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Example: more about clothes dryers!
Question: In a discussion question in the previous section, we
made the assumption that the clothes remain against the inside
of the drum as they go over the top. In light of the previous
example, is this a correct assumption.
Solution: No. We know that there must be some minimum speed
at which the motor can run that will result in the clothes just
barely staying against the inside of the drum as they go over the
top. If the clothes dryer ran at just this minimum speed, then
there would be no normal force on the clothes at the top: they
would be on the verge of losing contact. The only force acting on
them at the top would be the force of gravity, which would give
them an acceleration of g=9.8 m/s
2
. The actual dryer must be
running slower than this minimum speed, because it produces an
acceleration of only 8.8 m/s
2
. My theory is that this is done
intentionally, to make the clothes mix and tumble.
Discussion Question
A. A certain amount of force is needed to provide the acceleration of circular
motion. What if were are exerting a force perpendicular to the direction of
motion in an attempt to make an object trace a circle of radius r, but the force
isn’t as big as m|v|
2
/r.
B. Suppose a rotating space station is built that gives its occupants the illusion
of ordinary gravity. What happens when a person in the station lets go of a
ball. What happens when she throws a ball straight “up” in the air (i.e. towards
the center).
An artist’s conception of a rotating space
colony in the form of a giant wheel. A
person living in this noninertial frame of
reference has an illusion of a force pull-
ing her outward, toward the deck, for the
same reason that a person in the pickup
truck has the illusion of a force pulling
the bowling ball. By adjusting the speed
of rotation, the designers can make an
acceleration |v|
2
/r equal to the usual ac-
celeration of gravity on earth. On earth,
your acceleration standing on the ground
is zero, and a falling rock heads for your
feet with an acceleration of 9.8 m/s
2
. A
person standing on the deck of the space
colony has an upward acceleration of 9.8
m/s
2
, and when she lets go of a rock,
her feet head up at the nonaccelerating
rock. To her, it seems the same as true
gravity.
Art by NASA.
Chapter 9Circular Motion