Physics Exam 3
. The human circulation system has approximately 1 × 109 capillary vessels. Each vessel has a diameter of about 8 µm. Assuming cardiac output is 5 L/min, determine the average velocity of blood flow through each capillary vessel.
V = Q / A 8.33/(10^9 * pi *4.0*10-4)^2 = 0.166 cm/s
What is the pressure drop due to the Bernoulli effect as water goes into a 3.00-cmdiameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s?
v values = Q/A ( A = pi*radius ^2) P1-P2 = 1/2 p (v2^2-v1^2) = 1.58x10^6 N/m2
About how high would a column of water need to be to create a 60 psi (400 kPa) pressure? (Use g ≈ 10 m/s2 ) A) 4 m B) 40 m C) 60 m D) 400 m
B) 40 m
What is the average flow rate in cm3/s of gasoline to the engine of a car traveling at 100 km/h if it averages 10.0 km/L?
Q = V/t = speed / gas mileage --> cm/s = 2.78 cm^3/s
A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density?
A) 540 g - 342 g = 198 g B) Vt + Vw = mw/pw =198 C) p r = mr / Vr = 540/198 = 2.73 g/cm
A certain man has a mass of 80 kg and a density of 955 kg/m3 (excluding the air in his lungs). (a) Calculate his volume. (b) Find the buoyant force air exerts on him. (c) What is the ratio of the buoyant force to his weight?
A) V = m/p =0.0804 B) Fb = w fl = Vfl*pfl*g = 1.02 N C) Fb/w = 1.30 x 10^-3
Problem 1. Ball A in the image has half the radius of ball B, but weighs the same. If the density of B is ρB = 1.00 g/cm3 , what is the density of ball A? A) 1 g/cc B) 2 g/cc C) 4 g/cc D) 8 g/cc
D) 8 g/cc
Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of 220 m2? Typical air density in Boulder is 1.14 kg/m3 , and the corresponding atmospheric pressure is 8.89 × 104 .
F = ( P1 -P2)A = 1/2 p ( v2^2-v1^)A so that F = 2.51 x 10^5 N
What pressure is exerted on the bottom of a 0.500-m-wide by 0.900-m-long gas tank that can hold 50.0 kg of gasoline by the weight of the gasoline in it when it is full?
F= PA --> P = F/A ... 1.09x10^3 N/m^2
If your body has a density of 995 kg/m3 , what fraction of you will be submerged when floating gently in: (a) Freshwater? (b) Salt water, which has a density of 1027 kg/m3?
FS = p obj / p fl 0.995 = 91.7% FS = p obj / p fl (p of water changed) = 96.6 %
What fraction of ice is submerged when it floats in freshwater, given the density of water at 0°C is very close to 1000 kg/m3?
FS = p object / p fluid = 0.917 = 91.7%
The arterioles (small arteries) leading to an organ, constrict in order to decrease flow to the organ. To shut down an organ, blood flow is reduced naturally to 1.00% of its original value. By what factor did the radii of the arterioles constrict? Penguins do this when they stand on ice to reduce the blood flow to their feet.
If the rate is reduced to 1.00 % of its origional value, then Q2 = delta P * pi * radius 2 ^4 / 8 * n * l2 = 0.0100Q1 = 0.0100 * delta P * pi * radius 2 ^4 / 8 * n * l2 since the length of the arterioles is kept cinstant and the pressure difference is kept constant, we can get a relationship between the radii: r2^4 = 0.0100r1^4 = ( 0.0100)^(1/4)r1 = 0.316r1
How many pounds of air are sitting on your head?
