Physics

Robert Coleman Richardson; Betty McCarthy Richardson; Alan Giambattista

Chapter 9

Fluids - all with Video Answers

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Chapter Questions

Problem 1

Someone steps on your toe, exerting a force of $500 \mathrm{N}$ on an area of $1.0 \mathrm{cm}^{2} .$ What is the average pressure on that area in atm?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 2

What is the average pressure on the soles of the feet of a standing $90.0 \mathrm{kg}$ person due to the contact force with the floor? Each foot has a surface area of $0.020 \mathrm{m}^{2}$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 3

Atmospheric pressure is about $1.0 \times 10^{5} \mathrm{Pa}$ on average.
(a) What is the downward force of the air on a desktop with surface area $1.0 \mathrm{m}^{2} ?$ (b) Convert this force to pounds to help others understand how large it is. (c) Why does this huge force not cause the desk to collapse?

Narayan Hari

Numerade Educator

Problem 4

A $10 \mathrm{kg}$ baby sits on a three-legged stool. The diameter of each of the stool's round feet is $2.0 \mathrm{cm} .$ A $60 \mathrm{kg}$ adult sits on a four-legged chair that has four circular feet, each with a diameter of $6.0 \mathrm{cm} .$ Who applies the greater pressure to the floor and by how much?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 5

A lid is put on a box that is $15 \mathrm{cm}$ long, $13 \mathrm{cm}$ wide, and $8.0 \mathrm{cm}$ tall, and the box is then evacuated until its inner pressure is $0.80 \times 10^{5} \mathrm{Pa}$. How much force is required to lift the lid (a) at sea level; (b) in Denver, on a day when the atmospheric pressure is $67.5 \mathrm{kPa}\left(\frac{2}{3}\right.$ the value at sea level)?

Narayan Hari

Numerade Educator

Problem 6

A container is filled with gas at a pressure of $4.0 \times 10^{5} \mathrm{Pa}$. The container is a cube, $0.10 \mathrm{m}$ on a side, with one side facing south. What is the magnitude and direction of the force on the south side of the container due to the gas inside?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 7

A nurse applies a force of $4.40 \mathrm{N}$ to the piston of a syringe. The piston has an area of $5.00 \times 10^{-5} \mathrm{m}^{2} .$ What is the pressure increase in the fluid within the syringe?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 8

In a hydraulic lift, the radii of the pistons are $2.50 \mathrm{cm}$ and $10.0 \mathrm{cm} .$ A car weighing $W=10.0 \mathrm{kN}$ is to be lifted by the force of the large piston. (a) What force $F_{a}$ must be applied to the small piston? (b) When the small piston is pushed in by $10.0 \mathrm{cm},$ how far is the car lifted?
(c) Find the mechanical advantage of the lift, which is the ratio $W T F_{\alpha^{*}}$

Narayan Hari

Numerade Educator

Problem 9

At the surface of a freshwater lake the air pressure is $1.0 \mathrm{atm} .$ At what depth under water in the lake is the water pressure 4.0 atm?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 10

What is the pressure on a fish $10 \mathrm{m}$ under the ocean surface?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 11

The density of platinum is $21500 \mathrm{kg} / \mathrm{m}^{3}$. Find the ratio of the volume of $1.00 \mathrm{kg}$ of platinum to the volume of $1.00 \mathrm{kg}$ of aluminum.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 12

In the Netherlands, a dike holds back the sea from a town below sea level. The dike springs a leak $3.0 \mathrm{m}$ below the water surface. If the area of the hole in the dike is $1.0 \mathrm{cm}^{2},$ what force must the Dutch boy exert to save the town?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 13

Each of five cylindrical drums with radius $R$ is filled to a height $h$ above the bottom with a liquid of density $\rho$ Rank the drums in order of the pressure at the bottom of the drum, largest to smallest.
(a) $R=40 \mathrm{cm}, h=80 \mathrm{cm}, \rho=1000 \mathrm{kg} / \mathrm{m}^{3}$
(b) $R=40 \mathrm{cm}, h=100 \mathrm{cm}, \rho=1000 \mathrm{kg} / \mathrm{m}^{3}$
(c) $R=50 \mathrm{cm}, h=100 \mathrm{cm}, \rho=800 \mathrm{kg} / \mathrm{m}^{3}$
(d) $R=50 \mathrm{cm}, h=80 \mathrm{cm}, \rho=800 \mathrm{kg} / \mathrm{m}^{3}$
(e) $R=50 \mathrm{cm}, h=125 \mathrm{cm}, \rho=800 \mathrm{kg} / \mathrm{m}^{3}$

Matthew Baker

Numerade Educator

Problem 14

Each of six barrels is filled to a height $h$ above the bottom with a liquid of density $\rho$. Each barrel has a hole of radius $r$ in its side. The center of each hole is $20 \mathrm{cm}$ above the barrel bottom. A plug in the hole keeps the liquid from escaping. Rank the barrels in order of the force on the plug due to the liquid in the barrel, from largest to smallest.
(a) $r=1 \mathrm{cm}, h=100 \mathrm{cm}, \rho=1000 \mathrm{kg} / \mathrm{m}^{3}$
(b) $r=1 \mathrm{cm}, h=120 \mathrm{cm}, \rho=1000 \mathrm{kg} / \mathrm{m}^{3}$
(c) $r=1.25 \mathrm{cm}, h=120 \mathrm{cm}, \rho=800 \mathrm{kg} / \mathrm{m}^{3}$
(d) $r=1.25 \mathrm{cm}, h=100 \mathrm{cm}, \rho=800 \mathrm{kg} / \mathrm{m}^{3}$
(e) $r=1 \mathrm{cm}, h=145 \mathrm{cm}, \rho=1000 \mathrm{kg} / \mathrm{m}^{3}$

Matthew Baker

Numerade Educator

Problem 15

A giraffe's brain is approximately $3.4 \mathrm{m}$ above its heart. Estimate the minimum gauge pressure that its heart must produce to move the blood to his brain. Ignore any effects from the blood flow through arteries of different area, and assume that giraffe blood is identical to human blood.

