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Investigation of a Centripetal Force
We will investigate the centripetal force supplied by a spring when an object is
rotating with constant speed. A centripetal or center-seeking force is required to hold an
object in a circular path.
Advance Study Assignment
Review sections 10.3 and 5.2 in Principles of Physics, 4th edition, by Serway and
Jewett or sections 7.3 – 7.4 in College Physics, 7th ed., by Serway/Faughn. Write down
how the tangential speed, vt, is related to the angular speed, ω, for a particle moving in a
circular path of radius, r.
(1) _____________________________________________________
Write down how the Centripetal Force, F, is related to the tangential speed, vt,
for a particle of mass, m, moving in a circular path of radius, r.
(2) _____________________________________________________
Substitute Equation (1) into Equation (2) to come up with and equation which
shows how the Centripetal Force, F, is related to the angular speed, ω, for a
particle of mass, m, moving in a circular path of radius, r.
(3) _____________________________________________________
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Equipment Needed
Pasco Computer Based Centripetal Force Accessory (ME-8089)
Pasco Rotating Platform (ME-8951)
Pasco Rotational Motor Drive (ME-8955)
DC Power Supply, 0 – 15 Volts, 1.5 amp
Vernier Rotational Motion Sensor (RMS-BTD)
Vernier Dual Range Force Sensor (DFS-BTA)
Vernier Computer Interface
Windows compatible computer with Vernier Logger Pro Software
Introduction and Initial Guesses
Based on equation (3), if the angular speed, ω, increases, how will the Centripetal
Force, F, change (for constant radius and mass)? If you graphed F on the y-axis vs ω on
the x axis, what sort of graph will result?
________________________________________________________________________
________________________________________________________________________
Based on equation (3), if the mass, m, of the object increases, how do you think
the Centripetal Force, F, changes (for constant radius, r, and angular speed, ω)? If you
graphed F on the y-axis vs m on the x-axis, what sort of graph will result?
________________________________________________________________________
________________________________________________________________________
Based on equation (3), if the radius, r, increases, what happens to the Centripetal
Force, F (for constant angular speed, ω, and mass, m)? If you graphed F on the y-axis vs r
on the x-axis, what sort of graph will result?
________________________________________________________________________
________________________________________________________________________
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Apparatus and Software Setup
Set up the apparatus as pictured. Carefully level the rotating platform with a
bubble level.
Figure 2: Centripetal Force Apparatus
Connect the RMS cable to dig/sonic 1 and the Dual Range Force Probe to CH 1
on the LabPro and power up the Computer.
Start up the Logger Pro Program and then open the Centripetal Force using RMS
& Force Sensor Experiment File (you may need to scroll to the right to find it).
You will be acquiring the Force and angular speed data.
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Investigation 1: How force changes with ω (constant radius & mass)
The radius and the mass of the sliding object will be held constant for this part of
the experiment.
(1) Place 100 grams on both the
Fixed Mass Holder and
Sliding Mass Holder. Since
the mass of the Sliding Mass
Holder is 50 grams, the total
mass being accelerated is 150
grams.
(2) Adjust the height of the Dual
Range Force Sensor so that
the Sliding Mass is
positioned at 21 cm with the
connecting steel leader taut.
Adjust the Fixed Mass
Holder to this same position
on the opposite side.
(3) Push the Sliding Mass in
Figure 3
and
slightly and click on
click “ok”. Turn on the
power supply connected to
the Rotational Motor Drive
and increase the voltage to 5
Volts or until a force of about
9 N is displayed on Logger
Pro. Caution - The rotating
platform will be spinning
rapidly.
(4) Press the
button in Logger Pro, and quickly turn off the power supply. The
rotating platform will slow down to rest and a graph of Force vs angular speed will be
displayed in Logger Pro. (See sample on next page)
(5) Record the mass being accelerated and the location of the sliding mass below
Mass
____
(kg).
Radius (location of sliding mass)
______________(m).
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Analysis
(1) What do you guess is the quantitative relationship between Force and Angular
Velocity, ω?