P = F/A F=PA = 1.01 x 10^5 Pa x (0.1 m)^@ = 3170 N x 0.225 lb = 714 lbs
7. (a) As blood passes through the capillary bed in an organ, the capillaries join to form venules (small veins). If the blood speed increases by a factor of 4.00 and the total crosssectional area of the venules is 10.0 cm2 , what is the total cross-sectional area of the capillaries feeding these venules? (b) How many capillaries are involved if their average diameter is 10.0 µm ?
a) Q = A1*V1 = A2*V2... A1 = V2 / V1 *A2 = 40 cm b) A1 = NA N = A1/ A = 40/ pi*5*10-4 = 5.09*10^7
Water emerges straight down from a faucet with a 1.80-cm diameter at a speed of 0.500 m/s. (Because of the construction of the faucet, there is no variation in speed across the stream.) (a) What is the flow rate in cm3/s? (b) What is the diameter of the stream 0.200 m below the faucet? Neglect any effects due to surface tension.
a) Q = AV = pi * r^2 * v = 127 cm/s b) v^2 = v knot squared + 2gx ---> v = [ v knot squared + 2gx] ^ 1/2 = 2.042 m/s --> Q = pi* r^2 *v r = (Q/pi*v)^(1/2)= 4.45 x 10^-3 m or d = 2r = 0.890 cm
Water is moving at a velocity of 2.00 m/s through a hose with an internal diameter of 1.60 cm. (a) What is the flow rate in liters per second? (b) The fluid velocity in this hose's nozzle is 15.0 m/s. What is the nozzle's inside diameter?
a) Q = Av = pi * r^2 * v = 0.402 L/s b) Q = A1 V1 = A2V2 d1( v1/v2) ^(1/2) = 0.584 cm
Hoover Dam on the Colorado River is the highest dam in the United States at 221 m, with an output of 1300 MW. The dam generates electricity with water taken from a depth of 150 m and an average flow rate of 650 m3/s. (a) Calculate the power in this flow. (b) What is the ratio of this power to the facility's average of 680 MW?
a) power = pgh * Q = 9.56 x 10 ^ 8 Watts b) 956 MW / 450 MW = 2.12
A trash compactor can reduce the volume of its contents to 0.350 their original value. Neglecting the mass of air expelled, by what factor is the density of the rubbish increased?
p = m/v; p' = m/v = m/0.350 V p'/p = (m/0.350V)/(m/v) = 1/0.350 = 2.86 x denser
. The left ventricle of a resting adult's heart pumps blood at a flow rate of 83.0 cm3/s , increasing its pressure by 110 mm Hg, its speed from zero to 30.0 cm/s, and its height by 5.00 cm. (All numbers are averaged over the entire heartbeat.) Calculate the total power output of the left ventricle. Note that most of the power is used to increase blood pressure.
power = P +1/2 (pv^2 +pgh)*Q =1.463x10^4 N/m ^2 = 1.26 W
Angioplasty is a technique in which arteries partially blocked with plaque are dilated to increase blood flow. By what factor must the radius of an artery be increased in order to increase blood flow by a factor of 10?
r^4 * delta P2 = r^4 * delta P = 0.900
The heart of a resting adult pumps blood at a rate of 5.00 L/min. (a) Convert this to cm3/s. (b) What is this rate in m3/s?
A) conversion from L/min -> cm^3/L -> mi/sec = 1.39 cm^3/s B) cm/s --> m/cm = 1.39 x 10-6 m^3/s
In an immersion measurement of a woman's density, she is found to have a mass of 62.0 kg in air and an apparent mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density with lungs empty, and answer: Is she able to float without treading water with her lungs filled with air?
A) larger - smaller = 61.915 kg = 61.9 kg B) V = mw / pw = 0.0619 m C) p = m/V =1001.4 kg/m^3 This comes out exactly equal to the density of water. When her lungs are full of air, this density will decrease. Thus, she will float without treading water when her lungs are full of air.
9. (a) Estimate the time it would take to fill a private swimming pool with a capacity of 80,000 L using a garden hose delivering 60 L/min. (b) How long would it take to fill if you could divert a moderate size river, flowing at 5000 m3/s, into it?
a) t= V/Q = 80000 L / 60 L /min = 1300 min = 22 h b) t = V/Q = 80000 L / 5000000 L/s = 0.016 s
Suppose you measure a standing person's blood pressure by placing the cuff on his leg 0.500 m below the heart. Calculate the pressure you would observe (in units of mm Hg) if the pressure at the heart were 120 over 80 mm Hg. Assume that there is no loss of pressure due to resistance in the circulatory system (a reasonable assumption, since major arteries are large)
delta P = hpg then convert N/m to mm Hg =38.7 mm Hg Leg blood pressure:120/80 add 38.7 to both and find the ratio.
