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PHY 101
Centripetal Force
Name ___________________
Date: ______________
Lab Partners ___________________________________________
Introduction: As you now know, a force is required to change the velocity of an object. Velocity can change
in two ways, a change of direction and/or a change in magnitude. As you have learned, if the net force on an
object, and thus the acceleration, is perpendicular to the velocity at an instant in time then only the direction
of the velocity will change and the speed will remain constant. If the net force, and thus the acceleration, is
parallel, or anti-parallel, to the velocity then only the speed will change and not the direction. If the net force
is somehow created such that it is always perpendicular to the velocity then the particle will move at constant
speed and the velocity will continually change direction. The path of the object will be a circle if the force is
constant in magnitude.
The force, or combination of forces, that causes an object to move, or revolve, in a circle, or an arc, is called
the centripetal force. The centripetal force is not a new force, but rather it is the name given to the various
forces that cause the object to move in a circle. Examples are the tension in a string as you whirl a ball over
your head, static friction acting on the wheels of a car as it navigates a turn on a road, and gravity that acts on
the Moon to keep it in an (almost circular) orbit around Earth.
This lab is meant to take you through a process of discovery; a discovery of the correct relationship between
the magnitude of the centripetal force and other quantities like the mass of the revolving object, the object’s
speed and the radius of the circular path. From past experience you may know an equation for this
relationship, but for the purpose of this lab please pretend that you have forgotten that equation. In other
words, nowhere in this lab should you use that equation to calculate anything. Only in the end, in your
conclusion, can you compare what you discovered in this lab with what you thought was true from past
experience.
You will use the apparatus shown in the picture below.
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The apparatus consists of a nearly frictionless vertical rod that is free to rotate. Mounted on top of this rod is
another horizontal rod that serves to support the rotating mass and provide counterbalance so the whole
system does not wobble. The mass that you will be forcing to travel in a circular path is the black object with
the pointy bottom and the eye-bolt on top. We’ll call this mass the bob. (A bob is often the name given to a
hanging, or swinging mass.) A spring is connected between the vertical rod and the bob. This spring will be
providing the centripetal force. If the spring is not there then when you rotate the vertical rod, the bob will
swing outward and a component of tension in the support string would be providing the centripetal force. Do
not try this! The support string could break sending the bob flying off at a high speed possibly resulting in
injury or death! Ok, probably not death to you, but certainly death to your lab grade. DONOT TRY THIS
LAB WITHOUT THE SPRING.
Calibration Steps: For all steps in this lab you will want the support string to be in a vertical plane as
you rotate the vertical rod so that the centripetal force is provided solely by the spring. You may also need to
adjust the length of the support string so that the spring connecting the bob to the vertical rod is horizontal. A
vertical metal pointer is provided to help you ensure the bob’s path is indeed circular as you rotate it at a
constant speed. You would first adjust the pointer so that it is a specified distance from the center of the
vertical rod. Then you would disconnect the spring from the bob and adjust the horizontal rod so that the bob
hangs directly over the pointer. Before you do any rotating you must be sure the horizontal rod and the
counterweight are secure. It is a good idea to wear safety goggles in the event that something comes
loose. Once everything is secure you may reconnect the spring.
Now that you have established a radius for the bob’s circular path and reconnected the spring you will notice
that spring pulls the bob in toward the vertical rod. When you rotate the vertical rod, the bob will move
outward. If the angular velocity is just right the bob will pass directly over the pointer on each revolution.
The spring is now stretched by a certain amount and provides the centripetal force that keeps the bob moving
in the circular path.
You can directly measure the force (the centripetal force) that the spring will exert on the bob when the
bob is revolving in its circular path. To do this, stop the rotation and, without disconnecting the spring, loop
the string attached to the bob, opposite the spring, over the pulley and add hanging weights until the bob is
directly over the pointer. The spring is now stretched the same amount as when the bob was rotating. The
weight of the hanging weights will be a direct measure of the force the spring is providing when the bob is
revolving in its circular path.
Setting the radius of the circular path is easy, but how do you measure the bob’s speed? The easiest way to
do this is to measure the amount of time that it takes for the bob to revolve 15 to 25 times, divide this time by
the number of revolutions to get the time for one revolution, the period, T, and then divide the circle’s
circumference by T to get the speed.
