CollegePhysics2e-SSM-Ch11

Openstax College Physics 2e Student Solutions Manual Chapter 11 CHAPTER 11: FLUID STATICS 11.2 DENSITY 1. Gold is sold by the troy ounce (31.103 g). What is the volume of 1 troy ounce of pure gold? Solution 3. (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. Solution (a) (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. 4. 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 of water? (Note that the accuracy and practical applications of this technique are more limited than a variety of others that are based on Archimedes’ principle.) Solution 6. (a) A rectangular gasoline tank can hold 50.0 kg of gasoline when full. What is the depth of the tank if it is 0.500-m wide by 0.900-m long? (b) Discuss whether this gas tank has a reasonable volume for a passenger car.

Openstax College Physics 2e Student Solutions Manual Chapter 11 Solution (a) (b) The volume of this gasoline tank is 19.4 gallons, quite reasonably sized for a passenger car. 8. 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? Solution 9. What is the density of 18.0-karat gold that is a mixture of 18 parts gold, 5 parts silver, and 1 part copper? (These values are parts by mass, not volume.) Assume that this is a simple mixture having an average density equal to the weighted densities of its constituents. Solution m ( g ) ρ ( g / cm 3 ) V = m ρ ( c m 3 ) gold 18.019.320.9317 ¿ 5.0010.490.4766 copper 1.00 8.80.1136 Total 24.0 1.5219 ρ tot = 24.0 g 1.5219 cm 3 = 15.8 g / c m 3

Openstax College Physics 2e Student Solutions Manual Chapter 11 10. 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 . The nucleus of an atom has a radius about 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 )? Solution (a) 10 − 5 ¿ 3 V a ¿ ¿ ρ a 10 − 15 ¿ ¿ ρ N = m N V N .Sincem a ≈m N ∧ R N = 10 − 5 R a , ρ N = m a ¿ (b) m = ρV = ρ ( 4 3 π R 3 ) = 2.0 × ( massof sun )= 3.98 × 10 30 kg 10 18 kg / m 3 3 ( 3.98 × 10 30 kg ) 4 π ¿ 1 / 3 = 9.83 × 10 3 m = 9.83 km ¿ ¿ R = ( 3 m 4 πρ ) 1 / 3 = ¿ The radius of the neutron star would be about 10 km. 11.3 PRESSURE 11. 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 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.)

Openstax College Physics 2e Student Solutions Manual Chapter 11 Solution 13. 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 (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.) Solution 11.4 VARIATION OF PRESSURE WITH DEPTH IN A FLUID 14. What depth of mercury creates a pressure of 1.00 atm? Solution 16. Verify that the SI unit of is . Solution 18. The aqueous humor in a person’s eye is exerting a force of 0.300 N on the area of the cornea. (a) What pressure is this in mm Hg? (b) Is this value within the normal range for pressures in the eye? Solution (a) (b) The range of pressures in the eye is 12–24 mm Hg, so the result in part (a) is within that range. 20. 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?

Openstax College Physics 2e Student Solutions Manual Chapter 11 Solution 22. 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 . What force does it exert to accomplish this? Solution From Exercise 11.14 , 11.5 PASCAL’S PRINCIPLE 24. How much pressure is transmitted in the hydraulic system considered in Example 11.6 ? Express your answer in pascals and in atmospheres. Solution 26. A crass host pours the remnants of several bottles of wine into a jug after a party. He then inserts a cork with a 2.00-cm diameter into the bottle, placing it in direct contact with the wine. He is amazed when he pounds the cork into place and the bottom of the jug (with a 14.0-cm diameter) breaks away. Calculate the extra force exerted against the bottom if he pounded the cork with a 120-N force. Solution 28. (a) Verify that work input equals work output for a hydraulic system assuming no losses to friction. Do this by showing that the distance the output force moves is reduced by the same factor that the output force is increased. Assume the volume of the fluid is constant. (b) What effect would friction within the fluid and between components in the system have on the output force? How would this depend on whether or not the fluid is moving? Solution (a)