What is the ratio of heights to which ethyl alcohol and water are raised by capillary action in the same glass tub
h = 2 y cos theta / pgr ( this equation over itself one for e one for m ) 0.39
If water exits the nozzle of a fire hose at v0 = 56.6 m/s, to what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)
h = v knot squared / 2g = 163 m
Suppose water is raised by capillary action to a height of 5.00 cm in a glass tube. (a) To what height will it be raised in a paraffin tube of the same radius? (b) In a silver tube of the same radius?
hg = 2y w cos theta / pw gr hp = 2yw cos theta p/ pw gr hg / hp = cos g / cos p = 5 * cos 107/ cos 0 =-1.46 cm B) hs = hg (cos s / cos g) 5 cm * ( cos 90 / cos 0) = 0 cm
A 2.50-kg steel gasoline can holds 20.0 L of gasoline when full. What is the average density of the full gas can, taking into account the volume occupied by steel as well as by gasoline?
m = 2.50 kg + (20.0L) (10-3m/L) = 16.1 kg V = (20 L)(10-3)+ (2.50kg / 7.8*10^3) = 0.0203 m ^3 p= m/V = 16.1 kg /0.0203 = 793 kg/m^3 = 7.9*10^2 kg/m^3
Bird bones have air pockets in them to reduce their weight—this also gives them an average density significantly less than that of the bones of other animals. Suppose an ornithologist weighs a bird bone in air and in water and finds its mass is and its apparent mass when submerged is (the bone is watertight). (a) What mass of water is displaced? (b) What is the volume of the bone? (c) What is its average density?
m displaced = 45 g - 3.60 g = 41.4 b) vb = vw = mw/pw = 41.4 c) p(knot) = mb /Vb = 45/41.1 = 1.09 g/cm
A rectangular gasoline tank can hold 50.0 kg of gasoline. What is the depth of the tank if it is 0.500-m wide by 0.900-m long?
p= m/V --> m=pV = p(lwh)*h =m/plw.... 50kg / (0.680*10^3)(0.900)(0.500) = 0.163 m
A straightforward method of finding the density of an object is to measure its mass and then measure its volume by submerging it in a graduated cylinder. What is the density of a 240-g rock that displaces 89.0 cm3 of water?
p= m/V = 240 g/89 cm = 2.70g/cm
Gold is sold by the troy ounce (31.103 g). What is the volume of 1 troy ounce of pure gold?
p=m/V --> V=m/p = 31.013/19.32 = 1.610cm
(a) Calculate the pressure due to the ocean at the bottom of the Marianas Trench near the Philippines, given its depth is 11.0 km and assuming the density of sea water is constant all the way down. (b) Calculate the percent decrease in volume of sea water due to such a pressure, assuming its bulk modulus is the same as water: B = 2.2×109 N/m2
A) P = hpg = 1.09 x 10^3 atm B) delta V / V0 = 1/B*F/A =P/B = 5.02 x 10 -2 = 5 % decrease in volume.
. Calculate the maximum force in newtons exerted by the blood on an aneurysm, or ballooning, in a major artery, given the maximum blood pressure for this person is 150 mm Hg and the effective area of the aneurysm is 20.0 cm2 . Note that this force is great enough to cause further enlargement and subsequently greater force on the ever-thinner vessel wall.
F = PA = 39.9 N
Gauge pressure in the fluid surrounding an infant's brain may rise as high as 85.0 mm Hg (5 to 12 mm Hg is normal), creating an outward force large enough to make the skull grow abnormally large. Calculate this outward force in newtons on each side of an infant's skull if the effective area of each side is 70.0 cm2 .
