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Instruction Manual
Manual No. 012-08862
Discover Centripetal
Force Kit
Model No. ME-9837
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Table of Contents
Equipment List........................................................... 3
Introduction ............................................................. 4
Equipment Setup ........................................................ 5
The Classic Centripetal Force Lab..................................... 6
Velocity versus Force ................................................... 8
Velocity versus Mass ................................................... 9
Velocity versus Radius ................................................. 10
Questions ...............................................................11
Demonstrations .........................................................11
Model No. ME-9837
Appendix A: Technical Support .......................................12
Appendix B: Copyright and Warranty Information .................. 12
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Model No. ME-9837 Discover Centripetal Force Kit
Discover Centripetal Force Kit
Model No. ME-9837
Equipment List
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1 (#13)
1 (#10)
1 (#8)
1 (#6)
1 (#11.5)
Included Equipment Replacement
1. Rubber stoppers
(sizes: 6, 8, 10, 11.5, and 13)
2. Hollow tube (2)
3. Plastic ties (10)
4. Yellow string (73 m) ME-9876
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3
Model Number
* Please contact PASCO Technical Support when no replacement part number is provided.
Additional Equipment Recommended
Safety goggles
Marking pen
Force Sensor CI-6746 or PS-2104
Hooked Mass Set SE-8759
Newton Spring Scale (20N) SE-8718
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Discover Centripetal Force Kit Model No. ME-9837
Introduction
The Discover Centripetal Force Kit contains the materials necessary to
perform the classical centripetal force lab similar to the first example
listed in the table below. In addition, the Discover Centripetal Force
Kit can be used in conjunction with Force Sensors or Newton Spring
Scales.
Centripetal Force is an often misunderstood physical concept. Among
other things, the popular, yet, misused word "centrifugal" contributes
to students' misconceptions. An object moving in uniform circular
motion experiences a net inward-pointing force, called the centripetal
force. It is important for students to identify the agent for each force
that contributes to the centripetal force (net force) for an object moving
in uniform circular motion.
The table below gives examples of the centripetal force for certain
occurrences:
Situation
An object twirled in a horizontal
Centripetal Force
Tension from the string.
circle.
Car driving in a circle. Static friction on the tires directed
toward the center.
A satellite. Force due to gravity.
A “centrifuge.” The normal force from the wall of the
“centrifuge.”
Included with the Discover Centripetal Force Kit are rubber stoppers
of widely varying masses. Convenient blue ties are provided to attach
the stoppers easily to the bright, sturdy string. In addition, (2) two
tubes are included to use for multiple lab groups. The tubes are
chamfered to decrease friction on the string.
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Model No. ME-9837 Discover Centripetal Force Kit
Equipment Setup
hollow tube
string (1m)
loop in string
hooked mass
plastic tie
stopper
1. Cut a piece of string approximately 1 meter long and feed it through
the hollow tube.
2. Secure a plastic tie through the center hole in each stopper.
3. Tie one end of the st ring to the plastic tie to the stopper that is to be
used in the specific experiment.
4. Tie a loop at the other end of the string and hook a mass through the
loop.
Important! Please follow these SAFETY guidelines:
•Put on safety goggles!
•Make sure that no one is standing close to avoid hitting others!
•Hold the tube far enough away to avoid hitting self.
5. Firmly hold the tube and start rotating (spinning) the rubber stopper
as shown in the following photo (starting rotation). Continue
spinning the stopper until it reaches full rotation.
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Discover Centripetal Force Kit Model No. ME-9837
Spinning mass:
starting rotation
Spinning mass:
full rotation
Labs with the Discover
Centripetal Force Kit
The Classical Centripetal Force Lab
Set up the lab as shown in the general setup section.
Overview
In this lab, the dependent variable is always the linear velocity (v). The
independent variables are the radius (r), the hanging weight determined by the hanging mass (mh) - and the spinning mass (ms).
When the velocity is plotted as a function of one of the independent
variables, the other two independent variables must be kept constant.
It is important, therefore, to keep track of these values using the
following data table for each of the 3 sections of this lab:
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Model No. ME-9837 Discover Centripetal Force Kit
radius (m) mh (kg) ms (kg) V (m/s)
For each data point collected, students must:
• Select and mark a predetermined radius.
• Select and attach predetermined hanging and swinging masses.
• Adjust the "swing speed" until the predetermined radius is attained.
• Time ten (10) full rotations.
Calculate the Linear Velocity
To determine the linear velocity of the spinning mass, measure the
period (T) and the radius (r). To find the period, divide the time of the
10 full rotations by 10. To calculate the linear velocity (v) use the
following equation:
2πr
ν
---------=
T
In order to maintain a constant radius, mark the string with a pen.
