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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
(a) How high will water rise in a glass capillary tube with a 0.500-mm radius?(b) How much gravitational potential energy does the water gain?(c) Discuss possible sources of this energy.
The hydraulic system of a backhoe is used to lift a load as shown in Figure 11.42.(a) Calculate the force the secondary cylinder must exert to support the 400-kg load and the 150-kg brace and shovel. (b) What is the pressure in the hydraulic fluid if the secondary cylinder is 2.50 cm in
Suppose you hit a steel nail with a 0.500-kg hammer, initially moving at 15.0 m/s and brought to rest in 2.80 mm.(a) What average force is exerted on the nail?(b) How much is the nail compressed if it is 2.50 mm in diameter and 6.00-cm long?(c) What pressure is created on the 1.00-mm-diameter tip
Some miners wish to remove water from a mine shaft. A pipe is lowered to the water 90 m below, and a negative pressure is applied to raise the water. (a) Calculate the pressure needed to raise the water. (b) What is unreasonable about this pressure?(c) What is unreasonable about the premise?
You are pumping up a bicycle tire with a hand pump, the piston of which has a 2.00-cm radius. (a) What force in newtons must you exert to create a pressure of 6.90 x 105 Pa(b) What is unreasonable about this (a) result? (c) Which premises are unreasonable or inconsistent?
Consider a group of people trying to stay afloat after their boat strikes a log in a lake. Construct a problem in which you calculate the number of people that can cling to the log and keep their heads out of the water. Among the variables to be considered are the size and density of the log, and
The alveoli in emphysema victims are damaged and effectively form larger sacs. Construct a problem in which you calculate the loss of pressure due to surface tension in the alveoli because of their larger average diameters. (Part of the lung’s ability to expel air results from pressure created by
How many cubic meters of blood does the heart pump in a 75-year lifetime, assuming the average flow rate is 5.00 L/min?StrategyTime and flow rate Q are given, and so the volume V can be calculated from the definition of flow rate.
What is the difference between flow rate and fluid velocity? How are they related?
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 nozzle with a radius of 0.250 cm is attached to a garden hose with a radius of 0.900 cm. The flow rate through hose and nozzle is 0.500 L/s. Calculate the speed of the water (a) In the hose and(b) In the nozzle.StrategyWe can use the relationship between flow rate and speed to find both
The aorta is the principal blood vessel through which blood leaves the heart in order to circulate around the body.(a) Calculate the average speed of the blood in the aorta if the flow rate is 5.0 L/min. The aorta has a radius of 10 mm.(b) Blood also flows through smaller blood vessels known as
Identify some substances that are incompressible and some that are not.
Blood is flowing through an artery of radius 2 mm at a rate of 40 cm/s. Determine the flow rate and the volume that passes through the artery in a period of 30 s.
In Example 12.2, we found that the speed of water in a hose increased from 1.96 m/s to 25.5 m/s going from the hose to the nozzle. Calculate the pressure in the hose, given that the absolute pressure in the nozzle is 1.01 x 105 N/m2 (atmospheric, as it must be) and assuming level, frictionless
You can squirt water a considerably greater distance by placing your thumb over the end of a garden hose and then releasing, than by leaving it completely uncovered. Explain how this works.
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
Fire hoses used in major structure fires have inside diameters of 6.40 cm. Suppose such a hose carries a flow of 40.0 L/s starting at a gauge pressure of 1.62 x 106 N/m2. The hose goes 10.0 m up a ladder to a nozzle having an inside diameter of 3.00 cm. Assuming negligible resistance, what is the
Water is shot nearly vertically upward in a decorative fountain and the stream is observed to broaden as it rises. Conversely, a stream of water falling straight down from a faucet narrows. Explain why, and discuss whether surface tension enhances or reduces the effect in each case.
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?
Look back to Figure 12.4. Answer the following two questions. Why is PO less than atmospheric? Why is PO greater than P1? V₁ V/₂3 Po P P Po
Suppose the fire hose in the previous example is fed by a pump that receives water through a hose with a 6.40-cm diameter coming from a hydrant with a pressure of 0.700 × 106 N/m2. What power does the pump supply to the water?StrategyHere we must consider energy forms as well as how they relate to
Suppose the flow rate of blood in a coronary artery has been reduced to half its normal value by plaque deposits. By what factor has the radius of the artery been reduced, assuming no turbulence occurs?StrategyAssuming laminar flow, Poiseuille’s law states thatWe need to compare the artery radius
(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 cross-sectional area of the venules is 10.0 cm2, what is the total cross- sectional area of the capillaries feeding these
Many entrainment devices have a constriction, called a Venturi, such as shown in Figure 12.24. How does this bolster entrainment? Fluid flow → Entrained fluid Venturi constriction
The human circulation system has approximately 1 x 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.
An intravenous (IV) system is supplying saline solution to a patient at the rate of 0.120 cm3/s through a needle of radius 0.150 mm and length 2.50 cm. What pressure is needed at the entrance of the needle to cause this flow, assuming the viscosity of the saline solution to be the same as that of
(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?