F = PA = 79.1 N
Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of 3.00 × 109 N/m2? (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)
F = PA P(pi* R^2) = (3.00x10^9)*pi*(0.500*10^-3)^2 = 2.36 x 19^3 N
Assuming bicycle tires are perfectly flexible and support the weight of bicycle and rider by pressure alone, calculate the total area of the tires in contact with the ground. The bicycle plus rider has a mass of 80.0 kg, and the gauge pressure in the tires is 3.50 × 105 Pa (i.e., 3.5 extra atmospheres of pressure).
F = mg = PgA = A = mg/Pg = 2.24 x 10^-3 = 22.4 cm^2
During forced exhalation, such as when blowing up a balloon, the diaphragm and chest muscles create a pressure of 60.0 mm Hg between the lungs and chest wall. What force in newtons does this pressure create on the 600 cm2 surface area of the diaphragm?
F =PA = 479 N
What force must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on the slave cylinder? The master cylinder has a 2.00-cm diameter and the slave has a 24.0-cm diameter.
F1= F2 over A1=A2 --> F2 = (A2/A1)*F1 = (pi*r2^2 / pi*r1^2)*mg = r2^2/r1^2 * mg ---> = 136 N
Pressure cookers have been around for more than 300 years, although their use has strongly declined in recent years (early models had a nasty habit of exploding). How much force must the latches holding the lid onto a pressure cooker be able to withstand if the circular lid is 0.25 m in diameter and the gauge pressure inside is 300 atm? Neglect the weight of the lid.
F= PA ( atm * (N/m/atm)*pi*m) = 1.49 x 10^4 N Atmospheric pressure outside the cooker can be ignored, since we are given the gauge pressure inside, and the gauge pressure indicates pressure above atmospheric. So, 3 atm measures the pressure difference between the inside and outside of the lid.
. What fluid is in the device shown in the previous problem if the force is 3.16×10-3 N and the length of the wire is `= 2.50 cm? Calculate the surface tension gand find a likely match from Table 11.3
F= yL = 2yl -> y = F/ 2l = 6.32 *10 -2 N/m Glycerin
Calculate the force on the slide wire in the figure below if it is `= 3.50 cm in length and the fluid is ethyl alcohol
F= yL = 2yl = 2(0.0223N/m)(0.0350m) = 1.56×10-3 N
How much force is exerted on one side of an 8.50 cm by 11.0 cm sheet of paper by the atmosphere? How can the paper withstand such a force?
F=PA =(1.1013*10^5 N/m^2)(8.50in)(11)(6.452*10-4)b= 6.11 x 10^3 The paper can withstand this force because an equal force is exerted on the other side of the paper in the opposite direction.
a) What is the density of a woman who floats in freshwater with 4.00% of her volume above the surface? This could be measured by placing her in a tank with marks on the side to measure how much water she displaces when floating and when held under water (briefly). (b) What percent of her volume is above the surface when she floats in seawater?
FS= p obj / p fl p person = p fresh water * FS =960 kg/m3 b) FS = p person / p sea water 0.9366 1.00-0.9366= 6.34 %
What fraction of an iron anchor's weight will be supported by buoyant force when submerged in salt water?
Fb = w fl = V anchor p fl g ..... Fb / w = mg (pfl / p Fe) / mg = p fl/pFe = 0.13 or 13%
How tall must a water-filled manometer be to measure blood pressures as high as 300 mm Hg?
Hw = PmHm/Pw =4080 mm
Prove that the speed of an incompressible fluid through a constriction, such as in a Venturi tube, increases by a factor equal to the square of the factor by which the diameter decreases. (The converse applies for flow out of a constriction into a larger- diameter region.)
If the fluid is compressable the flow rate through both sides will be equal.
Suppose you have a wind speed gauge like the pitot tube shown in the figure below. By what factor must wind speed increase to double the value of h in the manometer? Is this independent of the moving fluid and the fluid in the manometer?
Let v1 be the initial wind speed and v2 be the final wind speed. v2/v1 = square root of 2 Yes, the wind speed factor is independent of the moving fluid and the fluid in the manometer.
What is the pressure inside an alveolus having a radius of 2.50×10-4 m if the surface tension of the fluid-lined wall is the same as for soapy water? You may assume the pressure is the same as that created by a spherical bubble.
