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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
In Example 11.1, we calculated the mass of water in a large reservoir. We will now consider the pressure and force acting on the dam retaining water. (See Figure 11.9.) The dam is 500 m wide, and the water is 80.0 m deep at the dam.(a) What is the average pressure on the dam due to the water?(b)
What physical characteristic distinguishes a fluid from a solid?
An astronaut is working outside the International Space Station where the atmospheric pressure is essentially zero. The pressure gauge on her air tank reads 6.90 x 106 Pa. What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter?StrategyWe
Which of the following substances are fluids at room temperature: air, mercury, water, glass?
Mercury is commonly supplied in flasks containing 34.5 kg (about 76 lb). What is the volume in liters of this much mercury?
Why are gases easier to compress than liquids and solids?
Calculate the average density of the atmosphere, given that it extends to an altitude of 120 km. Compare this density with that of air listed in Table 11.1.StrategyIf we solve P = hρg for density, we see thatWe then take P to be atmospheric pressure, h is given, and g is known, and so we can use
(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.
How do gases differ from liquids?
Consider the automobile hydraulic system shown in Figure 11.12. A force of 100 N is applied to the brake pedal, which acts on the pedal cylinder through a lever. A force of 500 N is exerted on the pedal cylinder. (The reader can verify that the force is 500 N using techniques of statics from
Calculate the depth below the surface of water at which the pressure due to the weight of the water equals 1.00 atm.StrategyWe begin by solving the equation P=hρg for depth h:Then we take P to be 1.00 atm and ρto be the density of the water that creates the pressure. P h == pg
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 cm3of water? (Note that the accuracy and practical applications of this technique are
Give an example in which density is used to identify the substance composing an object. Would information in addition to average density be needed to identify the substances in an object composed of more than one material?
Figure 11.37 shows a glass of ice water filled to the brim. Will the water overflow when the ice melts? Explain your answer.
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?
Intravenous infusions are usually made with the help of the gravitational force. Assuming that the density of thefluid being administered is 1.00 g/ml, at what height should the IV bag be placed above the entry point so that the fluid just enters the vein if the blood pressure in the vein is 18 mm
How is pressure related to the sharpness of a knife and its ability to cut?
Suppose a 60.0-kg woman floats in freshwater with 97.0% of her volume submerged when her lungs are full of air. What is her average density?StrategyWe can find the woman’s density by solving the equationfor the density of the object. This yieldsWe know both the fraction submerged and the density
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?
Why does a dull hypodermic needle hurt more than a sharp one?
Approximately how does the density of air vary with altitude?
Suppose you have a coffee mug with a circular cross section and vertical sides (uniform radius). What is its inside radius if it holds 375 g of coffee when filled to a depth of 7.50 cm? Assume coffee has the same density as water.
Blood is pumped from the heart at a rate of 5.0 L/ min into the aorta (of radius 1.0 cm). Determine the speed of blood through the aorta.
Calculate the Reynolds number for flow in the needle considered in Example 12.8 to verify the assumption that the flow is laminar. Assume that the density of the saline solution is 1025 kg/m3.StrategyWe have all of the information needed, except the fluid speed U, which can be calculated from v̅ =
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?
Why does atmospheric pressure decrease more rapidly than linearly with altitude?
What are two reasons why mercury rather than water is used in barometers?
Figure 11.38 shows how sandbags placed around a leak outside a river levee can effectively stop the flow of water under the levee. Explain how the small amount of water inside the column formed by the sandbags is able to balance the much larger body of water behind the levee. Water rises to this
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?
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?
Why is it difficult to swim under water in the Great Salt Lake?
Calculate the average pressure exerted on the palm of a shot-putter's hand by the shot if the area of contact is 50.0 cm2 and he exerts a force of 800 N on it. Express the pressure in N/m2 and compare it with the 1.00 × 106 Pa pressures sometimes encountered in the skeletal system.
Is there a net force on a dam due to atmospheric pressure? Explain your answer.
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?
Show that the total force on a rectangular dam due to the water behind it increases with the square of the water depth. In particular, show that this force is given by F = ρgh2 L/2, where ρ is the density of water, h is its depth at the dam, and L is the length of the dam. You may assume the face
Does atmospheric pressure add to the gas pressure in a rigid tank? In a toy balloon? When, in general, does atmospheric pressure not affect the total pressure in a fluid?