Vishal Gupta

Numerade Educator

Problem 16

How high can you suck water up a straw? The pressure in the lungs can be reduced to about $10 \mathrm{kPa}$ below atmospheric pressure.

Vishal Gupta

Numerade Educator

Problem 17

A sperm whale can reach depths of $2500 \mathrm{m}$ below the surface of the ocean. What is the pressure on the whale's skin at that depth, assuming that the density of seawater is constant from the surface to that depth?

Narayan Hari

Numerade Educator

Problem 18

A container has a large cylindrical lower part with a long thin cylindrical neck open at the top. The lower part of the container holds $12.5 \mathrm{m}^{3}$ of water and the surface area of the bottom of the container is $5.00 \mathrm{m}^{2}$ The height of the lower part of the container is $2.50 \mathrm{m},$ and the neck contains a column of water $8.50 \mathrm{m}$ high. The total volume of the column of water in the neck is $0.200 \mathrm{m}^{3}$. (a) What is the magnitude of the force exerted by the water on the bottom of the container? (b) Explain why it is not equal to the weight of the water.

Matthew Baker

Numerade Educator

Problem 19

The maximum pressure most organisms can survive is about 1000 times atmospheric pressure. Only small, simple organisms such as tadpoles and bacteria can survive such high pressures. What then is the maximum depth at which these organisms can live under the sea (assuming that the density of seawater is $1025 \mathrm{kg} / \mathrm{m}^{3}$ )?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 20

At the surface of a freshwater lake the pressure is $105 \mathrm{kPa}$. (a) What is the pressure increase in going $35.0 \mathrm{m}$ below the surface? (b) What is the approximate pressure decrease in going $35 \mathrm{m}$ above the surface? Air at $20^{\circ} \mathrm{C}$ has density of $1.20 \mathrm{kg} / \mathrm{m}^{3}$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 21

When a mercury manometer is connected to a gas main, the mercury stands $40.0 \mathrm{cm}$ higher in the tube that is open to the air than in the tube connected to the gas main. A barometer at the same location reads 740 mmHg. Determine the absolute pressure of the gas in mmHg.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 22

An experiment to determine the specific heat of a gas (Chapter 14) makes use of a water manometer attached to a flask. Initially the two columns of water are even. Atmospheric pressure is $1.0 \times 10^{5} \mathrm{Pa}$
After heating the gas, the water levels change to those shown. Find the change in pressure of the gas in pascals.

Narayan Hari

Numerade Educator

Problem 23

A manometer using oil (density $0.90 \mathrm{g} / \mathrm{cm}^{3}$ ) as a fluid is connected to an air tank. Suddenly the pressure in the tank increases by $7.4 \mathrm{mmHg}$.
(a) By how much does the fluid level rise in the side of the manometer that is open to the atmosphere?
(b) What would your answer be if the manometer used mercury instead?

Narayan Hari

Numerade Educator

Problem 24

An IV is connected to a patient's vein. The blood in the vein has a gauge pressure of 12 mmHg. At least how far above the vein must the IV bag be hung in order for fluid to flow into the vein? Assume the fluid in the IV
has the same density as blood.

Narayan Hari

Numerade Educator

Problem 25

Estimate the average blood pressure in a person"s foot if the foot is $1.37 \mathrm{m}$ below the aorta, where the average blood pressure is 104 mmHg. For the purposes of this estimate, assume the blood isn't flowing.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 26

A woman"s systolic blood pressure when resting is $160 \mathrm{mmHg} .$ What is this pressure in
(a) $\mathrm{Pa}$
(b) $\mathrm{Ib} / \mathrm{in}^{2}$
and (c) atm?

Narayan Hari

Numerade Educator

Problem 27

The gauge pressure of the air in an automobile tire is $32 \mathrm{lb} / \mathrm{in}^{2}$. Convert this to (a) $\mathrm{Pa}$, (b) $\mathrm{mmHg}$,
(c) atm.

Narayan Hari

Numerade Educator

Problem 28

(a) Which has the larger buoyant force acting on it when immersed in water, $1.0 \mathrm{kg}$ of lead or $1.0 \mathrm{kg}$ of aluminum? Explain. (b) Which has the larger buoyant force acting on it, $1.0 \mathrm{kg}$ of steel that is sinking to the bottom of a lake or $1.0 \mathrm{kg}$ of wood with a density of $500 \mathrm{kg} / \mathrm{m}^{3}$ that is floating on the lake? Explain. (c) Once you have answered the qualitative questions, find the quantitative answers to parts (a) and (b).

Matthew Baker

Numerade Educator

Problem 29

Six wooden blocks (mass $m$ ) float in a barrel of water. The blocks are not all made from the same type of wood. The bottom of each block is submerged to a depth $d$ below the water surface. Rank the blocks in order of the buoyant force on them, largest to smallest.
(a) $m=20 \mathrm{g}, d=2.5 \mathrm{cm}$
(b) $m=20 \mathrm{g}, d=2 \mathrm{cm}$
(c) $m=25 \mathrm{g}, d=2 \mathrm{cm}$
(d) $m=25 \mathrm{g}, d=2.5 \mathrm{cm}$
(e) $m=10 \mathrm{g}, d=2 \mathrm{cm}$
(f) $m=10 \mathrm{g}, d=1 \mathrm{cm}$

Matthew Baker

Numerade Educator

Problem 30

A Canada goose floats with $25 \%$ of its volume below water. What is the average density of the goose?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 31

A flat-bottomed barge, loaded with coal, has a mass of $3.0 \times 10^{5} \mathrm{kg} .$ The barge is $20.0 \mathrm{m}$ long and $10.0 \mathrm{m}$ wide. It floats in freshwater. What is the depth of the barge below the waterline?