P = 4Y / r = 4*0.0370 /2.50*10^-4 = 592
Calculate the gauge pressures inside 2.00-cm-radius bubbles of water, alcohol, and soapy water. Which liquid forms the most stable bubbles, neglecting any effects of evaporation?
P = 4y / r pw = 14.6 pa = 4.46 psw = 7.40 N/m Alcohol forms the most stable bubble, since the absolute pressure inside is closest to atmospheric pressure
You can chew through very tough objects with your incisors because they exert a large force on the small area of a pointed tooth. What pressure in pascals can you create by exerting a force of 500 N with your tooth on an area of 1.00 mm2?
P = P/A = 5.00*10^8 Pa
What depth of mercury creates a pressure of 1.00 atm?
P = hpg h = P/ pg = 0.760 m
Water towers store water above the level of consumers for times of heavy use, eliminating the need for high-speed pumps. How high above a user must the water level be to create a gauge pressure of 3.00 × 105 N/m2 (three extra atmospheres of pressure)?
P =hpg --> h = P/ pg = 30.6 m
A small artery has a length of 1.1×10-3 m and a radius of 2.5×10-5 m. If the pressure drop across the artery is 1.3 kPa, what is the flow rate through the artery? (Assume that the temperature is 37°C .)
Q = (p2 -P) 1 * pi * r ^4 / 8nl = 8.70*10-2 mm/s
Blood flows through a coronary artery that is partially blocked by deposits along the artery wall. Through which part of the artery is the flow rate largest? A) Narrow part B) Wide part C) Same in both D) Need to know the pressures
Q = Av v =Q/A= 5000 cm3/60 s (over ) (p(1.0 cm)^2) = 27 cm/s
The main uptake air duct of a forced air gas heater is 0.300 m in diameter. What is the average speed of air in the duct if it carries a volume equal to that of the house's interior every 15 min? The inside volume of the house is equivalent to a rectangular solid 13.0 m wide by 20.0 m long by 2.75 m high.
Q = Av --> v = Q/A = (V/t) / pi* r^2 = 11.2 m/s
A sump pump (used to drain water from the basement of houses built below the water table) is draining a flooded basement at the rate of 0.750 L/s, with an output pressure of 3.00 × 105n/m2 . (a) The water enters a hose with a 3.00 cm inside diameter and rises 2.50 m above the pump. What is its pressure at this point? (b) The hose goes over the foundation wall, losing 0.500 m in height, and widens to 4.00 cm in diameter. What is the pressure now? You may neglect frictional losses in both parts of the problem.
a) P1 +1/2 (pv^2 +pgh)= P2 +1/2 (pv^2 +pgh) P2 = P1+pg(h1-h2) = 2.76x 10^5 N/m^2 b) v1 = Q/A1 = 1.06 ms and V2 same thing = 0.597 = P2 = 2.81 x 10^5 N/m
A frequently quoted rule of thumb in aircraft design is that wings should produce about 1000 N of lift per square meter of wing. (The fact that a wing has a top and bottom surface does not double its area.) (a) At takeoff, an aircraft travels at 60.0 m/s, so that the air speed relative to the bottom of the wing is 60.0 m/s. Given the sea level density of air to be 1.29 kg/m3 , how fast must it move over the upper surface to create the ideal lift? (b) How fast must air move over the upper surface at a cruising speed of 245 m/s and at an altitude where air density is one-fourth that at sea level? (Note that this is not all of the aircraft's lift—some comes from the body of the plane, some from engine thrust, and so on. Furthermore, Bernoulli's principle gives an approximate answer because flow over the wing creates turbulence.)
a) P1-P2 = delts P = 1/2 pv2^2 - 1/2 pv1^2 v^2 = ( 2*delta P/p +v1^2)^(1/2) = 71.8 m/s b) v2 = 257m /s
. (a) What is the fluid speed in a fire hose with a 9.00-cm diameter carrying 80.0 L of water per second? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if salt water replaced the fresh water in the fire hose?
a) Q = Av = pi* r^2 * v --> v = Q/ pi*r^2=12.6 b) Q = 80.0 * 1/1000 L = 0.0800 m/s (c) No, the flow rate and the velocity are independent of the density of the fluid.