Some chimney pipes have a T-shape, with a crosspiece on top that helps draw up gases whenever there is even a slight breeze. Explain how this works in terms of Bernoulli’s principle.
Calculate the Reynolds number N'R for a ball with a 7.40-cm diameter thrown at 40.0 m/s.Strategy We can use NR and viscosity. = puL to calculate N', since all values in it are either given or can be found in tables of density "
The flow rate of blood through a 2.00 × 10-6-m -radius capillary is 3.80 x 10-9 cm/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
Is there a limit to the height to which an entrainment device can raise a fluid? Explain your answer.
Calculate the average time it takes a glucose molecule to move 1.0 cm in water.Strategy We can use Xrms = √2Dt, the expression for the average distance moved in time t, and solve it for t. All other quantities are known.
(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?
Why is it preferable for airplanes to take off into the wind rather than with the wind?
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
Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli’s principle to explain these phenomena.
Why does a sailboat need a keel?
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?
It is dangerous to stand close to railroad tracks when a rapidly moving commuter train passes. Explain why atmospheric pressure would push you toward the moving train.
Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.
A perfume bottle or atomizer sprays a fluid that is in the bottle. (Figure 12.25.) How does the fluid rise up in the vertical tube in the bottle? G
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
A mountain stream is 10.0 m wide and averages 2.00 m in depth. During the spring runoff, the flow in the stream reaches 100,000 m3/s.(a) What is the average velocity of the stream under these conditions? (b) What is unreasonable about this velocity? (c) What is unreasonable or inconsistent about
If you lower the window on a car while moving, an empty plastic bag can sometimes fly out the window. Why does this happen?
Verify that pressure has units of energy per unit volume.
Based on Bernoulli’s equation, what are three forms of energy in a fluid? (Note that these forms are conservative, unlike heat transfer and other dissipative forms not included in Bernoulli’s equation.)
Suppose you have a wind speed gauge like the pitot tube shown in Example 12.2(b). 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?Data given in Example 12.2(b)A nozzle with a radius of 0.250 cm
Water that has emerged from a hose into the atmosphere has a gauge pressure of zero. Why? When you put your hand in front of the emerging stream you feel a force, yet the water’s gauge pressure is zero. Explain where the force comes from in terms of energy.
The old rubber boot shown in Figure 12.26 has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of leak 1? Explain your responses in terms of energy. Leak 2 Leak 1
If the pressure reading of your pitot tube is 15.0 mm Hg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude?
Calculate the maximum height to which water could be squirted with the hose in Example 12.2 example if it:(a) Emerges from the nozzle. (b) Emerges with the nozzle removed, assuming the same flow rate.Data given in Example 12.2A nozzle with a radius of 0.250 cm is attached to a garden hose with a
Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.
Explain why the viscosity of a liquid decreases with temperature—that is, how might increased temperature reduce the effects of cohesive forces in a liquid? Also explain why the viscosity of a gas increases with temperature—that is, how does increased gas temperature create more collisions
(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
When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why.
(a) What is the pressure drop due to the Bernoulli effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s?(b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air
(a) Using Bernoulli's equation, show that the measured fluid speed v for a pitot tube, like the 1/2 one in Figure 12.7(b), is given by where h is the height of the manometer fluid, ρ' is the density of the manometer fluid, ρ is the density of the moving fluid, and g is the acceleration due to
Why does flow decrease in your shower when someone flushes the toilet?
Plumbing usually includes air-filled tubes near water faucets, as shown in Figure 12.27. Explain why they are needed and how they work. Air Water -Faucet
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
Doppler ultrasound can be used to measure the speed of blood in the body. If there is a partial constriction of an artery, where would you expect blood speed to be greatest, at or nearby the constriction? What are the two distinct causes of higher resistance in the constriction?
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
Sink drains often have a device such as that shown in Figure 12.28 to help speed the flow of water. How does this work?
Some ceiling fans have decorative wicker reeds on their blades. Discuss whether these fans are as quiet and efficient as those with smooth blades.
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 x 105 N/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
What direction will a helium balloon move inside a car that is slowing down—toward the front or back? Explain your answer.
(a) Calculate the retarding force due to the viscosity of the air layer between a cart and a level air track given the following information-air temperature is 20° C, the cart is moving at 0.400 m/s, its surface area is 2.50 x 10-2 m, and the thickness of the air layer is 6.00 x 10-5 m.(b) What is
Will identical raindrops fall more rapidly in 5° C air or 25° C air, neglecting any differences in air density? Explain your answer.
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?
If you took two marbles of different sizes, what would you expect to observe about the relative magnitudes of their terminal velocities?
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.
Why would you expect the rate of diffusion to increase with temperature? Can you give an example, such as the fact that you can dissolve sugar more rapidly in hot water?
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?