Narayan Hari

Numerade Educator

Problem 32

(a) When ice floats in water at $0^{\circ} \mathrm{C},$ what percent of its volume is submerged?
(b) What is the specific gravity of ice?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 33

(a) What is the density of an object that is $14 \%$ submerged when floating in water at $0^{\circ} \mathrm{C} ?$
(b) What percentage of the object will be submerged if it is placed in ethanol at $0^{\circ} \mathrm{C} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 34

(a) What is the buoyant force on $0.90 \mathrm{kg}$ of ice floating freely in liquid water?
(b) What is the buoyant force on $0.90 \mathrm{kg}$ of ice held completely submerged under water?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 35

A block of birch wood floats in oil with $90.0 \%$ of its volume submerged. What is the density of the oil? The density of the birch is $0.67 \mathrm{g} / \mathrm{cm}^{3}$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 36

When a block of ebony is placed in ethanol, what percentage of its volume is submerged?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 37

A cylindrical disk has volume $8.97 \times 10^{-3} \mathrm{m}^{3}$ and mass $8.16 \mathrm{kg} .$ The disk is floating on the surface of some water with its flat surfaces horizontal. The area of each flat surface is $0.640 \mathrm{m}^{2}$. (a) What is the specific gravity of the disk? (b) How far below the water level is its bottom surface?
(c) How far above the water level is its top surface?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 38

An aluminum cylinder weighs $1.03 \mathrm{N} .$ When this same cylinder is completely submerged in alcohol, the volume of the displaced alcohol is $3.90 \times 10^{-5} \mathrm{m}^{3}$. If the cylinder is suspended from a scale while submerged in the alcohol, the scale reading is $0.730 \mathrm{N}$. What is the specific gravity of the alcohol?

Narayan Hari

Numerade Educator

Problem 39

A fish uses a swim bladder to change its density so it is equal to that of water, enabling it to remain suspended under water. If a fish has an average density of $1080 \mathrm{kg} / \mathrm{m}^{3}$ and mass $10.0 \mathrm{g}$ with the bladder completely deflated, to what volume must the fish inflate the swim bladder in order to remain suspended in seawater of density $1060 \mathrm{kg} / \mathrm{m}^{3} ?$

Nishant Kumar

Numerade Educator

Problem 40

A solid piece of plastic, with a density of $890 \mathrm{kg} / \mathrm{m}^{3}$, is placed in oil with a density of $830 \mathrm{kg} / \mathrm{m}^{3}$ and the plastic sinks (1). Then the plastic is placed in water and it floats (2). (a) What percentage of the plastic is submerged in the water?
(b) Finally, the same oil in which the plastic sinks is poured over the plastic and the water. Will less ( 3 ) or more (4) of the plastic be submerged in the water compared to $2 ?$ Explain. (c) Calculate the percentage of the plastic submerged in the water.

Matthew Baker

Numerade Educator

Problem 41

Nine-banded armadillos (Dasypus novemcinctus) have a typical mass density of $1200 \mathrm{kg} / \mathrm{m}^{3}$ and a mass of $7.0 \mathrm{kg}$ (including their armor). When faced with a body of water to cross, the armadillo has two choices: to hold its breath and walk across the bottom or to swallow air into the stomach and intestine and float across. Approximately what volume of air does it need to swallow in order to float? Assume the swallowed air is at atmospheric pressure.

Satpal Satpal

Numerade Educator

Problem 42

The average density of a fish can be found by first weighing it in air and then finding the scale reading for the fish completely immersed in water and suspended from a scale. If a fish has weight $200.0 \mathrm{N}$ in air and scale reading $15.0 \mathrm{N}$ in water, what is the average density of the fish?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 43

You suspend the coin from a spring scale and find that its mass is $49.7 \mathrm{g}$. You then let the coin hang completely submerged in a glass of water but not touching the bottom and find that the scale reads $47.1 \mathrm{g}$. Should you get excited about the possibility that this coin might really be gold? Explain.

Matthew Baker

Numerade Educator

Problem 44

On a kitchen scale you measure the coin's mass to be $49.7 \mathrm{g} .$ You measure the mass of a small bowl of water as 314.8 g. You tie a slender thread around the coin and suspend it completely submerged in the water but not touching the bottom. The scale reading is now 317.4 g. Should you get excited about the possibility that this coin might really be gold? Explain.

Matthew Baker

Numerade Educator

Problem 45

(a) A piece of balsa wood with density $0.50 \mathrm{g} / \mathrm{cm}^{3}$ is released under water. What is its initial acceleration? (b) Repeat for a piece of maple with density $0.750 \mathrm{g} / \mathrm{cm}^{3}$.
(c) Repeat for a ping-pong ball with an average density of $0.125 \mathrm{g} / \mathrm{cm}^{3}$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 46

A piece of metal is released under water. The volume of the metal is $50.0 \mathrm{cm}^{3}$ and its specific gravity is $5.0 .$ What is its initial acceleration?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 47

A garden hose of inner radius $1.0 \mathrm{cm}$ carries water at $2.0 \mathrm{m} / \mathrm{s} .$ The nozzle at the end has inner radius $0.20 \mathrm{cm}$ How fast does the water move through the nozzle?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 48

If the average volume flow of blood through the aorta is $8.5 \times 10^{-5} \mathrm{m}^{3} / \mathrm{s}$ and the cross-sectional area of the aorta is $3.0 \times 10^{-4} \mathrm{m}^{2},$ what is the average speed of blood in the aorta?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 49

A nozzle of inner radius $1.00 \mathrm{mm}$ is connected to a hose of inner radius $8.00 \mathrm{mm}$. The nozzle shoots out water moving at $25.0 \mathrm{m} / \mathrm{s}$. (a) At what speed is the water in the hose moving? (b) What is the volume flow rate?
(c) What is the mass flow rate?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 50

Water entering a house flows with a speed of $0.20 \mathrm{m} / \mathrm{s}$ through a pipe of $1.0 \mathrm{cm}$ inside radius. What is the speed of the water at a point where the pipe tapers to a radius of $2.5 \mathrm{mm} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 51

A horizontal segment of pipe tapers from a cross- sectional area of $50.0 \mathrm{cm}^{2}$ to $0.500 \mathrm{cm}^{2}$. The pressure at the larger end of the pipe is $1.20 \times 10^{5} \mathrm{Pa}$, and the speed is $0.040 \mathrm{m} / \mathrm{s} .$ What is the pressure at the narrow end of the segment?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 52

