95
Chapter 11: Applications of Integration
725. Suppose a 20-foot hanging chain weighs
4 pounds per foot. In foot-pounds, how
much work is done in lifting the end of the
chain to the top so that the chain is folded
in half?
726. A 20-meter chain lying on the ground has a
mass of 100 kilograms. In joules, how much
work is required to raise one end of the
chain to a height of 5 meters? Assume that
the chain is L-shaped after being lifted
with a remaining 15 meters of chain on
the ground and that the chain slides
without friction as its end is lifted. Also
assume that the weight density of the
chain is constant and is equal to
100
20
9 8
49
kg/m
m/s
N/m
2
.
. Round to
the nearest joule. (Note: 1 newton-meter =
1 joule.)
727. A trough has a triangular face, and the
width and height of the triangle each equal
4 meters. The trough is 10 meters long and
has a 3-meter spout attached to the top of
the tank. If the tank is full of water, how
much work is required to empty it? Round
to the nearest joule. (Note: The acceleration
due to gravity is 9.8 meters per second
squared, and the density of water is
1,000 kilograms per cubic meter.)
721. A particle is located at a distance x meters
from the origin, and a force of 2
6
sin π x
( )
newtons acts on it. In joules, how much
work is done moving the particle from
x = 1 to x = 2? The force is directed
along the x-axis. Find an exact answer.
(Note: 1 newton-meter = 1 joule.)
722. Five joules of work is required to stretch a
spring from its natural length of 15 centimeters to a length of 25 centimeters. In joules,
how much work is required to stretch the
spring from a length of 30 centimeters to a
length of 42 centimeters? (Note: For a
spring, force equals the spring constant k
multiplied by the spring’s displacement
from its natural length: F(x) = kx. Also note
that 1 newton-meter = 1 joule.)
723. It takes a force of 15 pounds to stretch a
spring 6 inches beyond its natural length. In
foot-pounds, how much work is required to
stretch the spring 8 inches beyond its natural length? (Note: For a spring, force equals
the spring constant k multiplied by the
spring’s displacement from its natural
length: F(x) = kx.)
724. Suppose a spring has a natural length of
10 centimeters. If a force of 30 newtons is
required to stretch the spring to a length of
15 centimeters, how much work (in joules)
is required to stretch the spring from 15
centimeters to 20 centimeters? (Note: For a
spring, force equals the spring constant k
multiplied by the spring’s displacement
from its natural length: F(x) = kx. Also note
that 1 newton-meter = 1 joule.)
Chapter 11: Applications of Integration
725. Suppose a 20-foot hanging chain weighs
4 pounds per foot. In foot-pounds, how
much work is done in lifting the end of the
chain to the top so that the chain is folded
in half?
726. A 20-meter chain lying on the ground has a
mass of 100 kilograms. In joules, how much
work is required to raise one end of the
chain to a height of 5 meters? Assume that
the chain is L-shaped after being lifted
with a remaining 15 meters of chain on
the ground and that the chain slides
without friction as its end is lifted. Also
assume that the weight density of the
chain is constant and is equal to
100
20
9 8
49
kg/m
m/s
N/m
2
.
. Round to
the nearest joule. (Note: 1 newton-meter =
1 joule.)
727. A trough has a triangular face, and the
width and height of the triangle each equal
4 meters. The trough is 10 meters long and
has a 3-meter spout attached to the top of
the tank. If the tank is full of water, how
much work is required to empty it? Round
to the nearest joule. (Note: The acceleration
due to gravity is 9.8 meters per second
squared, and the density of water is
1,000 kilograms per cubic meter.)
721. A particle is located at a distance x meters
from the origin, and a force of 2
6
sin π x
( )
newtons acts on it. In joules, how much
work is done moving the particle from
x = 1 to x = 2? The force is directed
along the x-axis. Find an exact answer.
(Note: 1 newton-meter = 1 joule.)
722. Five joules of work is required to stretch a
spring from its natural length of 15 centimeters to a length of 25 centimeters. In joules,
how much work is required to stretch the
spring from a length of 30 centimeters to a
length of 42 centimeters? (Note: For a
spring, force equals the spring constant k
multiplied by the spring’s displacement
from its natural length: F(x) = kx. Also note
that 1 newton-meter = 1 joule.)
723. It takes a force of 15 pounds to stretch a
spring 6 inches beyond its natural length. In
foot-pounds, how much work is required to
stretch the spring 8 inches beyond its natural length? (Note: For a spring, force equals
the spring constant k multiplied by the
spring’s displacement from its natural
length: F(x) = kx.)
724. Suppose a spring has a natural length of
10 centimeters. If a force of 30 newtons is
required to stretch the spring to a length of
15 centimeters, how much work (in joules)
is required to stretch the spring from 15
centimeters to 20 centimeters? (Note: For a
spring, force equals the spring constant k
multiplied by the spring’s displacement
from its natural length: F(x) = kx. Also note
that 1 newton-meter = 1 joule.)