The term
centripetal force is a generic term. If you were to talk about gravity, you
would know that only mass exerts a gravitational force. But a “centripetal
force” can be exerted by many different things.
A force
which pulls an object toward the center of a circle is called a
centripetal force. How much centripetal force needs to be exerted to
cause an object to move in a circle? Your experience should tell you that
the amount of centripetal force that you need to exert depends on
a. The
mass of the object you are whirling - heavier objects require more force
b. How
fast you are whirling it - going faster requires more force, and
c. The
radius of the circle
The
textbook gives the equation FRadial = mv2/r, but
how can we verify the quantitative relationship between centripetal force
and mass, speed, and radius? This question can't be answered all at once,
since a scientific experiment is designed to vary one quantity (holding all
others constant) and measure its effect on one other quantity. The
most difficult quantity (of mass, speed, and radius) to hold constant from
trial to trial in an experiment is the speed of the object, so it is easiest
to study the effect of speed on centripetal force, since it is relatively
easy to hold the mass of the object and the radius of the circle constant.
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Measure Effect of speed on centripetal force. You will use an apparatus similar to the one pictured on the right.
a. Keep the mass constant. This can be done during a set of trials by always whirling the same object.
b. Keep the radius of the circle constant This can be done (with a little practice) by keeping the upper clip a fixed distance
below the glass tube while whirling the object.
Don’t let the clip touch the tube because it will provide an additional force that we
can not quantify.
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Procedure
Place a
small number of washers, of measured mass, on the bottom clip of the
apparatus. This part of the apparatus hangs straight down, and the weight of
the washers supplies the centripetal force.
Practice
whirling the stopper (or ball) until you can keep the top clip a short
distance below the bottom of the glass tube while the stopper whirls.
IMPORTANT! If the clip touches the bottom of the glass tube, the weights are
no longer supplying the centripetal force!
Details
1. Use a
stopwatch to measure the time taken for a reasonable number of revolutions
(20).
2. Record
your data.
3. Change
the number of washers on the bottom clip (centripetal force) and repeat
steps 1 and 2; repeat for
five different
weights.
4. Record
the data.
Format
for Data Table
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Trial |
Weight |
Time (20 Rev) |
Period |
V, Linear Speed |
V2 |
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1 |
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2 |
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3 |
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4 |
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5 |
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Calculate
the period of revolution, T (the time to go around once) for each trial.
Show a
sample calculation.
Calculate
the linear speed, v, of the stopper for each trial. Include a sample
calculation. (Note: v = 2 p r/T)
Theoretically, the centripetal force should be directly proportional to the
square of the speed. To check this, add a column to your data
table for v2. Construct a graph of centripetal force versus v2.
Remember
that it is customary to put the quantity you change (force, in this case) on
the horizontal axis, and the quantity that changes by itself (speed) on the
vertical axis. Be sure that you pick the largest convenient scale for your
graph and draw the best smooth curve through your data points.
In Your
Conclusions
Include
1. A
table with all data neatly displayed
2. All
calculations shown, and then recorded in the data table
3. A
graph that estimates the best fit function for your data
Discuss
the following
1. Is the
graph of centripetal force versus speed squared a straight line?
2. What
can you say about the relationship between centripetal force and speed,
then?
Submit
your report in the following format - use the stated heading for each of the
6 paragraphs.
1.
Problem statement: Clear statement of what you are trying to do
2.
Hypothesis: Suggested explanation of the observed phenomenon
3.
Approach: Short summary of how you plan to solve the problem
4. Data
recorded: Data obtained from the experiment – turn in your initialed data
sheet
5.
Analysis of the data: What the data means
6.
Conclusion:
a. Conclusions
drawn from above analysis
b. Possible
sources of error.