Part I: The First Trial:
Remove the bob from the supporting string and from the spring and measure it’s mass. Record this in the
Data section. Reattach the bob. Adjust the eye-bolt, connected to the spring, on the vertical rod by loosening
the wing nut so that the eye-bolt is centered on the vertical rod. Adjust the vertical pointer to a position
midway between its limits and secure it in place. Adjust the horizontal rod so that the bob hangs freely above
the pointer without the spring attached. Reconnect the spring and directly measure the spring force (as
described above) that will exist when the bob is revolving in a circle with this radius. Record this data in the
Data section for Part I.
Decide on the number of revolutions that you will be timing and record this number in the Data section. One
lab partner should practice rotating the vertical rod so that the bob moves at a constant speed and passes over
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the pointer every time. Once you are satisfied that this can be done precisely do three trials to determine the
total time for the number of revolutions that you decided on earlier. Record these times in Table 1.
Using these times calculate the average time per revolution and then the speed of the bob. Record these
numbers in the appropriate spots below Table 1.
What you have now done is established a starting point that we can use to compare how the centripetal force
changes as we change variables such as the mass of the bob, the speed of the bob, and the radius of the
circular path.
Part II: Dependence of Centripetal Force on Speed:
Do not change the position of the pointer, or the mass of the bob. We only want to change the speed of the
bob as it revolves in the same circular path as in Part I. How do we change the speed? Try spinning the
vertical rod slower than you had in Part I. Does the bob revolve in the same circular path? What should you
change so that the bob does revolve in the same circular path but at a slower speed? Discuss this with you lab
partners then with your instructor. Make the necessary change and do three trials as in Part I where you
measure the time for a certain number of revolutions, find the average time per revolution, find the bob’s
speed, and measure the centripetal force directly. Enter this data in Table 2 and in the area below Table 2.
(Hint: The change(s) you make may involve a significant change in how “the eye-bolt” is connected, but you
should not change the radius of the circular path and thus you should not move the horizontal rod or vertical
pointer.)
Do the above procedures again, but try to give the bob a speed faster than you had in Part I. What change is
necessary (without changing the bob’s mass, or the radius of the circle) to keep the bob traveling in the same
circular path but with a higher speed? Enter this data in Table 3 and the space below Table 3.
Since our goal is to determine how the centripetal force depends on speed we’d like to experiment with
several different speeds to be sure we find the correct relationship. So let’s do one more speed. You can
make a choice here, do you want to consider an even slower speed or an even faster speed? Make the
necessary adjustments (again without changing the radius or mass) and enter your data in Table 4.
Now you have four different speeds and the corresponding directly measured centripetal forces.
Proceed to the Questions section.
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Data
Mass of bob with eyebolt
Total number of
revolutions
Data For Part I:
Trail #
Total Time (s)
Time per Revolution
(s)
1
2
3
Table 1
Average Time per Revolution, T1
Radius of circular path, r1
Speed of bob
Mass of Hanger and Masses
Direct measurement of centripetal Force
Show calculation for the speed of the bob:
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Data For Part II:
Slower Speed
Same Radius as
Part I
Trail #
Total Time (s)
Time per Revolution (s)
1
2
3
Table 2
Average Time per Revolution
Speed of bob
Mass of Hanger and Masses
Direct measurement of centripetal Force
Show calculation for the speed of the bob:
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Greater Speed
Same Radius as
Part I
Trail #
Total Time (s)
Time per Revolution (s)
1
2
3
Table 3
Average Time per Revolution
Speed of bob
Mass of Hanger and Masses
Direct measurement of centripetal Force
Show calculation for the speed of the bob:
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Even Greater or
Even Slower
Speed
Same Radius as
Part I
Trail #
Total Time (s)
Time per Revolution (s)
1
2
3
Table 4
Average Time per Revolution
Speed of bob
Mass of Hanger and Masses
Direct measurement of centripetal Force
Show calculation for the speed of the bob:
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Questions
1. What change did you make to give the bob a slower speed than in Part I without changing the mass of
the bob, or radius of the circular path? Explain how you did this.
2. What change did you make to give the bob a greater speed than in Part I without changing the mass
of the bob, or radius of the circular path? Explain how you did this.
3. Make a graph of Measured Centripetal Force as function of speed (with constant radius and mass) for
the four different speeds that you got in Part I and Part II. (Be sure to properly label the graph, and its
axes.) What kind of function fits this data best? Is it linear, quadratic, or exponential? What does this
tell you about how centripetal force depends on speed? Explain.
4. What were the most significant sources of error in this lab and what did you do to minimize their
affect?
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