block (density 2800 kg/m3) floating in the mantle rock around it (density ~ 3300 kg/m3). Assuming the continent is 35 km thick (the average thickness of the Earths continental crust), estimate the height of the continent above the surrounding rock. FIGURE 13-57 Problem 87.

A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of 2240 m2 at the waterline. When unloaded, the ship rises 8.50 m higher in the sea. How many cubic meters of water was delivered?

During ascent, and especially during descent, volume changes of trapped air in the middle ear can cause ear discomfort until the middle-ear pressure and exterior pressure are equalized, (a) If a rapid descent at a rate of 7.0 m/s or faster commonly causes ear discomfort, what is the maximum rate of increase in atmospheric pressure (that is, dP/dt) tolerable to most people? (b) In a 350-m-tall building, what will be the fastest possible descent time for an elevator traveling from the top to ground floor, assuming the elevator is properly designed to account for human physiology?

A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.1 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

Estimate the total mass of the Earths atmosphere, using the known value of atmospheric pressure at sea level.

During each heartbeat, approximately 70 cm3 of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.

Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35 to the horizontal and covers a radius of 7.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver ner second? ( r\ H ow fast is the

A bucket of water is accelerated upward at 1.8 g. What is the buoyant force on a 3.0-kg granite rock (SG = 2.7) submerged in the water? Will the rock float? Why or why not?

The stream of water from a faucet decreases in diameter as it falls (Fig. 13-58). Derive an equation for the diameter of the stream as a function of the distance y below the faucet, given that the water has speed v0 when it leaves the faucet, whose diameter is d.FIGURE 13-58 Problem 95. Water coming from a faucet.

You need to siphon water from a clogged sink. The sink has an area of 0.38 m2 and is filled to a height of 4.0 cm. Your siphon tube rises 45 cm above the bottom of the sink and then descends 85 cm to a pail as shown in Fig. 13-59. The siphon tube has a diameter of 2.0 cm. (a) Assuming that the water level in the sink has almost zero velocity, estimate the water velocity when it enters the pail. (b) Estimate how long it will take to empty the sink. FIGURE 13-59 Problem 96.

An airplane has a mass of 1.7 X 106kg, and the air flows past the lower surface of the wings at 95 m/s. If the wings have a surface area of 1200 m2, how fast must the air flow over the upper surface of the wing if the plane is to stay in the air?

A drinking fountain shoots water about 14 cm up in the air from a nozzle of diameter 0.60 cm. The pump at the base of the unit (1.1 m below the nozzle) pushes water into a 1.2- cm-diameter supply pipe that goes up to the nozzle. What gauge pressure does the pump have to provide? Ignore the viscosity; your answer will therefore be an underestimate.

A hurricane-force wind of 200 km/h blows across the face of a storefront window. Estimate the force on the 2.0 m X 3.0 m window due to the difference in air pressure inside and outside the window. Assume the store is airtight so the inside pressure remains at 1.0 atm. (This is why you should not tightly seal a building in preparation for a hurricane).

Blood from an animal is placed in a bottle 1.30 m above a 3.8-cm-long needle, of inside diameter 0.40 mm, from which it flows at a rate of 4.1 cm3/min. What is the viscosity of this blood?

Three forces act significantly on a freely floating heliumfilled balloon: gravity, air resistance (or drag force), and a buoyant force. Consider a spherical helium-filled balloon of radius r = 15 cm rising upward through 0C air, and m = 2.8 g is the mass of the (deflated) balloon itself. For all speeds v, except the very slowest ones, the flow of air past a rising balloon is turbulent, and the drag force FD is given by the relation Fd = \C v Pairirr2v2 where the constant CD = 0.47 is the drag coefficient for a smooth sphere of radius r. If this balloon is released from rest, it will accelerate very quickly (in a few tenths of a second) to its terminal velocity Vj, where the buoyant force is cancelled by the drag force and the balloons total weight. Assuming the balloons acceleration takes place over a negligible time and distance, how long does it take the released balloon to rise a distance h = 12 m?

If cholesterol buildup reduces the diameter of an artery by 15%, by what % will the blood flow rate be reduced, assuming the same pressure difference?

A two-component model used to determine percent body fat in a human body assumes that a fraction / ( < 1) of the bodys total mass m is composed of fat with a density of 0.90 g/cm3, and that the remaining mass of the body is composed of fat-free tissue with a density of 1.10 g/cm3. If the specific gravity of the entire bodys density is X, show that the percent body fat ( = / X 100) is given by 495 % Body fat = 450.

Air pressure decreases with altitude. The following data show the air pressure at different altitudes. Altitude (m) Pressure (kPa) 0 101.3 1000 89.88 2000 79.50 3000 70.12 4000 61.66 5000 54.05 6000 47.22 7000 41.11 8000 35.65 9000 30.80 10,000 26.50 (a) Determine the best-fit quadratic equation that shows how the air pressure changes with altitude. (b) Determine the best-fit exponential equation that describes the change of air pressure with altitude. (c) Use each fit to find the air pressure at the summit of the mountain K2 at 8611 m, and give the % difference.