94 Part I: The Questions
717. A 300-pound uniform cable that’s 150 feet
long hangs vertically from the top of a tall
building. How much work is required to lift
the cable to the top of the building?
718. A container measuring 4 meters long,
2 meters wide, and 1 meter deep is full
of water. In joules, how much work is
required to pump the water out of the
container? (Note: The density of water
is 1,000 kilograms per cubic meter, and the
acceleration due to gravity is 9.8 meters per
second squared.)
719. If the work required to stretch a spring
2 feet beyond its natural length is
14 foot-pounds, how much work is
required to stretch the spring 18 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.)
720. A force of 8 newtons stretches a spring
9 centimeters beyond its natural length.
In joules, how much work is required to
stretch the spring from 12 centimeters
beyond its natural length to 22 centimeters
beyond its natural length? Round the
answer to the hundredths place. (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.)
Work Problems
712–735 Find the work required in each situation.
Note that if the force applied is constant, work equals
force times displacement (W = Fd); if the force is
variable, you use the integral W
f x dx
a
b
= ∫ ( ) , where
f
(x) is the force on the object at x and the object
moves from x = a to x = b.
712. In joules, how much work do you need
to lift a 50-kilogram weight 3 meters from
the floor? (Note: The acceleration due to
gravity is 9.8 meters per second squared.)
713. In joules, how much work is done pushing
a wagon a distance of 12 meters while
exerting a constant force of 800 newtons
in the direction of motion?
714. A heavy rope that is 30 feet long and weighs 0.75
pounds per foot hangs over the edge of a cliff.
In foot-pounds, how much work is required to
pull all the rope to the top of the cliff?
715. A heavy rope that is 30 feet long and weighs
0.75 pounds per foot hangs over the edge
of a cliff. In foot-pounds, how much work
is required to pull only half of the rope to
the top of the cliff?
716. A heavy industrial cable weighing 4 pounds
per foot is used to lift a 1,500-pound piece
of metal up to the top of a building. In footpounds, how much work is required if the
building is 300 feet tall?
717. A 300-pound uniform cable that’s 150 feet
long hangs vertically from the top of a tall
building. How much work is required to lift
the cable to the top of the building?
718. A container measuring 4 meters long,
2 meters wide, and 1 meter deep is full
of water. In joules, how much work is
required to pump the water out of the
container? (Note: The density of water
is 1,000 kilograms per cubic meter, and the
acceleration due to gravity is 9.8 meters per
second squared.)
719. If the work required to stretch a spring
2 feet beyond its natural length is
14 foot-pounds, how much work is
required to stretch the spring 18 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.)
720. A force of 8 newtons stretches a spring
9 centimeters beyond its natural length.
In joules, how much work is required to
stretch the spring from 12 centimeters
beyond its natural length to 22 centimeters
beyond its natural length? Round the
answer to the hundredths place. (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.)
Work Problems
712–735 Find the work required in each situation.
Note that if the force applied is constant, work equals
force times displacement (W = Fd); if the force is
variable, you use the integral W
f x dx
a
b
= ∫ ( ) , where
f
(x) is the force on the object at x and the object
moves from x = a to x = b.
712. In joules, how much work do you need
to lift a 50-kilogram weight 3 meters from
the floor? (Note: The acceleration due to
gravity is 9.8 meters per second squared.)
713. In joules, how much work is done pushing
a wagon a distance of 12 meters while
exerting a constant force of 800 newtons
in the direction of motion?
714. A heavy rope that is 30 feet long and weighs 0.75
pounds per foot hangs over the edge of a cliff.
In foot-pounds, how much work is required to
pull all the rope to the top of the cliff?
715. A heavy rope that is 30 feet long and weighs
0.75 pounds per foot hangs over the edge
of a cliff. In foot-pounds, how much work
is required to pull only half of the rope to
the top of the cliff?
716. A heavy industrial cable weighing 4 pounds
per foot is used to lift a 1,500-pound piece
of metal up to the top of a building. In footpounds, how much work is required if the
building is 300 feet tall?