Calculate the contact angle for olive oil if capillary action raises it to a height of 7.07 cm in a glass tube with a radius of 0.100 mm. Is this value consistent with that for most organic liquids?
h = 2 y cos theta / pgr theta = inverse cos (hpgr/2y) 5.14 degreees
A submarine is stranded on the bottom of the ocean with its hatch 25.0 m below the surface. Calculate the force needed to open the hatch from the inside, given it is circular and 0.450 m in diameter. Air pressure inside the submarine is 1.00 atm.
water pressure = Pw = hpg = 2.51 x 10^5 N/m^2 Since atmospheric pressure is roughly the same inside and outside: F=PA (pi R^2) = 3.99 x 10^4 N
A ping-pong ball is held submerged in a bucket of water by a string attached to the bucket's bottom. (a) Alcohol is now added to the water in the bucket, decreasing the density of the liquid. What happens to the tension in the string, and why? (Give a reason.) (b) Return to the ball in pure water. What happens to the tension in the string if the Ping-Pong ball is replaced by a wooden ball (heavier) of equal size? (Give a reason.)
(a) The magnitude of upwards buoyant force (FB) on the ball equals to the weight of displaced fluid, and balances the string tension plus the ball's weight: FB = FT + w. Since FB decreases when the alcohol is added, the string tension must also decrease. (b) The magnitude of upwards buoyant force FB is equal to the string tension plus the ball's weight, FB = FT + w. If the ball's weight w increases, the string tension FT must decrease.
Verify that the SI unit of rgh is N/m2 .
(pgh)units = (kg/m^3)(m/s^2)(m) = kg x m^2/m^3 *s^2 = (kg * m/s^2)(1/m^2) = N/m^2
Verify that pressure has units of energy per unit volume.
F = P A ⇒ P = F/A , Units of P = N/m2 = N·m/m3 = J/m3 = energy/volume
What force is needed to pull one microscope slide over another at a speed of 1.00 cm/s, if there is a 0.500-mm-thick layer of 20°C water between them and the contact area is 8.00 cm2 ?
F = n * vA/L = 1.61 x 10 -5
The left side of the heart creates a pressure of 120 mm Hg by exerting a force directly on the blood over an effective area of 15.0 cm2 . What force does it exert to accomplish this? Note that 1 atm = 1.103 × 105 N/m2 = 760 mm Hg.
F= PA --> P= F/A = 24N
. What is the gauge pressure in millimeters of mercury inside a soap bubble 0.100 m in diameter?
P = 4Y / r --> mm Hg = 2.23 x 10 ^-2 mm Hg
Find the gauge pressure (in Pa) in the peanut jar shown in the figure, assuming the manometer connected to the jar uses mercury (density 13600 kg/m3 ) and the meter stick is marked in centimeters.
Pg = -pga =-9336 Pa
Find the gauge pressure (in Pa) in the balloon shown in the figure, assuming the manometer connected to the balloon uses water and the meter stick is marked in centimeters.
Pg = p*g*h = 686 Pa
(OSC Example 11.10) The mass of an ancient Greek coin is determined in air to be 8.630 g. When the coin is submerged in water as shown in the lower figure, its apparent mass is 7.800 g. Calculate its density, given that water has a density of 1.000 g/cm3 and that effects caused by the wire suspending the coin are negligible.
The submerged T2 is reduced by the weight of water displaced, ρwVc times g. The reading T1 in air is ρcVc times g. The ratio of the reading in air to the change in readings is T1/T1 − T2 = ρcVc/ρwVc=ρc/ρw The scale gives numbers divided by g (to read out mass, or grams) but we can still take the ratio, T1/T1 − T2=8.630 g/8.630 g - 7.800 g = 10.4 This is ρc/ρw, so ρc = 10.4 g/cm3 .
Mercury is commonly supplied in flasks containing 34.5 kg (about 76 lb). What is the volume in liters of this much mercury?
