Unformatted text preview: Homework Solutions Chapter 10 5, 9, 13, 16, 22, 27, 31, 36, 48,77 , 52*, 61*, P5. A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 88.78 g. What is the specific gravity of this other fluid? Solution: Specific gravity by definition is the ratio of the density of the material to the density of water (at 4°C). ? kg kg
kg kg kg kg kg kg P9. (a) Calculate the total force of the atmosphere acting on the top of a table that measures 1.6 m 2.9 m (b) What is the total force acting upward on the underside of the table? Solution: (a) (b) ! N N ! " ! ## P13. How high would the level be in an alcohol barometer at normal atmospheric pressure? Solution:
P=0 h Po A
N m$ # !# ( )! ( )! !
kg m N m$ % "
N m$ & ' m/s$ m P16. Water and then oil (which don't mix) are poured into a U-shaped tube, open at both ends. They come to equilibrium as shown in Fig. 10-49. What is the density of the oil? Solution: Pressure at p.a and p.b is the same: ( ) $ $m (
$ $m $ $m m kg m $ $m
kg m m P22. A geologist finds that a Moon rock whose mass is 9.28 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock? Solution: ## "
+ ) ) & &* &* $ kg , kg kg m m
kg m $ kg m P27. What is the likely identity of a metal (see Table 10-1) if a sample has a mass of 63.5 g when measured in air and an apparent mass of 55.4 g when submerged in water? Solution:
+ , kg
, , kg m
kg ,m kg m kg m - iron or steel P31. Archimedes's principle can be used not only to determine the specific gravity of a solid using a known liquid; the reverse can be done as well. (a) As an example, a 3.40 kg aluminum ball has an apparent mass of 2.10 kg when submerged in a particular liquid: calculate the density of the liquid. (b) Derive a formula for determining the density of a liquid using this procedure. Solution:
+ . .
& & & kg m & & & .
& & P36. A 15-cm radius air duct is used to replenish the air of a room 9.2 m every 16 min. How fast does air flow in the duct? Solution: / " 9.2 m 5.0 m 4.5 m / 5.0 m 4.5 m $ m ! 0. 0
$. % " $ m $ m --, min ,s ---min 3.1 m/s P48*. In Fig. 10-54, take into account the speed of the top surface of the tank and show that the speed of fluid leaving the opening at the bottom is 0
$ $ $ , where ! 1$ 1$ , and and $ are the areas of the opening and of the top surface, respectively. Assume 2 $ so that the flow remains nearly steady and laminar. — — P52 . P61 . P77. A copper weight is placed on top of a 0.50 kg block of wood density = 0.60
kg m floating in water, as shown in Fig.10-57. What is the mass of the copper if the top of the wood block is exactly at the water's surface? Solution: )( )( )(
3 3 3 3 ) ) ) & ) ) kg ...
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