How much pressure is transmitted in the hydraulic system considered in Example 11.6? Express your answer in pascals and in atmospheres.Data given in Example 11.6Consider the automobile hydraulic system shown in Figure 11.12. A force of 100 N is applied to the brake pedal, which acts on the pedal
You can break a strong wine bottle by pounding a cork into it with your fist, but the cork must press directly against the liquid filling the bottle—there can be no air between the cork and liquid. Explain why the bottle breaks, and why it will not if there is air between the cork and liquid.
Suppose the pedal cylinder in a hydraulic system is at a greater height than the wheel cylinder. Explain how this will affect the force produced at the wheel cylinder.
What force must be exerted on the pedal cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on the wheel cylinder? The pedal cylinder has a 2.00-cm diameter and the wheel has a 24.0-cm diameter.
Figure 11.15 shows how a common measurement of arterial blood pressure is made. Is there any effect on the measured pressure if the manometer is lowered? What is the effect of raising the arm above the shoulder? What is the effect of placing the cuff on the upper leg with the person standing?
Explain why the fluid reaches equal levels on either side of a manometer if both sides are open to the atmosphere, even if the tubes are of different diameters.
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 wheel cylinder to the area of the pedal cylinder? (b) What must be the ratio of their diameters?(c) By what factor is the distance through which the
Considering the magnitude of typical arterial blood pressures, why are mercury rather than water manometers used for these measurements?
More force is required to pull the plug in a full bathtub than when it is empty. Does this contradict Archimedes’ principle? Explain your answer.
Find the gauge and absolute pressures in the balloon and peanut jar shown in Figure 11.14, assuming the manometer connected to the balloon uses water whereas the manometer connected to the jar contains mercury. Express in units of centimeters of water for the balloon and millimeters of mercury for
Do fluids exert buoyant forces in a “weightless” environment, such as in the space shuttle? Explain your answer.
(a) Convert normal blood pressure readings of 120 over 80 mm Hg to newtons per meter squared using the relationship for pressure due to the weight of a fluid (P=hρg) rather than a conversion factor.(b) Discuss why blood pressures for an infant could be smaller than those for an adult.
Will the same ship float higher in salt water than in freshwater? Explain your answer.
How tall must a water-filled manometer be to measure blood pressures as high as 300 mm Hg?
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 25.0 cm in diameter
Marbles dropped into a partially filled bathtub sink to the bottom. Part of their weight is supported by buoyant force, yet the downward force on the bottom of the tub increases by exactly the weight of the marbles. Explain why.
The density of oil is less than that of water, yet a loaded oil tanker sits lower in the water than an empty one. Why?
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
Is surface tension due to cohesive or adhesive forces, or both?
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.
Is capillary action due to cohesive or adhesive forces, or both?
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.
Birds such as ducks, geese, and swans have greater densities than water, yet they are able to sit on its surface. Explain this ability, noting that water does not wet their feathers and that they cannot sit on soapy water.
What fraction of ice is submerged when it floats in freshwater, given the density of water at 0°C is very close to 1000kg/m3?
Water beads up on an oily sunbather, but not on her neighbor, whose skin is not oiled. Explain in terms of cohesive and adhesive forces.
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?
Could capillary action be used to move fluids in a “weightless” environment, such as in an orbiting space probe?
Find the density of a fluid in which a hydrometer having a density of 0.750 g/mL floats with 92.0% of its volume submerged.
What effect does capillary action have on the reading of a manometer with uniform diameter? Explain your answer.
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?
Pressure between the inside chest wall and the outside of the lungs normally remains negative. Explain how pressure inside the lungs can become positive (to cause exhalation) without muscle action.
Archimedes’ principle can be used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 g when completely submerged in an unknown liquid.(a) What mass of fluid does the iron displace?(b)
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. (d) If her lung capacity is
Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force must an 85.0-kg grouper exert to stay submerged in salt water if its body density is 1015kg/m3?
(a) Calculate the buoyant force on a 2.00-L helium balloon.(b) Given the mass of the rubber in the balloon is 1.50 g, what is the net vertical force on the balloon if it is let go? You can neglect the volume of the rubber.
