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Lesson Goals and New Content
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Students gain an understanding of
centripetal and centrifugal force and learn to differentiate the two,
and practice using a force analysis to solve circular motion
problems. The goal is for the students to correctly use inertia
and centripetal force to explain why we "feel" a centrifugal
force when moving in a circle.
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Procedure
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Opener (~10 min.)
(When doing this lesson, be sure to practice ahead of time, and
be careful of your surroundings!)
Bring out the bucket with a bit of water in the bottom. Have a
rope tied to the bucket prior to class. Show the students that
there is water in the bottom, and take a poll on who thinks you can keep
it in the bucket when you swing it. Then, swing it in both a
horizontal and a vertical circle. You can also invite some of the
students to come try it themselves; most find it surprising how heavy
the bucket feels when being swung.
Development (~25 min.)
Distribute the worksheet and have the students start the problems
on the front. The problems on the front do not require any
calculations, but it is my experience that the questions can start some
good discussions. In particular, since the students already know
that anything moving in a circle has a centripetal force acting on it,
many of them find it contradictory that this force helps keep the
water in the bucket, when it points out of the bucket, not
in. Walk around and listen in on the groups, but allow the
discussions to take their course. If some groups progress quickly,
you can have them begin the problems on the back.
Closure (~10 min.)
Briefly go over the worksheet front with them. Take a poll
to see what people decided on for their free-body diagram in problem 1
b. In my experience, a large fraction will choose free-body
diagram B, since they expect a force to keep the water in the
bucket. If this is the case, introduce as a discrepant event the
fact that the bucket moves in a circle, and lead them towards the
concept of centripetal force. Conclude with them that the correct
free-body diagram is diagram A.
Now, ask them how this is consistent with the water staying in the
bucket. Some will probably have figured out that inertia is
responsible, but you can ask them some leading questions to help them
along. Ask them what path the bucket will follow if the rope
suddenly breaks. You can also have them think back on the inertia
lesson, if you did it with them earlier.
You should leave them with the conclusion that the centripetal force
always points towards the center of the circle, and that the inertia of
the water is what keeps it from falling out.
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Evaluation
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For evaluation, you can use the worksheet
as homework. Have the students fill out the front, or finish the
work they didn't complete in class. You can also assign them a
similar problem and have them explain as on the worksheet. (I.e.,
a car driving on a circular track or a roller coaster doing a
loop. In both cases, you feel pushed to the outside, even though
the centripetal force is directed towards the center of the circle.)
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