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Chapter 15
Due: 12:00am on Saturday, July 3, 2010
No t e: Y ou w il l r ec ei ve no c re di t f or l at e s ub mi ss io ns . To learn more, read your instructor's Grading Policy
A Water Tank on Mars
Description: Find the net downward force on the bottom of a water tank on Mars.
You are assigned the design of a cylindrical, pressurized water tank for a future colony on Mars, where the acceleration due
to gravity is 3.71 meters per second per second. The pressure at the surface of the water will be 150
, and the depth of
the water will be 14.5
. The pressure of the air in the building outside the tank will be 87.0
.
Part A
Find the net downward force on the tank's flat bottom, of area 1.60
, exerted by the water and air inside the tank and
the air outside the tank.
Hint A.1
The net force
The net force on the tank's flat bottom is the sum of the (downward) force exerted on the bottom of the tank by the water
and the (upward) force exerted on the bottom of the tank by the air outside the tank.
Hint A.2
What is
(a Pascal)?
The SI unit of pressure, a Pascal, is a force per unit area: 1
Hint A.3
= 1
.
Density of water
The density of water is 1
Hint A.4
.
Find the force exerted on the tank's bottom by the air outside the tank
Write an expression for the force exerted on the tank's bottom by the air outside the tank.
Hint A.4.1 Pressure and force
The pressure
in a gas is defined as the normal force
exerted by the gas on a surface in contact with it. If the
force is the same at all points of a finite plane surface with area
, then the pressure is uniform and given by
.
Express your answer numerically to three significant figures.
ANSWER:
Hint A.5
Find the force exerted on the tank's bottom by the water
Write an expression for the force exerted on the tank's bottom by the water in the tank. Keep in mind that the water tank
is located on Mars, so weights depend on the acceleration due to gravity on that particular planet.
Hint A.5.1 Find the pressure exerted by the water on the bottom of the tank
In a fluid of uniform density
, the pressure
at a depth
is given by the pressure
at the surface plus a term
due to the weight of the fluid above that point. In other words,
where
is the magnitude of the acceleration due to gravity.
Given this information, find the pressure exerted by the water on the bottom of the tank.
Express your answer numerically in pascals, to three significant figures.
ANSWER:
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Hint A.5.2 Pressure and force
The pressure
in a gas is defined as the normal force
exerted by the gas on a surface in contact with it. If the
force is the same at all points of a finite plane surface with area
, then the pressure is uniform and given by
.
Express your answer numerically in Newtons, to three significant figures.
ANSWER:
Express your answer numerically in Newtons, to three significant figures.
ANSWER:
Problem 15.76
Description: One vertical wall of an above-ground swimming pool is in the shape of a regular trapezoid, with one base 10
m long on level ground and the other 20 m long a height of 3 m above it. (a) If the pool is filled to the top with water,
what is the net...
One vertical wall of an above-ground swimming pool is in the shape of a regular trapezoid, with one base 10
ground and the other 20
long a height of 3
above it.
long on level
Part A
If the pool is filled to the top with water, what is the net fluid force on the wall?
Hint A.1
Consider both the force exerted by the water on one side of the wall, and the force exerted by the atmosphere on the
other side.
Express your answer using two significant figures.
ANSWER:
=
Problem 15.27
Description: A vertical tube open at the top contains h of oil (density 0.82 ( g/cm)^3) floating on h of water. (a) Find
the gauge pressure at the bottom of the tube.
A vertical tube open at the top contains 8.0
of oil (density 0.82
) floating on 8.0
of water.
Part A
Find the gauge pressure at the bottom of the tube.
Express your answer using two significant figures.
ANSWER:
=
Problem 15.41
Description: A fully loaded Volvo station wagon has a mass of 1950 kg. (a) If each of its four tires is inflated to a
gauge pressure of P, what is the total tire area in contact with the road?
A fully loaded Volvo station wagon has a mass of 1950
.
Part A
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If each of its four tires is inflated to a gauge pressure of 290
, what is the total tire area in contact with the
road?
ANSWER:
=
Problem 15.47
Description: A garage lift has a D diameter piston supporting the load. Compressed air with a maximum pressure of P is
applied to a small piston at the other end of the hydraulic system. (a) What is the maximum mass the lift can support?
A garage lift has a 42
diameter piston supporting the load. Compressed air with a maximum pressure of 500
is
applied to a small piston at the other end of the hydraulic system.
Part A
What is the maximum mass the lift can support?
Express your answer using four significant figures.
ANSWER:
=
Problem 15.58
Description: The venturi flowmeter shown in the figure is used to measure the flow rate of water in a solar collector
system. The flowmeter is inserted in a pipe with diameter D1; at the venturi of the flowmeter the diameter is reduced to
D2. The manometer tube...
The venturi flowmeter shown in the figure is used to measure the flow rate
of water in a solar collector system. The flowmeter is inserted in a pipe
with diameter 1.9
; at the venturi of the flowmeter the diameter is
reduced to 0.64
. The manometer tube contains oil with density 0.82 times
that of water.
Part A
If the difference in oil levels on the two sides of the manometer tube is 1.1
, what is the volume flow rate?
Express your answer using two significant figures.
ANSWER:
=
Problem 15.63
Description: A drinking straw 20 cm long and 3.0 mm in diameter stands vertically in a cup of juice D1 in diameter. A
section of straw s long extends above the juice. A child sucks on the straw, and the level of juice in the glass begins
dropping at v. (a) By how ...
A drinking straw 20
long and 3.0
in diameter stands vertically in a cup of juice 8.0
in diameter. A section of
straw 7.0
long extends above the juice. A child sucks on the straw, and the level of juice in the glass begins dropping
at 0.16
.
Part A
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By how much does the pressure in the child's mouth differ from atmospheric pressure?
Express your answer using two significant figures.
ANSWER:
=
Part B
What is the greatest height from which the child could drink, assuming this same mouth pressure?
Express your answer using two significant figures.
ANSWER:
=
Problem 15.73
Description: The density of a solid sphere of radius R and mass M varies with distance from the center according to the
equation rho (kern 1pt) = rho_0 (kern 1pt) e^(r/R). (a) Determine the constant rho_0.
The density of a solid sphere of radius 10
equation
and mass 25
varies with distance from the center according to the
.
Part A
Determine the constant
.
Express your answer using two significant figures.
ANSWER:
=
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2009/11/14 上午 11:10