In a tornado or hurricane, a roof may tear away from the house because of a difference in pressure between the air inside and the air outside. Suppose that air is blowing across the top of a $2000 \mathrm{ft}^{2}$ roof at $150 \mathrm{mi} / \mathrm{h}$. What is the magnitude of the force on the roof?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 53

Use Bernoulli's equation to estimate the upward force on an airplane's wing if the average flow speed of air is $190 \mathrm{m} / \mathrm{s}$ above the wing and $160 \mathrm{m} / \mathrm{s}$ below the wing. The density of the air is $1.3 \mathrm{kg} / \mathrm{m}^{3},$ and the area of each wing surface is $28 \mathrm{m}^{2}$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 54

An airplane flies on a level path. There is a pressure difference of $500 \mathrm{Pa}$ between the lower and upper surfaces of the wings. The area of each wing surface is about $100 \mathrm{m}^{2} .$ The air moves below the wings at a speed of $80.5 \mathrm{m} / \mathrm{s} .$ Estimate
(a) the weight of the plane and the air speed above the wings.

Narayan Hari

Numerade Educator

Problem 55

A nozzle is connected to a horizontal hose. The nozzle shoots out water moving at $25 \mathrm{m} / \mathrm{s}$. What is the gauge pressure of the water in the hose? Ignore viscosity and assume that the diameter of the nozzle is much smaller than the inner diameter of the hose.

Narayan Hari

Numerade Educator

Problem 56

Suppose air, with a density of $1.29 \mathrm{kg} / \mathrm{m}^{3},$ is flowing into a Venturi meter. The narrow section of the pipe at point $A$ has a diameter that is $\frac{1}{3}$ of the diameter of the larger section of the pipe at point $B$. The U-shaped tube is filled with water and the difference in height between the two sections of pipe is $1.75 \mathrm{cm}$. How fast is the air moving at point $B ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 57

A water tower supplies water through the plumbing in a house. A 2.54 cm diameter faucet in the house can fill a cylindrical container with a diameter of $44 \mathrm{cm}$ and a height of $52 \mathrm{cm}$ in $12 \mathrm{s}$. How high above the faucet is the top of the water in the tower? (Assume that the diameter of the tower is so large compared to that of the faucet that the water at the top of the tower does not move.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 58

The volume flow rate of the water supplied by a well is $2.0 \times 10^{-4} \mathrm{m}^{3} / \mathrm{s} .$ The well is $40.0 \mathrm{m}$ deep.
(a) What is the power output of the pump -in other words, at what rate does the well do work on the water?
(b) Find the pressure difference the pump must maintain. (c) Can the pump be at the top of the well or must it be at the bottom? Explain.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 59

Using Poiseuille's law [Eq. (9-41)], show that viscosity has SI units of pascal-seconds.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 60

A hypodermic syringe is attached to a needle that has an internal radius of $0.300 \mathrm{mm}$ and a length of $3.00 \mathrm{cm} .$ The needle is filled with a solution of viscosity $2.00 \times 10^{-3} \mathrm{Pa} \cdot \mathrm{s} ;$ it is injected into a vein at a gauge pressure of $16.0 \mathrm{mmHg}$. Ignore the extra pressure required to accelerate the fluid from the syringe into the entrance of the needle. (a) What must the pressure of the fluid in the syringe be in order to inject the solution at a rate of $0.250 \mathrm{mL} / \mathrm{s} ?$ (b) What force must be applied to the plunger, which has an area of $1.00 \mathrm{cm}^{2} ?$

Matthew Baker

Numerade Educator

Problem 61

A hypodermic syringe is attached to a needle that has an internal radius of $0.300 \mathrm{mm}$ and a length of $3.00 \mathrm{cm} .$ The needle is filled with a solution of viscosity $2.00 \times 10^{-3} \mathrm{Pa} \cdot \mathrm{s} ;$ it is injected into a vein at a gauge pressure of $16.0 \mathrm{mmHg}$. Ignore the extra pressure required to accelerate the fluid from the syringe into the entrance of the needle. (a) What must the pressure of the fluid in the syringe be in order to inject the solution at a rate of $0.250 \mathrm{ml} / \mathrm{s} ?$ (b) What force must be applied to the plunger, which has an area of $1.00 \mathrm{cm}^{2} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 62

A bug from South America known as Rhodnius prolixus extracts the blood of animals. Suppose Rhodnius . prolixus extracts $0.30 \mathrm{cm}^{3}$ of blood in $25 \mathrm{min}$ from a human arm through its feeding tube of length $0.20 \mathrm{mm}$ and radius $5.0 \mu \mathrm{m}$. What is the absolute pressure at the bug"s end of the feeding tube if the absolute pressure at the other end (in the human arm) is $105 \mathrm{kPa}$ ? Assume the viscosity of blood is 0.0013 Pars. [Note: Negative absolute pressures are possible in liquids in very slender tubes.]

Satpal Satpal

Numerade Educator

Problem 63

If the total volume flow rates in systems A and C are the same and the average flow speed in each of the pipes i C is $3.0 \mathrm{m} / \mathrm{s},$ what is the average flow speed in system $\mathrm{A}$.

Satpal Satpal

Numerade Educator

Problem 64

If the total volume flow rate in system $\mathrm{B}$ is $0.020 \mathrm{m}^{3} / \mathrm{s}$, what is the total volume flow rate in system C?

Satpal Satpal

Numerade Educator

Problem 65

If the total volume flow rates in systems A and B are the same, at what pressure does the pump supply water in system A?

Satpal Satpal

Numerade Educator

Problem 66

A capillary carries blood in the direction shown. Viscosity is not negligible. Points $C$ and $D$ are on the central axis of the capillary. Rank the points in order of decreasing fluid speed.