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 simple compass can be made by placing a small bar magnet on a cork floating in water.(a) What fraction of a plain cork will be submerged when floating in water?(b) If the cork has a mass of 10.0 g and a 20.0-g magnet is placed on it, what fraction of the cork will be submerged? (c) Will the bar
What fraction of an iron anchor’s weight will be supported by buoyant force when submerged in saltwater?
Scurrilous con artists have been known to represent gold-plated tungsten ingots as pure gold and sell them at prices much below gold value but deservedly far above the cost of tungsten. With what accuracy must you be able to measure the mass of such an ingot in and out of water to tell that it is
A twin-sized air mattress used for camping has dimensions of 100 cm by 200 cm by 15 cm when blown up. The weight of the mattress is 2 kg. How heavy a person could the air mattress hold if it is placed in freshwater?
Referring to Figure 11.19, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant force is F2-F1 and that the ends of the cylinder have equal areas A. Note that the volume of the cylinder (and that of the
(a) The pressure inside an alveolus with a 2.00 x 10-4-m radius is 1.40 x 103 Pa, due to its fluid-lined walls. Assuming the alveolus acts like a spherical bubble, what is the surface tension of the fluid?(b) Identify the likely fluid. (You may need to extrapolate between values in Table 11.3.)Data
(a) A 75.0-kg man floats in freshwater with 3.00% of his volume above water when his lungs are empty, and 5.00% of his volume above water when his lungs are full. Calculate the volume of air he inhales-called his lung capacity-in liters.(b) Does this lung volume seem reasonable?
What is the pressure inside an alveolus having a radius of 2.50 x 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.
What fluid is in the device shown in Figure 11.26 if the force is 3.16 × 10-3 N and the length of the wire is 2.50 cm? Calculate the surface tension γ and find a likely match from Table 11.3.Data given in Table 11.3Data given in figure 11.26 Liquid Water at 0°C Water at 20°C Water at
Calculate the force on the slide wire in Figure 11.26 if it is 3.50 cm long and the fluid is ethyl alcohol. Film surfaces Side view Wire F = y(21)
Figure 11.32(a) shows the effect of tube radius on the height to which capillary action can raise a fluid. (a) Calculate the height for water in a glass tube with a radius of 0.900 cm—a rather large tube like the one on the left. (b) What is the radius of the glass tube on the right if it
What is the gauge pressure in millimeters of mercury inside a soap bubble 0.100 m in diameter?
If the gauge pressure inside a rubber balloon with a 10.0-cm radius is 1.50 cm of water, what is the effective surface tension of the balloon?
Calculate the gauge pressures inside 2.00-cmradius bubbles of water, alcohol, and soapy water. Which liquid forms the most stable bubbles, neglecting any effects of evaporation?
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?
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?
Calculate the ratio of the heights to which water and mercury are raised by capillary action in the same glass tube.
What is the ratio of heights to which ethyl alcohol and water are raised by capillary action in the same glass tube?
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?
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?
One way to force air into an unconscious person's lungs is to squeeze on a balloon appropriately connected to the subject. What force must you exert on the balloon with your hands to create a gauge pressure of 4.00 cm water, assuming you squeeze on an effective area of 50.0 cm2?
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.(a) Calculate this outward force in newtons on each side of an infant's skull if the effective area of
A full-term fetus typically has a mass of 3.50 kg.(a) What pressure does the weight of such a fetus create if it rests on the mother's bladder, supported on an area of 90.0 cm2?(b) Convert this pressure to millimeters of mercury and determine if it alone is great enough to trigger the micturition
If the pressure in the esophagus is -2.00 mm Hg while that in the stomach is +20.0 mm Hg, to what height could stomach fluid rise in the esophagus, assuming a density of 1.10 g/mL? (This movement will not occur if the muscle closing the lower end of the esophagus is working properly.)
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
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
When a person sits erect, increasing the vertical position of their brain by 36.0 cm, the heart must continue to pump blood to the brain at the same rate.(a) What is the gain in gravitational potential energy for 100 mL of blood raised 36.0 cm?(b) What is the drop in pressure, neglecting any losses
A negative pressure of 25.0 atm can sometimes be achieved with the device in Figure 11.41 before the water separates.(a) To what height could such a negative gauge pressure raise water?(b) How much would a steel wire of the same diameter and length as this capillary stretch if suspended from above?
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