________________________________________________________________________
(2) Click on
. Click on “Define Function” and type in A*x^2 + B . Click “ok” and
then “Try Fit”. (See example below) Print your graph with the resulting fit showing.
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Did this functional relationship give a good fit to your data?
_____________________________________________________________
(3) Record the value of the fit constant A = _________________________.
Comparing to Equation 3, we see that A should be equal to m.r . Compute this value
below.
m.r = ___________________________.
(4) Calculate a percent difference between m.r and A _______________.
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Investigation 2: How F changes with m (constant r and ω)
The radius of rotation and the angular speed will be held constant for this part of the
experiment.
(1) In Logger Pro, Open the Centripetal Force using RMS & Force Sensor, Part 2
Experiment File (you may need to scroll to the right to find it).
(2) Remove the 100 gram mass from the Fixed and Sliding mass holders. Check to see
that the location of the sliding mass holder is 21 cm. Push the Sliding Mass in slightly
and click “ok”. Turn on the power supply connected to the Rotational
and click on
Motor Drive and increase the voltage to 4.0 volts. Caution - The rotating platform will be
spinning rapidly at about 10 rad/s.
(3) Press the
button in Logger Pro. After 10 seconds of data are collected, shut
button. Repeat this for
off the power supply. Click on the Force graph and then the
the Angular Speed graph. An example graph set is shown below.
Record the mean Force and mean Angular speed on the appropriate row in the data
table on the next page.
(4) Add 50 grams to the sliding and fixed mass holders. Turn on the power supply and
repeat step (3).
(5) Continue this process until the data table is filled.
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Table 1: Varying the Mass of the Object
Trial #
1
2
3
4
5
Sliding Mass (kg)
0.050
0.100
0.150
0.200
0.250
Force (N)
ω (rad/s)
Average Angular Speed for above 5 trials ________ _____(rad/s).
Constant radius for this table ________0.210_______(m).
Analysis
(1) What functional relationship between Force and Mass is suggested by this table?
____________________________________________________________
(2) Go to Page 3 in Logger Pro by clicking
twice. Enter the Mass and Force data
from the above table into the appropriate columns. Click on
and select a
proportional fit to the data. Print your graph with the resulting fit showing.
Did this functional relationship give a good fit to your data?
_____________________________________________________________
(3) Record the slope of the fit = _________________________.
Comparing to Equation 3, we see that the slope should be equal to r.ω2 . Compute this
value below.
r.ω2 = ___________________________.
(4) Calculate a percent difference between r.ω2and the slope _______________.
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Investigation 3: How force changes with radius (constant ω & m)
The angular speed and the mass of the sliding object will be held constant for this part of
the experiment.
Return to Page 1 in Logger Pro. Place 100 grams on the Sliding and Fixed Mass
holders. Follow the same procedures as in Investigation 2 and record the appropriate
data in table 2 below. The radius of the circular motion may be changed by lowering
the force probe so that the sliding mass has the positions in the data table. You will
also have to adjust the fixed mass to the same positions on the opposite side of the
rotating platform.
Table 2: Varying the Radius of the Circular Motion
Trial #
1
2
3
4
5
6
Position of sliding mass, r
(m)
0.210
0.180
0.150
0.120
0.090
0.060
Force (N)
ω (rad/s)
Sliding mass used ____0.150___(kg).
Average Angular Speed for above 6 trials ________ _____(rad/s).
Analysis
(1) What functional relationship between Force and Radius is suggested by this table?
____________________________________________________________
(2) Go to Page 4 in Logger Pro by clicking
three times. Enter the Radius and Force
and select a
data from the above table into the appropriate columns. Click on
proportional fit to the data. Print your graph with the resulting fit showing.
Did this functional relationship give a good fit to your data?
_____________________________________________________________
(3) Record the slope of the fit = _________________________.
Comparing to Equation 3, we see that the slope should be equal to mω2 . Compute this
value below.
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mω2 = ___________________________.
(4) Calculate a percent difference between m.ω2and the slope _______________.
Conclusion
After group discussion, write a conclusion that summarizes the results of your
investigations into Centripetal Force.