Matthew Baker

Numerade Educator

Problem 67

(a) What is the pressure difference required to make blood flow through an artery of inner radius $2.0 \mathrm{mm}$ and length $0.20 \mathrm{m}$ at an average speed of $6.0 \mathrm{cm} / \mathrm{s} ?$ (b) What is the pressure difference required to make blood flow at an average speed of $0.60 \mathrm{mm} / \mathrm{s}$ through a capillary of radius $3.0 \mu \mathrm{m}$ and length $1.0 \mathrm{mm} ?$
(c) Compare both answers to your average blood pressure, about $100 \mathrm{mmHg}$.

Matthew Baker

Numerade Educator

Problem 68

(a) since the flow rate is proportional to the pressure difference, show that Poiseuille's law can be written in the form $\Delta P=I R,$ where $I$ is the volume flow rate and $R$ is a constant of proportionality called the fluid flow resistance. (Written this way, Poiseuille's law is analogous to Ohm 's \mathrm{law for electric current to be studied in } ~ Chapter $18: \Delta V=I R,$ where $\Delta V$ is the potential drop across a conductor, $I$ is the electric current flowing through the conductor, and $R$ is the electrical resistance of the conductor.) (b) Find $R$ in terms of the viscosity of the fluid and the length and radius of the pipe.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 69

Blood plasma (at $37^{\circ} \mathrm{C}$ ) is to be supplied to a patient at the rate of $2.8 \times 10^{-6} \mathrm{m}^{3} / \mathrm{s} .$ If the tube connecting the plasma to the patient's vein has a radius of $2.0 \mathrm{mm}$ and a length of $50 \mathrm{cm},$ what is the pressure difference between the plasma and the patient's vein?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 70

Five spheres are falling through the same viscous fluid, not necessarily at their terminal speeds. The radii $r$ and speeds $v$ of the spheres are given. Rank the spheres in order of decreasing viscous drag force on them.
(a) $r=1.0 \mathrm{mm}, v=15 \mathrm{mm} / \mathrm{s}$
(b) $r=1.0 \mathrm{mm}, v=30 \mathrm{mm} / \mathrm{s}$
(c) $r=2.0 \mathrm{mm}, v=15 \mathrm{mm} / \mathrm{s}$
(d) $r=2.0 \mathrm{mm}, v=30 \mathrm{mm} / \mathrm{s}$
(e) $r=3.0 \mathrm{mm}, v=20 \mathrm{mm} / \mathrm{s}$

Matthew Baker

Numerade Educator

Problem 71

Two identical spheres are dropped into two different columns: one column contains a liquid of viscosity $0.5 \mathrm{Pa} \cdot \mathrm{s} ;$ the other contains a liquid of the same density but unknown viscosity. The sedimentation velocity in the second tube is $20 \%$ higher than the sedimentation velocity in the first tube. What is the viscosity of the second liquid?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 72

A sphere of radius $1.0 \mathrm{cm}$ is dropped into a glass cylinder filled with a viscous liquid. The mass of the sphere is $12.0 \mathrm{g}$, and the density of the liquid is $1200 \mathrm{kg} / \mathrm{m}^{3}$. The sphere reaches a terminal speed of $0.15 \mathrm{m} / \mathrm{s}$. What is the viscosity of the liquid?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 73

An air bubble of $1.0 \mathrm{mm}$ radius is rising in a container of vegetable oil with specific gravity 0.85 and viscosity $0.12 \mathrm{Pa} \cdot \mathrm{s},$ The container of oil and the air bubble are at 20 $^{\circ} \mathrm{C} .$ What is its terminal velocity?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 74

What keeps a cloud from falling? A cumulus (fairweather ) cloud consists of tiny water droplets of average radius $5.0 \mu \mathrm{m}$. Find the terminal velocity for these droplets at $20^{\circ} \mathrm{C},$ assuming viscous drag. (Besides the viscous drag force, there are also upward air currents called thermals that push the droplets upward.)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 75

A flea is on the back of a squirrel climbing a tall tree. When the squirrel is near the top, the flea jumps off.
(a) Assuming the drag force is viscous, estimate the terminal speed of the flea. Treat the flea as a drop of water of radius $1.0 \mathrm{mm}$ falling through air at $20^{\circ} \mathrm{C}$.
(b) Does your result seem reasonable? If not, what do you think the problem is?

Matthew Baker

Numerade Educator

Problem 76

An aluminum sphere (specific gravity $=2.7$ ) falling through water reaches a terminal speed of $5.0 \mathrm{cm} / \mathrm{s}$ What is the terminal speed of an air bubble of the same radius rising through water? Assume viscous drag in both cases and ignore the possibility of changes in size or shape of the air bubble; the temperature is $20^{\circ} \mathrm{C}$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 77

An underwater air bubble has an excess inside pressure of $10 \mathrm{Pa}$. What is the excess pressure inside an air bubble with twice the radius?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 78

Assume a water strider has a roughly circular foot of radius $0.02 \mathrm{mm}$. (a) What is the maximum possible upward force on the foot due to surface tension of the water? (b) What is the maximum mass of this water strider so that it can keep from breaking through the water surface? The strider has six legs.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 79

A hollow hemispherical object is filled with air as in part (a) of the figure. (a) Show that the magnitude of the force due to fluid pressure on the curved surface of the hemisphere has magnitude $F=\pi r^{2} P,$ where $r$ is the radius of the hemisphere and $P$ is the pressure of the air. Ignore the weight of the air. [Hint: First find the force on the flat surface. What is the net force on the hemisphere due to the air?] (b) Consider an underwater air bubble to be divided into two hemispheres along the circumference as in part (b) of the figure. The upper hemisphere of the water surface exerts a force of magnitude $2 \pi r \gamma$ (circumference times force per unit length) on the lower hemisphere due to surface tension. Show that the air pressure inside the bubble must exceed the water pressure outside by $\Delta P=2 \gamma / r$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 80

