®
Instruction Manual
Super Pulley with
Clamp (3)
String Tie
Assembly
(3)
Nylon
Thread
Force Table with 3
detachable legs
Stacking
peg
Storage
recess
String Tie
Assembly
012-13471A
*012-13471*
PASCO Mechanics
Super Pulley Force Table
ME-9447B
®
Super Pulley Force Table
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
About the Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Experiment 1: Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Protractor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Warranty, Copyright, and Trademarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
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ME-9447B 012-13471A Introduction
®
Outer part snaps into
the Force Table
Clear
disk
Thread strings
through this hole.
Ring on
label
Introduction
Included Equipment Quantity Included Equipment Quantity
Force Table Assembly with Legs 1 String Tie Assembly 3
Super Pulley with Clamp 3 Spool of Thread 1
The Super Pulley Force Table includes equipment for vector addition experiments. You will also need masses,
mass hangers, 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.
About the Equipment
The PASCO Model ME-9447B 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 adjustable pulley clamps allow the string to be positioned close to the angle markings on the table, reducing the parallax error in reading the angle.
• Equilibrium is achieved when the String Tie Assembly is centered in the middle of the Force Table.
The Force Table has three detachable legs that can be stored in the leg holders and clips on the underside of the
table and the table includes spare String Tie Assemblies.
String Tie Assembly
The circular String Tie Assembly has two main parts: a clear disk
through which the strings are tied and which is free to move from side to
side over a short distance, and the outer part that snaps into the center of
the Force Table. The label on the outer part has a ring that shows when
the clear disk is centered.
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Super Pulley Force Table Introduction
®
Storage
clip
Threaded
hole
Leg
holder
Underside of
Force Table
1. Remove a leg from its
storage clip and holder.
2. Line up the leg screw
with a threaded hole.
3. Rotate the leg into the
threaded hole.
1.
2.
3.
ME-9448B
Super Pulley
with Clamp
Clamp
Thumbscrew
Yoke
Storage recess
Stacking
peg
String
Tie the ends
together.
• Assemble the Force Table
• Turn the Force Table upside
down..Remove a leg from its storage clip
and holder.
• 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.
NOTE: Do not tighten the legs more than
“finger tight”. They will be removed later for
storage.
• 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.
Each clamp has two positions for holding 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 more easily aligned
with the top surface of the table. To do this,
unscrew the thumbscrews on both sides of the
clamp. Arrange the pulley yoke so the holes
in the yoke are aligned with the lower
threaded holes of the clamp. Replace the two
thumbscrews but do not overtighten. NOTE:
Each thumbscrew has a slotted head. If the
thumbscrew is too tight, use a flat blade
screwdriver to loosen it.
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.
Get three pieces of string (thread), each about 30 centimeters long. Twist
the ends of the strings together and thread the three strings through the
hole in the middle of the clear plastic disk on the String Tie Assembly.
Pull the ends of the threads through the hole and tie them together with an
overhand knot so that the strings cannot be pulled back through the clear
plastic disk
Insert the String Tie Assembly
The String Tie Assembly fits into the circular recess in the middle of the Force Table. The circular recess has two
rectangular holes in the bottom and two shallow notches on its edge. The two short “legs” of the outer part of the
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ME-9447B 012-13471A Introduction
®
1. Insert one “leg” into one
of the rectangular holes.
2. Press firmly to push the
other “leg” into its hole.
String Tie
NOTE: Masses and mass
hangers are not included.
Clamp shown with
the pulley yoke in
the lower position..
String Tie fit into the rectangular holes in the recess. Align the short “legs” with the shallow notches. Insert one
“leg” into one of the rectangular holes and then press down firmly on the other side of the String Tie until the other
“leg” snaps into the other rectangular hole. NOTE: Press firmly. When the String Tie is correctly inserted, the top
surface of the clear plastic disk will be flush with the surface of the Force Table.
To remove the String Tie from the Force Table, turn the Force Table over and press the two short “tabs” of the
String Tie inward toward each other.
Setup
Arrange the strings over the pulleys. Attach a mass hangers to each string. NOTE: A string can be attached to a
PASCO mass hanger by wrapping the string four or five times around the notch at the top of the mass hanger.
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Super Pulley Force Table Introduction
®
Stacking peg
Storage recess
Storage
The Force Table may be stored with or without the ME-9448B
Super Pulley with Clamp 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 leg holders and storage clips that
are on the underside of the force table. The disassembled force
tables can be stacked on top of each other. The three stacking pegs
on the underside of one Force Table fit into the storage recesses on
the top surface of a second Force Table to eliminate slipping.
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Vector Addition
®
FE– F
R
FAFB+==
F
A
F
E
F
B
F
R
Vector Addition
Equipment Needed Equipment Needed
Super Pulley Force Table (ME-9447B) String (spool of thread)
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/s
2
.
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 (F
lishes equilibrium. The equilibriant is not the same as the resultant (F
). The resultant is the addition of the two
R
) because it is the force that estab-
E
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.
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. Arrange the strings from the String Tie over the pulleys.
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3. Hang the following masses over two of the super pulleys and clamp the pulleys at the given angles.
Table 1.1:
Force Mass Angle
F
A
F
B
F
E
50 g (0.050 kg) 0°
100 g (0.100 kg) 120°
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 (F
) because it establishes equilibrium. The equilibriant is the negative of the resultant.
E
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.
Method of Finding Equilibrium
The clear disk will be centered in the String Tie when the system is in equilibrium. Pull the clear disk slightly to
one side and let it go. Check to see that the disk returns to the center. If not, adjust the mass and/or the angle of the
super pulley clamp until the disk always returns to the center when pulled slightly to one side.
Analysis
T o 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 equ ili briant
(F
) will have the same magnitude, but it will be opposite in direction. In other words, the direction will be 180°
E
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 R
and Ry in Table 1.2. Use trigonometry to find the direction of the equilib-
x
riant (remember, the equilibriant is exactly opposite in direction to the resultant.) Record the results in Table 1.2.
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 (F
Method Magnitude Direction
Experimental
Component
Graphical
R
= ______________ Ry = ______________
x
)
E
8
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Question
How do the theoretical values for the magnitude and direction of the equilibriant compare to the actual magnitude
and direction?
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Appendix
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The protractor on this page is a version of the degree scale on 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.
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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 the PASCO web site at www.pasco.com and enter ME-9447B
into the Search window.
Limited Warranty For a description of the product warranty, see the PASCO catalog. Copyright The PASCO scientific
012-13471A 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 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.
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