Instruction Manual
012-12560A
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*012-12560*
PASCO Mechanics
Super Pulley Force Table
ME-9447A
NOTE: Masses not included
Super Pulley Force Table
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
About the Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Experiment 1: Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Protractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Warranty, Copyright, and Trademarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
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ME-9447A
012-12560A
Introduction
Introduction
Force Table Assembly with
Detachable Legs
Mass Hangers
(3)
Super Pulley with Clamp
(3)
Plastic Ring
Included Equipment
Quantity
Part Number
1. Force Table Assembly with Legs
1
003-09948
2. Super Pulley with Clamp
3
ME-9448B
3. Mass Hanger
3
648-09987
4. Plastic Ring
1
699-059
5. Spool of Thread (not shown)
1
699-011
The Super Pulley Force Table includes equipment for vector addition experiments. You will also need masses and
a balance..
Required Equipment
Recommended Equipment
Mass and Hanger Set (ME-8979)
Mass Balance (see PASCO catalog)
This manual contains descriptions of the included equipment and instructions for one experiment.
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Super Pulley Force Table
Introduction
About the Equipment
The PASCO Model ME-9447A Force Table is used to physically demonstrate the addition of vectors using the
concept of equilibrium (net force is zero). The vectors are forces supplied by the weight of masses (not included)
that hang over pulleys. Masses hanging over pulleys placed at given angles are balanced by another mass over a
pulley at another angle.
Among the features of the Force Table are:
•
It is lightweight. (NOTE: Do not exceed 200 grams (0.20 kg) on each pulley.)
•
It can be stored in a small space.
•
The pulleys are low friction.
•
The pulley clamps allow the string to be lowered close to the angle markings on the table, reducing the parallax error in reading the angle.
•
Equilibrium can be obtained by centering a knot (which gives greater precision) or by centering the plastic
ring.
The Force Table Assembly has a Center Post and three detachable legs that can be stored in the clips on the underside of the table. The Center Post can be used during the setup of the force table so that the plastic ring will stay in
the center of the table until all the pulleys and masses are arranged.
Assemble the Force Table
•
Turn the Force Table upside down..
•
Remove a leg from its storage clip.
•
Line up the leg screw with a threaded
hole in the underside of the Force Table.
•
Rotate the leg clockwise (left-to-right)
until it is firmly attached to the table.
•
Repeat for the other legs.
1. Remove a leg from its
storage clip.
2. Line up the leg screw
with a threaded hole.
3. Rotate the leg into the
threaded hole.
2.
NOTE: Do not tighten the legs more than
“finger tight”. They will be removed later for
storage.
•
3.
Underside of
Force Table
Turn the Force Table right side up.
Attach the Pulleys
Attach three of the ME-9448B Super Pulley
with Clamp to the edge of the force table.
Leg Screw
1.
Center Post
Threaded Hole
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ME-9447A
012-12560A
Introduction
The clamp has two positions for placing the
pulley yoke. You may want to move the pulley yoke to the lower position so that the top
edge of the pulley can be aligned with the top
surface of the table. To do this, unscrew the
thumbscrews on either side of the clamp.
Move the pulley yoke so the holes in the
yoke are aligned with the lower threaded
holes of the clamp. Replace the thumbscrews..
NOTE: If more than two forces are to be
added, use the desired number plus one pulley and clamp for the equilibrium force.
Attach the Strings
There are two ways to attach the strings (thread) to the table. The first method uses the plastic ring placed in the
center of the table. The second method uses an “anchor string” through the hole in the Center Post. The advantage
of the anchor string method is that a higher precision can be achieved because a single knot is being centered
instead of the plastic ring (which has some mass). The anchor string keeps the masses from falling to the table top
when the system is not yet in port the weight of carts and related apparatus.
NOTE: For both methods it is important to adjust the pulleys so that the strings are parallel to the top surface of the
force table, and as close to the top surface as possible. When using the plastic ring, keep the strings far enough
above the table so that the ring does not rest on the table.
Ring Method
Screw the Center Post up until it sticks above the top surface of the table. Place the plastic ring over the post. Tie
one 30 cm string (thread) to the plastic ring for each pulley. (The strings must be long enough to reach over the
pulleys.) Place each string over a pulley and tie a mass hanger on the each of the string.
NOTE: A string or thread can be attached to a PASCO mass hanger by wrapping the string or thread four or five
times around the notch at the top of the mass hanger.
Pulley yoke in
lower position
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Super Pulley Force Table
Introduction
Anchor String Method
Make sure that the top of the Center Post is flush with the top surface of the table. Cut two 60 cm lengths of string
(thread) and tie them together at their centers so they form an “X”. Thread one of the strings (the “anchor string”)
down through the hole in the Center Post and tie its end to one of the legs. Place each of the other strings over a
pulley and tie a mass hanger on the end of each string..
Knot
Center
Post
Anchor
String
Mass
Hanger
Storage
The force table may be stored with or without the super pulley clamps attached. To minimize the storage space
needed for the force table, remove the legs by unscrewing them from the table. Store the legs in the clips that are
on the underside of the force table. The disassembled force tables can be stacked on a shelf for storage.
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ME-9447A
012-12560A
I n t r o d u c t i o n Ex p e r i m e n t 1 : V e c t o r
Experiment 1: Vector Addition
Equipment Needed
Equipment Needed
Super Pulley Force Table (ME-9447A)
String (SE-8050)
Super Pulley Table Clamp (ME-9448B)
Protractor
Mass and Hanger Set (ME-8979)
Metric Ruler
Mass Balance (SE-8723)
Sheet of paper (2)
Purpose
The purpose of this experiment is to use the force table to experimentally determine the force that balances two
other forces. This result is checked by adding the two forces using their horizontal and vertical vector components,
and by graphically adding the force vectors.