A wooden barrel full of water has a flat circular top of radius $25.0 \mathrm{cm}$ with a small hole in it. A tube of height $8.00 \mathrm{m}$ and inner radius $0.250 \mathrm{cm}$ is suspended above the barrel with its lower end inserted snugly in the hole. Water is poured into the upper end of the tube until it is full. (a) What is the weight of the water in the tube? (b) What is the force with which the water in the barrel pushes up on the top of the barrel? (c) How can adding such a small weight of water lead to such a large force on the top of the barrel? (As a demonstration of the principle now named for him, Pascal astonished spectators by showing that the addition of a small amount of water to the tube could make the barrel burst.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 81

You are hiking through a lush forest with some of your friends when you come to a large river that seems impossible to cross. However, one of your friends notices an old metal barrel sitting on the shore. The barrel is shaped like a cylinder and is $1.20 \mathrm{m}$ high and $0.76 \mathrm{m}$ in diameter. One of the circular ends of the barrel is open and the barrel is empty. When you put the barrel in the water with the open end facing up, you find that the barrel floats with $33 \%$ of it under water. You decide that you can use the barrel as a boat to cross the river, as long as you leave about 30 cm sticking above the water. How much extra mass can you put in this barrel when you use it as a boat?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 82

On a nice day when the temperature outside is 20 $^{\circ}$ C, you take the elevator to the top of the Willis Tower in Chicago, which is $440 \mathrm{m}$ tall.
(a) How much less is the air pressure at the top than the air pressure at the bottom? Express your answer both in $\mathrm{Pa}$ and atm. [Hint: The altitude change is small enough to treat the density of air as constant.] (b) How many pascals does the pressure decrease for every meter of altitude? (c) If the pressure gradient - the pressure decrease per meter of altitude-were uniform, at what altitude would the atmospheric pressure reach zero?
(d) Atmospheric pressure does not decrease with a uniform gradient since the density of air decreases as you go up. Which is true: the pressure reaches zero at a lower altitude than your answer to (c), or the pressure is nonzero at that altitude and the atmosphere extends to a higher altitude? Explain.

David González Cornejo

David González Cornejo

Numerade Educator

Problem 83

A house with its own well has a pump in the basement with an output pipe of inner radius $6.3 \mathrm{mm} .$ The pump can maintain a gauge pressure of $410 \mathrm{kPa}$ in the output pipe. A showerhead on the second floor (6.7 $\mathrm{m}$ above the pump's output pipe) has 36 holes, each of radius $0.33 \mathrm{mm} .$ The shower is on "full blast" and no other faucet in the house is open. (a) Ignoring viscosity, with what speed does water leave the shower head? (b) With what speed does water move through the output pipe of the pump?

David González Cornejo

David González Cornejo

Numerade Educator

Problem 84

The average speed of blood in the aorta is $0.3 \mathrm{m} / \mathrm{s}$ and the radius of the aorta is $1 \mathrm{cm}$. There are about $2 \times \mathrm{k}$ $10^{9}$ capillaries with an average radius of $6 \mu \mathrm{m}$. What is the approximate average speed of the blood flow in the capillaries?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 85

The diameter of a certain artery has decreased by 25 $\%$ due to arteriosclerosis. (a) If the same amount of blood flows through it per unit time as when it was unobstructed, by what percentage has the blood pressure difference between its ends increased? (b) If, instead, the pressure drop across the artery stays the same, by what factor does the blood flow rate through it decrease? (In reality we are likely to see a combination of some pressure increase with some reduction in flow.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 86

The average adult has about $5 \mathrm{L}$ of blood, and a healthy adult heart pumps blood at a rate of about $80 \mathrm{cm}^{3} / \mathrm{s} .$ Estimate how long it takes for medicine delivered intravenously to travel throughout a person's body.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 87

A block of aluminum that has dimensions $2.00 \mathrm{cm}$ by $3.00 \mathrm{cm}$ by $5.00 \mathrm{cm}$ is suspended by a thread from a spring scale. (a) What is the scale reading in grams?
(b) A beaker full of oil (density $850 \mathrm{kg} / \mathrm{m}^{3}$ ) rests on a second scale, which reads $460.0 \mathrm{g}$. The block is then lowered so it is fully submerged in oil without touching the bottom of the beaker. What are the readings of the two scales now?

Satpal Satpal

Numerade Educator

Problem 88

A $85.0 \mathrm{kg}$ canoe made of thin aluminum has the shape of half of a hollowed-out log with a radius of $0.475 \mathrm{m}$ and a length of $3.23 \mathrm{m}$. (a) When this is placed in the water, what percentage of the volume of the canoe is below the waterline?
(b) How much additional mass can be placed in this canoe before it begins to sink?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 89

Two identical beakers are filled to the brim and placed on balance scales. The base area of the beakers is large enough that any water that spills out of the beakers will fall onto the table the scales are resting on. A block of pine (density $=420 \mathrm{kg} / \mathrm{m}^{3}$ ) is placed in one of the beakers. The block has a volume of $8.00 \mathrm{cm}^{3}$. Another block of the same size, but made of steel, is placed in the other beaker. How does the scale reading change in each case?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 90

A very large vat of water has a hole $1.00 \mathrm{cm}$ in diameter located a distance $1.80 \mathrm{m}$ below the water level. (a) How fast does water exit the hole? (b) How would your answer differ if the vat were filled with gasoline? (c) How would your answer differ if the vat contained water, but was on the Moon, where the gravitational field strength is 1.6 N/kg?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 91

An atomizer is a device that delivers a fine mist of some liquid such as perfume by blowing air horizontally over the top of a tube immersed in the liquid. Suppose a perfume with density $800 \mathrm{kg} / \mathrm{m}^{3}$ has a $3.0 \mathrm{cm}$ tube extending vertically from the top of the liquid. What minimum speed does air flow over the top of the tube when the liquid just reaches the top of the tube?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 92

The deepest place in the ocean is the Marianas Trench in the western Pacific Ocean, which is over $11.0 \mathrm{km}$ deep. On January $23,1960,$ the research sub Trieste went to a depth of $10.915 \mathrm{km},$ nearly to the bottom of the trench. This still is the deepest dive on record. The density of seawater is $1025 \mathrm{kg} / \mathrm{m}^{3}$.
(a) What is the water pressure at that depth? (b) What was the force due to water pressure on a flat section of area $1.0 \mathrm{m}^{2}$ on the top of the sub's hull?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 93