Practice spinning the mass and observing the mark on the string.
Calculate the Force
The centripetal force on the spinning mass is roughly equal to the
weight of the hanging mass. Measure the hanging mass and use this
value to calculate the centripetal force.
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Discover Centripetal Force Kit Model No. ME-9837
Velocity versus Force
While using the same spinning mass and maintaining the same radius,
students find the corresponding velocities for different hanging
masses. A graph of Force versus Velocity should yield a square root
graph and a relationship of
ν k1F=
where k1 is a constant.
Sample Data:
The following data is for a spinning mass of 22 g (#6 stopper) and a
radius of 0.5 m.
radius (m) mh (kg) ms (kg) V (m/s)
.5 .1 .022 4.4
.5 .2 .022 6.3
.5 .3 .022 8.0
.5 .4 .022 9.2
.5 .5 .022 10.2
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Model No. ME-9837 Discover Centripetal Force Kit
Velocity versus Mass
While maintaining the same hanging mass and radius, students find the
corresponding velocity for different spinning masses. A graph of
Velocity versus Ms should yield a graph with the relationship of
k
ν
------=
m
2
s
where k2 is a constant.
Sample Data:
The following data is for a hanging mass of 500 g and a radius of
0.5 m.
radius (m) mh (kg) ms (kg) V (m/s)
.5 .5 .022 10.0
.5 .5 .034 8.2
.5 .5 .056 6.4
.5 .5 .086 5.2
.5 .5 .109 4.5
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Discover Centripetal Force Kit Model No. ME-9837
Velocity versus Radius
While maintaining the same hanging mass and spinning mass, students
find the corresponding velocity for different radii. A graph of Velocity
versus Radius should yield a graph with a relationship of
ν k3r=
where k3 is a constant.
Sample Data:
The following data is for a hanging mass of 500 g and a s pinning mass
of 56 g (#10 stopper).
radius (m) mh (kg) ms (kg) V (m/s)
.2 .5 .056 3.8
.3 .5 .056 4.9
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.4 .5 .056 5.8
.5 .5 .056 6.5
.6 .5 .056 7.1
.8 .5 .056 8.2
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Model No. ME-9837 Discover Centripetal Force Kit
After completing the lab, students should derive the full equation for
the centripetal force:
2
mv
F
----------=
r
Questions
1. Using words and a mathematical expression, describe the relationship
between force and velocity in uniform circular motion.
2. Using words and a mathematical expression, describe the
relationship between mass and velocity in uniform circular motion.
3. Using words and a mathematical expression, describe the
relationship between radius and velocity in uniform circular
motion.
4. Combine the three relationships above to create one relationship for
force, mass, velocity, and radius. Solve it for force.
5. How would you convert this expression into an equation?
6. What is the constant of proportionality for this equation? Explain.
7. How could such an equation be used?
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Discover Centripetal Force Kit Model No. ME-9837
8. The figure below represents an overhead view of the rotating mass.
For each of the 4 points, draw the direction and relative magnitude
of the force.
Demonstration Using a Force Sensor
Set up the Discover Centripetal Force Kit as instructed. Replace the
hanging mass with a Force Sensor. The measurements of the Force
Sensor are roughly equal to the centripetal force. Have an assistant
hold the sensor. Move it up or down to change the radius.
Demonstration Using a Newton Spring
Scale
Set up the Discover Centripetal Force Kit as shown in the Classical
Centripetal Force Lab. Replace the hanging mass with a Newton
Spring Scale. The measurements of the Newton Spring Scale are
roughly equal to the centripetal force. Have an assistant hold the
sensor. Move it up or down to change the radius. This method allows
the student to "feel" the changing in the centripetal force.
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Model No. ME-9837 Discover Centripetal Force Kit
Appendix A: Technical Support
For assistance with the ME-9837 or any other PASCO products, contact PASCO as follows:
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95747-7100
Phone: (916) 786-3800
FAX: (916) 786-3292
Web: www.pasco.com
Email: techsupp@pasco.com
Appendix B: Copyright and Warranty Information
Copyright Notice
The PASCO scientific 012-08862A Discover Centripetal Force Manual is copyrighted and
all rights reserved. However, permission is granted to non-profit educational institutions for
reproduction of any part of this manual, providing the reproductions are used only for their
laboratories and are not sold for profit. Reproduction under any other circumstances, without
the written consent of PASCO scientific, is prohibited.
Limited Warranty
For a description of the product warranty, see the PASCO catalog.
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