PASCO ME-9837A User manual

Instruction Manual
012-15873A
Discover Centripetal Force Kit
ME-9837A

ME-9837A
2 012-15873A
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..................................................................... 12
Technical Support, Copyright and Warranty Information ...........................13

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Discover Centripetal Force Kit
ME-9837A
Equipment List
Included Equipment Model Number
1. Yellow string (73 m) ME-9876
2. Rubber stoppers (sizes: 6, 8, and 10)
3. Hollow tube (1)
4. Plastic ties (10)
Additional Equipment Recommended Model Number
Safety goggles
Marking pen
Force Sensor CI-6746, PS-2104, or PS-3202
Hooked Mass Set SE-8759
Metric Spring Scale 20 N Range ME-9513
12
3
4
#10
#8
#6

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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:
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, one tubes is
included that is chamfered to decrease friction on the string.
Situation Centripetal Force
An object twirled in a horizontal circle. Tension from the string.
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.”

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Equipment Setup
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 string 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.
hollow tube
stopper
hooked mass
string (1m)
loop in string
plastic tie

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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:
Spinning mass:
starting rotation
Spinning mass:
full rotation

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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:
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.
radius (m) mh(kg) ms(kg) V (m/s)
2r
T
---------
=

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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
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
k1F=

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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
where k2 is a constant.
Sample Data:
The following data are 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

k2
ms
------=

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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
where k3 is a constant.
Sample Data:
The following data is for a hanging mass of 500 g and a spinning 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
.4 .5 .056 5.8
.5 .5 .056 6.5
.6 .5 .056 7.1
.8 .5 .056 8.2
k3r=

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After completing the lab, students should derive the full equation for the centripetal force:
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?
Fmv2
r
----------
=

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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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Technical Support
For assistance with any PASCO product, contact PASCO at:
Limited Warranty For a description of the product warranty, see the PASCO web site.
Copyright This PASCO scientific
Instruction Manual is copyrighted with all rights reserved. Permission is granted to non-profit educa-
tional institutions for reproduction of any part of this manual, providing the reproductions are used only in their laboratories and class-
rooms, and are not sold for profit. Reproduction under any other circumstances, without the written consent of PASCO scientific, is
prohibited. Revised 1/18.
Trademarks PASCO and PASCO scientific are trademarks or registered trademarks of PASCO scientific, in the United States and/or in
other countries. All other brands, products, or service names are or may be trademarks or service marks of, and are used to identify,
products or services of, their respective owners. For more information visit www.pasco.com/legal.
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95747-7100
Web: www.pasco.com
Phone: [phone] (worldwide)
800-772-8700 (U.S.)
Email: [email protected]