The pressure in a water pipe in the basement of an apartment house is $4.10 \times 10^{5} \mathrm{Pa}$, but on the seventh floor it is only $1.85 \times 10^{5} \mathrm{Pa}$. What is the height between the basement and the seventh floor? Assume the water is not flowing; no faucets are opened.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 94

The body of a $90.0 \mathrm{kg}$ person contains $0.020 \mathrm{m}^{3}$ of body fat. If the density of fat is $890 \mathrm{kg} / \mathrm{m}^{3},$ what percentage of the person's body weight is composed of fat?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 95

Near sea level, how high a hill must you ascend for the reading of a barometer you are carrying to drop by $10 \mathrm{mmHg} ?$ Assume the temperature remains at $20^{\circ} \mathrm{C}$ as you climb. The reading of a barometer on an average day at sea level is $760 \mathrm{mmHg}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 96

If you watch water falling from a faucet, you will notice that the flow decreases in radius as the water falls.
This can be explained by the equation of continuity, since the cross-sectional area of the water decreases as the speed increases. If the water flows with an initial velocity of $0.62 \mathrm{m} / \mathrm{s}$ and a diameter of $2.2 \mathrm{cm}$ at the faucet opening, what is the diameter of the water flow after the water has fallen $30 \mathrm{cm} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 97

If the cardiac output of a small dog is $4.1 \times$ $10^{-5} \mathrm{m}^{3} / \mathrm{s},$ the radius of its aorta is $0.50 \mathrm{cm},$ and the aorta length is $40.0 \mathrm{cm},$ determine the pressure drop across the aorta of the dog. Assume the viscosity of blood is $4.0 \times 10^{-3} \mathrm{Pa}$ -s.

Satpal Satpal

Numerade Educator

Problem 98

In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius $1.0 \mathrm{cm}$ ) enters an aneurysm with a radius of $3.0 \mathrm{cm},$ how much on average is the blood pressure higher inside the aneurysm than the pressure in the unenlarged part of the aorta? The average flow rate through the aorta is $120 \mathrm{cm}^{3} / \mathrm{s} .$ Assume the blood is nonviscous and the patient is lying down so there is no change in height.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 99

Scuba divers are admonished not to rise faster than their air bubbles when rising to the surface. This rule helps them avoid the rapid pressure changes that cause the "bends." Air bubbles of $1.0 \mathrm{mm}$ radius are rising from a scuba diver to the surface of the sea. Assume a water temperature of $20^{\circ} \mathrm{C} .$ (a) If the viscosity of the water is $1.0 \times 10^{-3} \mathrm{Pa} \cdot \mathrm{s},$ what is the terminal velocity of the bubbles?
(b) What is the largest rate of pressure change tolerable for the diver according to this rule?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 100

A shallow well usually has the pump at the top of the well. (a) What is the deepest possible well for which a surface pump will work? [Hint: A pump maintains a pressure difference, keeping the outflow pressure higher than the intake pressure.] (b) Why is there not the same depth restriction on wells with the pump at the bottom?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 101

A stone of weight $W$ has specific gravity 2.50 .
(a) When the stone is suspended from a scale and submerged in water, what is the scale reading in terms of its weight in air? (b) What is the scale reading for the stone when it is submerged in oil (specific gravity $=0.90$ )?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 102

A plastic beach ball has radius $20.0 \mathrm{cm}$ and mass $0.10 \mathrm{kg},$ not including the air inside.
(a) What is the weight of the beach ball including the air inside? Assume the air density is $1.3 \mathrm{kg} / \mathrm{m}^{3}$ both inside and outside. (b) What is the buoyant force on the beach ball in air? The thickness of the plastic is about $2 \mathrm{mm}-$ negligible compared with the radius of the ball. (c) The ball is thrown straight up in the air. At the top of its trajectory, what is its acceleration? [Hint: When $v=0$, there is no drag force.]

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 103

A block of wood, with density $780 \mathrm{kg} / \mathrm{m}^{3},$ has a cubic shape with sides $0.330 \mathrm{m}$ long. A cord of negligible mass is used to tie a piece of lead to the bottom of the wood. The lead pulls the wood into the water until it is just completely covered with water. What is the mass of the lead? [Hint: Don't forget to consider the buoyant force on both the wood and the lead. $.]$

Satpal Satpal

Numerade Educator

Problem 104

Suppose the hydrometer has a cylindrical stem of crosssectional area $0.400 \mathrm{cm}^{2} .$ The total volume of the bulb and stem is $8.80 \mathrm{cm}^{3}$, and the mass of the hydrometer is $4.80 \mathrm{g} .$ (a) How far from the top of the cylinder should a mark be placed to indicate a specific gravity of $1.00 ?$
(b) When the hydrometer is placed in alcohol, it floats with $7.25 \mathrm{cm}$ of stem above the surface. What is the specific gravity of the alcohol?
(c) What is the lowest specific gravity that can be measured with this hydrometer?

Mayukh Banik

Numerade Educator

Problem 105

Are evenly spaced specific-gravity markings on the cylinder of a hydrometer equal distances apart? In other words, is the depth $d$ to which the cylinder is submerged linearly related to the density $\rho$ of the fluid? To answer this question, assume that the cylinder has radius $r$ and mass $m$. Find an expression for $d$ in terms of $\rho, r,$ and $m,$ and see if $d$ is a linear function of $\rho$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 106

To measure the airspeed of a plane, a device called a Pitot tube is used. A simplified model of the Pitot tube is a manometer with one side connected to a tube facing directly into the "wind" (stopping the air that hits it head-on) and the other side connected to a tube so that the "wind" blows across its openings. If the manometer uses mercury and the levels differ by $25 \mathrm{cm},$ what is the plane's airspeed? The density of air at the plane"s altitude is $0.90 \mathrm{kg} / \mathrm{m}^{3}$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 107

