PHYSICS 101 Laboratory
Circular Motion and Centripetal Force
Name ____________________________
Date _____________________________
Table Number _____________________
Equipment needed:
Group Members______________________
___________________________________
___________________________________
Centripetal measurement device. Stop watch. Meter Stick. Mass Set.
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Introduction:
We learned in our class lectures that whenever we see an object moving in a circle at some constant
speed that it must be subjected to a constant force directed towards the center of the circle. We learned that this
force is called a centripetal force. In class lecture and in your textbook the expression for this force is given by
Fc = mac = m (v2 / r)
where Fc is the centripetal force, m is the mass of the object, ac = v2 / r is the centripetal acceleration, v is the
speed of the object and r is the radius of the circle.
We are now "experts" at indirectly determining speed for a moving object by measuring the time and distance
traveled by the object. Thus, we will determine speed by measuring the time it takes the object to travel the
distance around the circle and rewrite our equation in terms of this distance (circumference, 2πr) and the time
(period, T). Thus
v = distance / time
=2πr/T
and therefore
Fc = m ( 4π2r / T2 )
We will do a simple experiment to verify this relationship. We will use a rubber stopper on the end of a string and
cause the stopper to follow a circular "orbit" under a variety of centripetal force conditions. Such a centripetal
device is shown in the figure.
A rubber stopper of mass m is attached to
one end of a string and a hanging mass ( mh ) is
attached to the other end. The string passes
through a tube to permit the stopper to be swung
in a horizontal circle of radius r as shown in the
figure. The radius of the circle is kept constant
during the motion by insuring that a metal
paperclip attached to the string is at a constant
distance below the tube that is held by the hand
and used to twirl the string around. Maintaining
the clip at a constant distance below the bottom of
the tube insures that the distance from the top of
the tube to the stopper remains constant. We will
maintain the mass of the stopper constant
throughout this experiment.
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PHYSICS 101 Laboratory
Circular Motion and Centripetal Force
Procedure: NOTE – this is not to be just a one or two person activity. Rotate responsibilities so all may
participate
PLEASE READ THE INSTRUCTIONS VERY CAREFULLY
1. Pull enough string through the tube to allow for a radius of about 0.75 meter. Hang a single 50-g mass from the
end of the string to provide a centripetal force via tension in the string.
2.
Practice swinging the stopper so that it revolves in a plane as close to horizontal as possible. With the 50-g mass
( mh ) on the string to keep the stopper from getting away, whirl the stopper over your head while holding onto the
string below the tube with your other hand. Notice what happens as you increase the speed of the stopper or
change the radius of the circle.
Comment on how you must change the pull on the string as you change the speed or radius. Be sure to explain
how this may or may not fit what you predict from your knowledge of the force expression.
Each member of the group must do this part of the exercise (#2) in order to experience some
of the properties of centripetal force as well as to appreciate some of the difficulties with this
experiment.
3.
Using a circle radius of about 0.75 meter, carefully swing the stopper around at constant speed. Keep the clip
exactly in a fixed relation to the tube, about one centimeter below the tube, to insure that the radius remains
constant. Putting a mark on the string to be at the bottom of the tube is also a good reference. Do not let the clip
touch the tube, nor your fingers touch the clip or string, since this will contribute unknown force to the string! THIS
TAKES PRACTICE SO DON'T EXPECT TO BE ABLE TO ACCOMPLISH THE TASK WITHOUT WORKING AT IT!
4.
Find the amount of time for the stopper to complete one revolution (this is the period). Think about how you might
do this in a way to reduce the error of timing just one revolution. Use two timers and record each. Use the average
of the two times for the calculations. Enter your measurements in the data table below and compute the indicated
parameters.
5.
Repeat the experiment using masses ( mh ) of 100g, 150g, 200g, and 250g for your "centripetal force" masses.
NOTE: If necessary, use the appropriate number of washers as substitute for the masses.
Radius ( r ) =
Trial
Swinger
Timer
mh
(kg)
1
.05
2
.10
3
.15
4
.20
5
.25
Revs Time
(#)
(s)
2
Time/rev Fc= mh g v = 2πr/T
(s)
(m/s)
ac = v2/r
(m/s2)
PHYSICS 101 Laboratory
Circular Motion and Centripetal Force
6.
Now, test what we just obtained by comparing "theoretical" with the experimental results. Plot the experimental
centripetal force ( weight of the hanging mass ) vs the calculated (theoretical) centripetal acceleration. Label the
values of the axes as FORCE (N) for y-axis and ACCELERATION (m/s2) for the x-axis.
7.
Is the relationship linear ( a straight line )? Carefully fit a "best straight line" through your data. Discuss with your
instructor how to do this.
8.
According to Newton's second law, the force acting on the stopper should be directly proportional to its
acceleration. If we double the force, then the acceleration should be double. If one triples, so must the other.
Comment on how well your experiment matches this concept, mentioning how well your data corresponds to a
proportional relationship and what the constant of proportionality, i.e. the slope of the graph, represents.
9.
Measure the slope of the line using two widely separated points on the line ( not data points ). If you need
assistance, ask your instructor to show you on the board how to do this. Show your calculations. Label the slope
on your graph, indicating the two points used.
10. Measure the mass of the rubber stopper and compare to the slope value just calculated. Calculate a percent
difference.
11. Comment on the accuracy of your results and describe at least two sources of experimental error you may be
aware of.
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PHYSICS 101 Laboratory
Circular Motion and Centripetal Force
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