Stewart_Calc_7ET ch06sec04
MULTIPLE CHOICE
1. A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to
a length of 15 cm. How much work is done in stretching the spring from cm to cm?
a.
b.
c.
d.
e.
2. A heavy rope, ft long, weighs lb/ft and hangs over the edge of a building 110 ft
high. How much work is done in pulling the rope to the top of the building?
a.
b.
c.
d.
e.
3. A tank is full of water. Find the work required to pump the water out of the outlet.
a.
b.
c.
d.
e.
None of these
4. A spring has a natural length of cm. If a force of N is required to keep it stretched to
a length of cm, how much work is required to stretch it from cm to cm?
a.
b.
c.
d.
e.
5. If J of work are needed to stretch a spring from cm to cm and another J are
needed to stretch it from cm to cm, what is the natural length of the spring? Round
the answer to nearest integer.
a.
b.
c.
d.
e.
6. A bucket weighs lb and a rope of negligible weight are used to draw water from a well
that is ft deep. The bucket starts with 50 lb of water and is pulled up at a rate of 10 ft/s,
but water leaks out of a hole in the bucket at a rate of 0.5 lb/s. Find the work done in pulling
the bucket to the top of the well.
a.
b.
c.
d.
e.
7. Newton’s Law of Gravitation states that two bodies with masses attract each
other with a force
where r is the distance between the bodies and G is the gravitation constant. If one of bodies
is fixed, find the work needed to move the other from to .
a.
b.
c.
d.
e.
8. An aquarium m long, 1 m wide, and 1 m deep is full of water. Find the work needed to
pump half of the water out of the aquarium. (Use the facts that the density of water is
)
a.
b.
c.
d.
e.
9. A particle moves a distance of 150 ft along a straight line. As it moves, it is acted upon by
a constant force of magnitude 15 lb in a direction opposite to that of the motion. What is
the work done by the force?
a.
ft–lb
b.
ft–lb
c.
–2250 ft-lb
d.
ft–lb
NUMERIC RESPONSE
−1
2250
−10
−1
10
1. Find the work done in pushing a car a distance of m while exerting a constant force of
N.
2. In a steam engine the pressure and volume of steam satisfy the equation , where k
is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no
heat transfer between the cylinder and its surroundings.) Calculate the work done by the
engine (in ft-lb) during a cycle when the steam starts at a pressure of and a
volume of and expands to a volume of Use the fact that the work done by
the gas when the volume expands from to volume is
.
3. True or False?
If a force of 6 lbs is required to hold a spring stretched 5 inches beyond its natural length,
then 38.4 lb-in. of work is done in stretching it from its natural length to 8 in. beyond its
natural length.