A U-shaped tube is partly filled with water and partly filled with a liquid that does not mix with water. Both sides of the tube are open to the atmosphere. What is the density of the liquid (in $g / \mathrm{cm}^{3}$ )?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 108

Atmospheric pressure is equal to the weight of a vertical column of air, extending all the way up through the atmosphere, divided by the cross-sectional area of the column. (a) Explain why that must be true. [Hint:
Apply Newton's second law to the column of air.]
(b) If the air all the way up had a uniform density of $1.29 \mathrm{kg} / \mathrm{m}^{3}$ (the density at sea level at $0^{\circ} \mathrm{C}$ ), how high would the column of air be? (c) In reality, the density of air decreases with increasing altitude. Does that mean that the height found in (b) is a lower limit or an upper limit on the height of the atmosphere?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 109

Water enters an apartment building $0.90 \mathrm{m}$ below the street level with a gauge pressure of $52.0 \mathrm{kPa}$ through the main pipe, which has a $5.00 \mathrm{cm}$ radius. A second-story bathroom has an open faucet with a $1.20 \mathrm{cm}$ radius that is located $4.20 \mathrm{m}$ above the street. How fast is the water moving through the main pipe?

Matthew Baker

Numerade Educator

Problem 110

The pressure inside a bottle of champagne is 4.5 atm higher than the air pressure outside. The neck of the bottle has an inner radius of $1.0 \mathrm{cm}$. (a) What is the frictional force on the cork due to the neck of the bottle?
(b) The cork (mass 7.5 g) is loosened until the friction force is zero and then released, allowing the cork to shoot out of the bottle. If the cork moves $1.0 \mathrm{cm}$ along the neck of the bottle as the gauge pressure in the bottle decreases from 4.5 atm to zero, estimate the speed at which the cork shoots out of the bottle. [Hint: Estimate the average force on the cork to be half of the maximum.

Aishwarya Krishnakumar

Aishwarya Krishnakumar

Numerade Educator

Problem 111

A hydraulic lift is lifting a car that weighs $12 \mathrm{kN}$. The area of the piston supporting the car is $A$, the area of the other piston is $a$, and the ratio $A / a$ is $100.0 .$ How far must the small piston be pushed down to raise the car a distance of $1.0 \mathrm{cm} ?[$Hint: Consider the work to be done.]

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 112

Depressing the brake pedal in a car pushes on a piston with cross-sectional area $3.0 \mathrm{cm}^{2} .$ The piston applies pressure to the brake fluid, which is connected to two pistons, each with area $12.0 \mathrm{cm}^{2} .$ Each of these pistons presses a brake pad against one side of a rotor attached to one of the rotating wheels. See the figure for this problem. (a) When the force applied by the brake pedal to the small piston is $7.5 \mathrm{N},$ what is the normal force applied to each side of the rotor? (b) If the coefficient of kinetic friction between a brake pad and the rotor is 0.80 and each pad is (on average) $12 \mathrm{cm}$ from the rotation axis of the rotor, what is the magnitude of the torque on the rotor due to the two pads?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 113

A dinoflagellate takes $5.0 \mathrm{s}$ to travel $1.0 \mathrm{mm}$. Approximate a dinoflagellate as a sphere of radius $35.0 \mu \mathrm{m}$ (ignoring the flagellum).
(a) What is the drag force on the dinoflagellate in seawater of viscosity $0.0010 \mathrm{Pa} \cdot \mathrm{s} ?(\mathrm{b}) \mathrm{What}$ is the power output of the flagellate?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 114

The potential energy associated with surface tension is much like the elastic potential energy of a stretched spring or a balloon. Suppose we do work on a puddle of liquid, spreading it out through a distance of $\Delta s$ along a line $L$ perpendicular to the force. (a) What is the work done on the fluid surface in terms of $\gamma, L,$ and $\Delta \mathrm{s} ?$ (b) The work done is equal to the increase in surface energy of the fluid. Show that the increase in energy is proportional to the increase in area. (c) Show that we can think of $\gamma$ as the surface energy per unit area. (d) Show that the SI units of surface tension can be expressed either as $\mathrm{N} / \mathrm{m}($ force per unit length $)$ or $\mathrm{J} / \mathrm{m}^{2}$ (energy per unit area).

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 115

A cube that is $4.00 \mathrm{cm}$ on a side and of density $8.00 \times$ $10^{2} \mathrm{kg} / \mathrm{m}^{3}$ is attached to one end of a spring. The other end of the spring is attached to the base of a beaker. When the beaker is filled with water until the entire cube is submerged, the spring is stretched by $1.00 \mathrm{cm}$. What is the spring constant?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 116

A beach ball is thrown straight up in the air. The graph shows its vertical velocity component as a function of time. The dashed line is tangent to the curve at the point where $v_{y}=0 .$ (a) What shape would the $v_{y}(t)$ graph have if air drag on the beach ball were always negligibly small?
(b) Describe feature(s) of the $v_{y}(t)$ graph that tell you that the force of air drag on the ball is not negligible. (c) Describe feature(s) of the graph that indicate that the buoyant force on the ball is significant. [Hint: Look at a part of the graph where air drag $i s$ negligible.] (d) Estimate the buoyant force on the ball as a fraction of its weight. (e) If the ball is thrown from a height of $1.0 \mathrm{m}$ above the ground, approximately when does it hit the ground?

Dominador Tan

Numerade Educator

Problem 117

A section of pipe with an internal diameter of $10.0 \mathrm{cm}$ tapers to an inner diameter of $6.00 \mathrm{cm}$ as it rises through a height of $1.70 \mathrm{m}$ at an angle of $60.0^{\circ}$ with respect to the horizontal. The pipe carries water and its higher end is open to air. (a) If the speed of the water at the lower point is $15.0 \mathrm{cm} / \mathrm{s},$ what are the pressure at the lower end and the speed of the water as it exits the pipe? (b) If the higher end of the pipe is $0.300 \mathrm{m}$ above ground, at what horizontal distance from the pipe outlet does the water land?

Ajay Singhal

Numerade Educator