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Multiple Choice:
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1. A person sips a drink through a straw. At which of the following three positions
is the pressure lowest?
I.
Inside the person's mouth
II.
At the surface of the drink
III.
At the bottom of the drink
only at position I
only at position II
only at position III
both at positions I and III
both at positions I and II
2. The circulatory system can be modeled as an interconnected network of flexible
pipes (the arteries and veins) through which a pump (the heart) causes blood to
flow. Which of the following actions, while keeping all other aspects of the
system the same, would NOT cause the velocity of the blood to increase inside a
vein?
expanding the vein's diameter
cutting off blood flow to some other area of the body
increasing the heart rate
increasing the total amount of blood in the circulatory system
increasing the pressure difference between ends of the vein
3. A pirate ship hides out in a small inshore lake. It carries twenty ill-gotten
treasure chests in its hold. But lo, on the horizon the lookout spies a gunboat. To
get away, the pirate captain orders the heavy treasure chests jettisoned. The
chests sink to the lake bottom. What happens to the water level of the lake?
The water level drops.
The water level rises.
The water level does not change.
4. Brian saves 2-liter soda bottles so that he can construct a raft and float out onto
Haverford College's Duck Pond. If Brian has a mass of 80 kg, what minimum
number of bottles is necessary to support him? The density of water is 1000
kg/m3, and 1000 L = 1 m3.
A.
1600 bottles
800 bottles
200 bottles
40 bottles
4 bottles
Free Response:
5. The water tower in the drawing above is drained by a pipe that extends to the
ground. The amount of water in the top spherical portion of the tank is
significantly greater than the amount of water in the supporting column.
Information you may need: Density of water = 1000 kg/m3.
a. What is the absolute pressure at the position of the valve if the valve is
closed, assuming that the top surface of the water at point P is at
atmospheric pressure?
b. Now the valve is opened; thus, the pressure at the valve is forced to be
atmospheric pressure. What is the speed of the water past the valve?
c. Assuming that the radius of the circular valve opening is 10 cm, find the
volume flow rate out of the valve.
d. Considering that virtually all of the water is originally contained in the
top spherical portion of the tank, estimate the initial volume of water
contained by the water tower. Explain your reasoning thoroughly.
e. Estimate how long it would take to drain the tank completely using this
single valve.
6. Mercury is commonly supplied in flasks containing 34.5 kg (about 76 lb). What is the
volume in liters of this much mercury?
7. (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) 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.
8. 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 89.0cm 3 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: 2.70g/cm 3
9. 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.
10. (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.
Solution: (a) 0.163 m
(b) Equivalent to 19.4 gallons, which is reasonable
11. 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?
12. 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: 7.9×10 2 kg/m 3
13. 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.
14. 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 10 3 kg/m 3 . 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 7×10 8 m )?
Solution: (a) 10 18 kg/m 3
; (b) 2×10 4 m
Glossary
density: the mass per unit volume of a substance or object