V=m/p = 34500 g/13.6g/cm = 2.537*10^3 cm =2.54 L
Calculate the maximum height to which water could be squirted with a hose if it (a) Emerges from the nozzle at a speed of v = 25.5 m/s; (b) Emerges with the nozzle removed, at a speed of v = 1.96 m/s.
a) P1 + 1/2 pv1^2 + pgh = P2 + 1/2 pv2^2 + pgh2 h2 = v1^2 /2g = 33.1 m b) h2 = v1^2 / 2g = 0.196 m = 19.6 cm
A Ping-Pong ball is held submerged in a bucket of water by a string attached to the bucket's bottom. (a) Salt is now added to the water in the bucket, increasing the density of the liquid. What happens to the tension in the string ? (b) What happens to the tension in the string if the Ping-Pong ball is replaced by a smaller spherical object of equal weight?
(a) The tension increases. (Buoyant force is equal to the weight of displaced fluid, which is larger.) (b) The tension decreases. (Since the volume of displaced fluid is smaller, the buoyant force is now smaller.)
There is relatively little empty space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale—approximately 103 kg/m3 . The nucleus of an atom has a radius about 10-5 that of the atom and contains nearly all the mass of the entire atom. (a) What is the approximate density of a nucleus? (b) One remnant of a supernova, called a neutron star, can have the density of a nucleus. What would be the radius of a neutron star with a mass 10 times that of our Sun (the radius of the Sun is 7 × 108 m)?
A) Pn = mn/Vn (ma= mn and Rn = 10-5 Ra, Pn = ma/10-5 Va = Pa/10-5=10^3/10^-5 = 10^18 kg/m^3 B) m = pV = p(4/3*pi*R^3) = 10 x (mass sum) = 1.99 x 10^31 kg R=(3m/4*pi*p)^(1/3) = [(3*1.99x10^31 kg)/4*pi*10^18 kg/m)]^(1/3) = 16.8 x 10^3 m = 16.8 km
. Heroes in movies hide beneath water and breathe through a hollow reed (villains never catch on to this trick). In practice, you cannot inhale in this manner if your lungs are more than 60.0 cm below the surface. If this is true, what is the maximum negative gauge pressure, in Pa and also in atmospheres, that you can create in your lungs on dry land?
Breathing through a 60 cm reed means that your lungs can make a negative pressure of ρgh = (1000 kg/m3)(9.8 m/s2)(0.60 m)= 5880 Pa. Dividing by 1 atm = 1.103 × 105 Pa, your lungs can provide a negative gauge pressure of -0.06 atm.
Logs sometimes float vertically in a lake because one end has become water-logged and denser than the other. What is the average density of a uniform-diameter log that floats with 20.0% of its length above water?
FS = p obj / p fl p obj = p fluid * FS = 800 kg/m
During heavy lifting, a disk between spinal vertebrae is subjected to a 5000-N compressional force. (a) What pressure is created, assuming that the disk has a uniform circular cross section 2.00 cm in radius? (b) What deformation is produced if the disk is 0.800 cm thick and has a Young's modulus of 1.5×109 N/m2?
P = F/A = 5000N / pi* (0.0220m^)2 3.98 x 10^6 Pa delta L = 1/ Y * F/A *L0 = 2.1 x 10 -3 cm
Pressure in the spinal fluid is measured as shown in Figure 11.43. If the pressure in the spinal fluid is 10.0 mm Hg: (a) What is the reading of the water manometer in cm water? (b) What is the reading if the person sits up, placing the top of the fluid 60 cm above the tap? The fluid density is 1.05 g/mL.
P knot = 10 mmHg (133 N/m /1.0 mmHg) * (1.0 cm H20 / 98.1 N/m) = 13.6 m H20 B) P= P0 + delta P = P0 + hpg = 76.5 cm H20
As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of 1.50 cm2 and the woman's mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)
P= F/A --> mg/A P= (55kg)(9.80)/1.50*10-4= 3.59*10^6 N/m^2 = 3.59 x 10^6 N/m^2 / 4.448 N * 6.452 *10^-4 m^2 = 521 lb/in
The greatest ocean depths on the Earth are found in the Marianas Trench near the Philippines. Calculate the pressure due to the ocean at the bottom of this trench, given its depth is 11.0 km and assuming the density of seawater is constant all the way down.