How are osmosis and dialysis similar? How do they differ?
A small artery has a length of 1.1 x 10-3 radius of 2.5 x 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.)
Fluid originally flows through a tube at a rate of 100 cm3/s. To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate for the following changes with all other factors remaining the same as in the original conditions. (a) Pressure difference increases by a factor
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?
A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, Fs = 6πrηv. Show that the
(a) Suppose a blood vessel’s radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase?(b) If turbulence is created by
A skydiver will reach a terminal velocity when the air drag equals their weight. For a skydiver with high speed and a large body, turbulence is a factor. The drag force then is approximately proportional to the square of the velocity. Taking the drag force to be and setting this equal to the
Using the equation of the previous problem, find the viscosity of motor oil in which a steel ball of radius 0.8 mm falls with a terminal speed of 4.32 cm/s. The densities of the ball and the oil are 7.86 and 0.88 g/mL, respectively.
A layer of oil 1.50 mm thick is placed between two microscope slides. Researchers find that a force of 5.50 x 10-4 N is required to glide one over the other at a speed of 1.00 cm/s when their contact area is 6.00 cm2. What is the oil's viscosity? What type of oil might it be?
(a) Verify that a 19.0% decrease in laminar flow through a tube is caused by a 5.00% decrease in radius, assuming that all other factors remain constant, as stated in the text.(b) What increase in flow is obtained from a 5.00% increase in radius, again assuming all other factors remain constant?
When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in an artery has been reduced to 10.0% of its normal value by a blood clot and the average pressure difference has increased by 20.0%, by what factor has the clot reduced the radius of the artery?
During a marathon race, a runner’s blood flow increases to 10.0 times her resting rate. Her blood’s viscosity has dropped to 95.0% of its normal value, and the blood pressure difference across the circulatory system has increased by 50.0%. By what factor has the average radii of her blood
Water supplied to a house by a water main has a pressure of 3.00 x 105 N/m2 early on a summer day when neighborhood use is low. This pressure produces a flow of 20.0 L/min through a garden hose. Later in the day, pressure at the exit of the water main and entrance to the house drops, and a flow of
Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 200.0 L/min through a 50.0-m-long, 8.00-cm-diameter hose, and the pressure at the pump is 8.00 x 106 N/m2.(a) Calculate the resistance of the hose.(b) What is the
Consider a coronary artery constricted by arteriosclerosis. Construct a problem in which you calculate the amount by which the diameter of the artery is decreased, based on an assessment of the decrease in flow rate.
Consider a river that spreads out in a delta region on its way to the sea. Construct a problem in which you calculate the average speed at which water moves in the delta region, based on the speed at which it was moving up river. Among the things to consider are the size and flow rate of the river
Show that the Reynolds number NR is unitless by substituting units for all the quantities in its definition and cancelling.
Calculate the Reynolds numbers for the flow of water through(a) A nozzle with a radius of 0.250 cm and(b) A garden hose with a radius of 0.900 cm, when the nozzle is attached to the hose. The flow rate through hose and nozzle is 0.500 L/s. Can the flow in either possibly be laminar?
A fire hose has an inside diameter of 6.40 cm. Suppose such a hose carries a flow of 40.0 L/s starting at a gauge pressure of 1.62 × 106 N/m2. The hose goes 10.0 m up a ladder to a nozzle having an inside diameter of 3.00 cm. Calculate the Reynolds numbers for flow in the fire hose and nozzle to
Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 200.0 L/min through a 50.0-m-long, 8.00-cm-diameter hose, and the pressure at the pump is 8.00 × 106 N/m2. Verify that the flow of concrete is laminar taking concrete's
At what flow rate might turbulence begin to develop in a water main with a 0.200-m diameter? Assume a 20° C temperature.
What is the greatest average speed of blood flow at 37° C in an artery of radius 2.00 mm if the flow is to remain laminar? What is the corresponding flow rate? Take the density of blood to be 1025 kg/m3.
In Take-Home Experiment: Inhalation, we measured the average flow rate Q of air traveling through the trachea during each inhalation. Now calculate the average air speed in meters per second through your trachea during each inhalation. The radius of the trachea in adult humans is approximately 10-2
Assuming that blood is an ideal fluid, calculate the critical flow rate at which turbulence is a certainty in the aorta. Take the diameter of the aorta to be 2.50 cm. (Turbulence will actually occur at lower average flow rates, because blood is not an ideal fluid. Furthermore, since blood flow
A fairly large garden hose has an internal radius of 0.600 cm and a length of 23.0 m. The nozzleless horizontal hose is attached to a faucet, and it delivers 50.0 L/s.(a) What water pressure is supplied by the faucet? (b) What is unreasonable about this pressure? (c) What is unreasonable about
You can smell perfume very shortly after opening the bottle. To show that it is not reaching your nose by diffusion, calculate the average distance a perfume molecule moves in one second in air, given its diffusion constant D to be 1.00 x 10-6 m2/s.
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