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453
Chapter 7: Applications of Integration
____
9.
A tank with a base of 4 feet by 3 feet and a height of 4 feet is full of water. The water
weighs 62.4 pounds per cubic foot. How much work is done in pumping water out over the top
edge in order to empty half of the tank. Round your answer to one decimal place.
499.2 ft-lb
748.8 ft-lb
5,990.4 ft-lb
1,996.8 ft-lb
1,497.6 ft-lb
____ 10. A cylindrical water tank 5 meters high with a radius of 2 meters is buried so that the top of
the tank is 1 meter below ground level. How much work is done in pumping a full tank of water up
to ground level? (The water weighs 9800 newtons per cubic meter.)
548,800 joules
686,000 joules
411,600 joules
1,234,800 joules
1,029,000 joules
____ 11. An open tank has the shape of a right circular cone. The tank is 9 feet across the top and 8
feet high. How much work is done in emptying the tank by pumping the water over the top edge?
Note: The density of water is 62.4 lbs per cubic foot.
6,739.20 ft-lb
4,043.52 ft-lb
5,391.36 ft-lb
10,108.80 ft-lb
12,130.56 ft-lb
7.5 Work
454
____ 12.
A cylindrical gasoline tank 4 feet in diameter and 4 feet long is carried on the bank of
a truck and is used to fuel tractors. The axis of the tank is horizontal. The opening on the tractor tank
is 5 feet above the top of the tank in the truck. Find the work done in pumping the entire gasoline
contents that weighs 42 pounds per cubic feet of the fuel tank into a tractor. (Hint: Evaluate one
integral by geometric formula and the other by observing that the integrand is an odd function.)
9,408 ft-lb
4,704 ft-lb
2,352 ft-lb
25,088 ft-lb
20,608 ft-lb
____ 13. A 17-foot chain that weighs 4 pounds per cubic foot hangs from a winch 17 feet above
ground level. Find the work done by the winch in winding up the entire chain.
346.80 ft-lb
1,040.40 ft-lb
867.00 ft-lb
462.40 ft-lb
578.00 ft-lb
____ 14. A quantity of gas with an initial volume of 8 cubic feet and a pressure of 1500 pounds
per square foot expands to a volume of 10 cubic feet. Find the work done by the gas for the given
volume and pressure. Round your answer to two decimal places.
1,606.63 ft-lb
4,016.58 ft-lb
4,819.90 ft-lb
2,677.72 ft-lb
2,142.18 ft-lb
____ 15. A quantity of a gas with an initial volume of 1 cubic foot and a pressure of 2000 pounds
per square foot expands to a volume of 7 cubic feet. Find the work done by the gas. Round your
answer to two decimal places.
3,841.82 ft-lb
3,891.82 ft-lb
1,714.29 ft-lb
1,959.18 ft-lb
3,583.52 ft-lb
455 Chapter 7: Applications of Integration
____ 16. Two electrons repel each other with a force that varies inversely as the square of the
distance between them, where k is the constant of proportionality. One electron is fixed at the point
. Find the work done in moving the second electron from to .
units of work
units of work
units of work
units of work
units of work
7.5 Work
456
7.5 Work
Answer Section
457 Chapter 7: Applications of Integration
7.6 Moments, Centers of Mass, and Centroids
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the center of mass of the point masses lying on the x-axis.
a.
b.
c.
d.
e.
____ 2. Find the center of mass of the point masses lying on the x-axis.
a.
b.
c.
d.
e.
7.6 Moments, Centers of Mass, and Centroids
458
____ 3.
Find the center of mass of the point masses lying on the x-axis.
a.
b.
c.
d.
e.
____ 4. Consider a beam of length feet with a fulcrum x feet from one end as shown in the
figure. Two objects weighing 36 pounds and 108 pounds are placed at opposite ends of the beam.
Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is
equilibrium.
10 feet
11 feet
8 feet
9 feet
7 feet
459
Chapter 7: Applications of Integration
____
5.
Consider a beam of length
feet with a fulcrum x feet from one end as shown in
the figure. In order to move a 550-pound object, a person weighing 214 pounds wants to balance it on
the beam. Find x (the distance between the person and the fulcrum) such that the system is
equilibrium. Round your answer to two decimal places.
5.10 feet
3.35 feet
3.45 feet
4.60 feet
3.60 feet
____ 6. Find the center of mass of the given system of point masses.
a.
b.
c.
d.
e.
7.6 Moments, Centers of Mass, and Centroids
460
____ 7.
Find the center of mass of the given system of point masses.
a.
b.
c.
d.
e.
____ 8. Find the center of mass of the given system of point masses.
a.
b.
c.
d.
e.
461
Chapter 7: Applications of Integration
____
9.
Find
for the lamina of uniform density
bounded by the graphs of the
equations
.
a.
b.
c.
d.
e.
____ 10. Find for the lamina of uniform density bounded by the graphs of the
equations
.
a.
b.
c.
d.
e.
____ 11. Find Mx, My, and for the lamina of uniform density bounded by the graphs of the
equations .
a.
7.6 Moments, Centers of Mass, and Centroids
462
b.
c.
d.
e.
____ 12. Find Mx, My, and for the lamina of uniform density bounded by the graphs
of the equations .
a.
b.
c.
d.
e.
____ 13. Find for the lamina of uniform density bounded by the graphs of the
equations .
a.
463 Chapter 7: Applications of Integration
b.
c.
d.
e.
____
14.
Find
for the lamina of uniform density
bounded by the graphs of the
equations
.
a.
b.
c.
d.
e.
____
15.
Set up and evaluate integrals for finding the moment about the y-axis for the region
bounded by the graphs of the equations. (Assume
.)
.
a.
b.
c.
d.
e.