P=hpg = 1.10x10^8 Pa = 1.09x10^3 atm
10. Solution The flow rate of blood through a 2.00×10-6-m-radius capillary is 3.80×10-9 cm3/s. (a) What is the speed of the blood flow? (This small speed allows time for diffusion of materials to and from the blood.) (b) Assuming all the blood in the body passes through capillaries, how many of them must there be to carry a total flow of 90.0 cm3/s ? (The large number obtained is an overestimate, but it is still reasonable.)
Q = Av = pi * r^2 * v --> v = Q / pi* r^2 b) single capillary flow = total / Q 90/ 3.80 x 10-9 = 2.37 x 10^10
The Huka Falls on the Waikato River is one of New Zealand's most visited natural tourist attractions (see Figure 12.29). On average the river has a flow rate of about 300,000 L/s. At the gorge, the river narrows to 20 m wide and averages 20 m deep. (a) What is the average speed of the river in the gorge? (b) What is the average speed of the water in the river downstream of the falls when it widens to 60 m and its depth increases to an average of 40 m?
Q = Av=pr^2v =p(0.20 cm)^2 (40 cm/s)=5.03 cm3/s V = Qt=(5.03cm3/s)(30s)=151 cm3
A glucose solution being administered with an IV has a flow rate of 4.00 cm3/min . What will the new flow rate be if the glucose is replaced by whole blood having the same density but a viscosity 2.50 times that of the glucose? All other factors remain constant.
Q'= Q ( n/n') = 1.60 cm/min
A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the slave cylinder to the area of the master cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves?
a) 100/1 b) square root of d.. =10 c) inverse.. 1/100 This tells us that the distance through which the output force moves is reduced by a factor of 100, relative to the distance through which the input force moves.
. (a) Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 6.00 m/s parallel to its front surface and 3.50 m/s along its back surface. Take the density of air to be 1.29 kg/m3 . (The calculation, based on Bernoulli's principle, is approximate due to the effects of turbulence.) (b) Discuss whether this force is great enough to be effective for propelling a sailboat.
a) F = (P1- P2)A = 1/2 p (v2^2 - v1^2)A = 1/2(1.29) [ 6 -3.5] *1.00 m^2 =15.3 N (b) This force is small, but when the sails are large, the forces can be great enough to propel a sailboat. For larger sailboats, sometimes more than one sail is used to increase the surface areas thereby increasing the force applied.
(a) A golf ball hangs by a string from a fishing pole. The golf ball is then lowered just below the surface of a swimming pool. What happens to the tension in the string as the ball submerges? (b) The golf ball is replaced by a much smaller lead fishing sinker of equal weight, and again lowered beneath the water. Is the tension less, the same, or greater than it was for the submerged golf ball?
a) The tension decreases. (b) The tension is greater for the submerged lead sinker than for the submerged golf ball.
A major artery with a cross-sectional area of 1.00 cm2 branches into 18 smaller arteries, each with an average cross-sectional area of 0.400 cm2. By what factor is the average velocity of the blood reduced when it passes into these branches?
a) V = Q / A = 0.75 m/s b) v = Q/ wd = 300 / (60*40) = 0.13 m/s
(a) What is the mass of a deep breath of air having a volume of 2.00 L? (b) Discuss the effect taking such a breath has on your body's volume and density.
a) m=pV = (1.29*10-3092.00 L) (1000cm/1L) =2.58 g (b) The volume of your body increases by the volume of air you inhale. The average density of your body decreases when you take a deep breath, because the density of air is substantially smaller than the average density of the body before you took the deep breath.
The pressure drop along a length of artery is 100 Pa, the radius is 10 mm, and the flow is laminar. The average speed of the blood is 15 mm/s. (a) What is the net force on the blood in this section of artery? (b) What is the power expended maintaining the flow?
a) nwtF = delta PA = 3.14 N b) P = Fv = 47.1 mW