Theory
This experiment finds the resultant of adding two vectors by three methods: experimentally, by adding components, and graphically
NOTE: In all cases, the force caused by the mass hanging over the pulley is found by multiplying the mass by the
acceleration due to gravity, 9.8 m/s2.
Experimental Method
Two forces are applied on the force table by handing masses over pulleys position at certain angles. Next, the
angle and amount of mass hanging over the third pulley are adjusted until the force from this pulley balances the
forces from the other two pulleys. The third force is called the equilibriant (FE) because it is the force that establishes equilibrium. The equilibriant is not the same as the resultant (FR). The resultant is the addition of the two
forces. The equilibriant has the same magnitude as the resultant, but it is in the opposite direction of the resultant
because it must balance the resultant. The equilibriant is the ‘negative’ of the resultant.
–FE = FR = FA + FB
FB
FE
FR
FA
Setup
1.
Assemble the force table as shown in the Assembly section. Use three super pulley clamps (two for the
forces that will be added and one for the force that balances the sum of the other two forces).
2.
Ring Method: Screw the center post up so that it can hold the plastic ring in place when the masses are suspended over the pulleys.
Anchor String Method: Leave the center post so that it is flush with the top surface of the force table. Make
sure that the anchor string is tied to one of the legs of the force table so that the anchor string will hold the
strings in place when the masses are suspended over the pulleys.
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3.
Hang the following masses over two of the super pulley clamps and clamp them at the given angles.
Table 1.1:
Force
Mass
Angle
FA
50 g (0.050 kg)
0°
FB
100 g (0.100 kg)
120°
FE
Procedure (Experimental Method)
By trial and error, find the angle for the third super pulley clamp and the mass that must be suspended over the pulley so that its weight will balance the forces exerted on the strings by the other two masses. This third force is
called the equilibriant (FE) because it establishes equilibrium. The equilibriant is the negative of the resultant.
Record the mass and angle for the third pulley to put the system into equilibrium into Table 1.1.
To test whether the system is in equilibrium, use the following criteria.
Ring Method of Finding Equilibrium
The plastic ring will be centered over the post when the system is in equilibrium. Screw the center post down so
that it is flush with the top surface of the force table and no longer able to hold the plastic ring in position. Pull the
ring slightly to one side and let it go. Check to see that the ring returns to the center. If not, adjust the mass and/or
the angle of the super pulley clamp until the ring always returns to the center when pulled slightly to one side.
Anchor String Method of Finding Equilibrium
The knot will be centered over the small hole in the middle of the center post when the system is in equilibrium.
The anchor string should be slack. Adjust the pulleys downward until the strings are close to the top surface of the
force table. Pull the knot slightly to one side and let it go. Check to see that the knot returns to the center. If not,
adjust the mass and/or the angle of the super pulley clamp until the knot always returns to the center when pulled
slightly to one side.
Analysis
To theoretically determine what mass should be suspended over the third pulley, and at what angle, calculate the
magnitude and direction of the resultant by the component method and the graphical method. The equilibriant
(FE) will have the same magnitude, but it will be opposite in direction. In other words, the direction will be 180°
from the direction of the resultant.
Component Method
On a separate sheet of paper, add the vector components of Force A and Force B to determine the magnitude of the
equilibriant. Record the components Rx and Ry in Table 1.2. Use trigonometry to find the direction of the equilibriant (remember, the equalibriant is exactly opposite in direction to the resultant.) Record the results in Table 1.2.
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Graphical Method
On a separate sheet of paper, construct a tail-to-head diagram of the vectors of Force A and Force B. Use a metric
ruler and protractor to measure the magnitude and direction of the resultant. Record the results in Table 1.2.
Remember to record the direction of the equilibriant as opposite in direction to the resultant..
Table 1.2:
Equilibriant (FE)
Method
Magnitude
Direction
Experimental
Component
Graphical
Rx = ______________ Ry = ______________
Question
How do the theoretical values for the magnitude and direction of the equlibriant compare to the actual magnitude
and direction?
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Appendix
The protractor on this page is a version of the top surface of the Force Table. It can be duplicated, trimmed, and
used as an overlay on the Force Table for drawing and tracing the string positions.
15
180
190
200
21
0
22
0
0
12
0
0
13
0
14
0
170
160
23
24
0
110
160
180
200
22
0
14
0
0
12
0
24
260
260
100
100
250
90
270
80
80
280
280
70
0
60
30
290
32
40
0
20
60
0
0
30
340
50
0
31
32
0
33
0
10
340
350
0
10
20
30
40
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Technical Support
For assistance with any PASCO product, contact PASCO at:
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95747-7100
Phone:
916-786-3800 (worldwide)
800-772-8700 (U.S.)
Fax:
(916) 786-7565
Web:
www.pasco.com
Email:
support@pasco.com
For the latest revision of this Instruction Manual, visit:
www.pasco.com/go?ME-9447A
Limited Warranty For a description of the product warranty, see the PASCO catalog. Copyright
012-12560A Super Pulley Force Table Instruction Manual is copyrighted with all rights reserved. Permission is granted to non-profit
educational institutions for reproduction of any part of this manual, providing the reproductions are used only in their laboratories and
classrooms, and are not sold for profit. Reproduction under any other circumstances, without the written consent of PASCO scientific,
is prohibited. Trademarks
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.
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Super Pulley Force Table
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I n t r o d u c t i o n E x p e r i m e n t 1 : V e c t o r A d d it i o n
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