PASCO ME-6991 User manual

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Bridge Set
ME-6991
Instruction Manual
012-10656D
*012-10656*

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2
Table of Contents
Included Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Related Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
About the Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Adding Load Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Properties of I-Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Simple Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Common Truss Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Different Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
Measuring Bridge Deflection Under Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Bridge Challenges for Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Measuring Static and Dynamic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Bridges That Require Two or More Bridge Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Dynamics Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Rollercoaster Design Challenges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Limited Warranty, Copyright, Trademarks and Patents Pending. . . . . . . . . . . . . . . . . . 16

Bridge Set
ME-6991
®
3
*NOTE: When storing the Road Bed, do not crimp or fold the material. Do not roll the Road Bed into a coil that
is less than 30 cm (12 in) in diameter.
Included Equipment Qty Included Equipment Qty
A. #5 Beam (24 cm long) 16 I. Mini-car Starter Bracket 1
B. #4 Beams (17 cm long) 36 J. Mini-car 1
C. #3 Beams (11.5 cm long) 36 K. Photogate Flag 1
D. #2 Beams (8 cm long) 16 L. Mini-car Mass (about 200 g) 1
E. #1 Beams (5.5 cm long) 16 M. Road Bed (3 m)* 1
F. Half Round Connector 28 N. Road Bed Coupler 2
G. Screw (6-32) 150 O. Cord Tensioning Clip 32
H. Road Bed Clip 24 P. Yellow Cord 76 m
A
B
C
D
E
F
G
L
I
J
K
H
M
N
OP

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Bridge Set
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Introduction
The Bridge Set is one part of the PASCO Structures System. Although the Bridge Set can be used as a
stand-alone set, it can also be combined with other parts of the PASCO Structures System. The Load Cell and
Amplifier Set (PS-2199) can be added to measure compression and tension forces in the structure members and
other sets of plastic parts are available.
The PASCO Structures System includes:
Truss Set (ME-6990) - A small set for building trusses
Bridge Set (ME-6991) - A larger set with road bed and cables for building bridges and rollercoasters
Advanced Set (ME-6992A) - The largest set with pulleys, axles, and additional connectors that make possible
bridges which have angles other than 45 and 90 degrees. This set can also be used to build suspension bridges,
cranes, cars and catapults.
Load Cell and Amplifier Set (PS-2199) - Load Cell Amplifier (PS-2198) with four 100 N Load Cells
(PS-2200)
Load Cell Amplifier (PS-2198) - Can plug in up to six Load Cells; requires a PASPORT interface to connect to
the USB port of a computer.
100 N Load Cell (PS-2200) - Strain gauges mounted on a beam; no electronics so a Load Cell requires the Load
Cell Amplifier (PS-2198).
The Bridge Set includes beams, brackets, screws, cord tensioning clamps, a Mini-car, and a flexible road bed for
building various trusses and bridges. Dynamics tracks can also be constructed to study motion. In addition, roll-
ercoaster design can be studied.
About the Components
Assembling Beams
Attach beams to connectors as illustrated.
Each half round connector has eight slots,
labeled A through H, for accepting beams.
There are five sizes of beams, labeled #1
through #5. Beam #1 is the shortest beam.
Related Equipment Related Equipment
Load Cell and Amplifier Set (PS-2199) Road Bed Spares (ME-6995)
Load Cell Amplifier (PS-2198) PASCO Interfaces
100 N Load Cell (PS-2200) PASCO Data Acquisition Software
Truss Set (ME-6990)
Thumbscrew
I-Beam
Half Round
Connector
Figure 1: Attaching a beam to a bracket

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Model No. ME-6991 About the Components
5
Attaching Cords
When attaching cords for lateral bracing or for suspension or
cable-stayed bridges, Cord Tensioning Clips are used to assist in
adjusting the tension in the cords.
The Cord Clip does not come apart. It is best to thread the cord through
the clamp before the clamp is installed on the bridge. Prepare to thread
the cord by holding the top half of the clip as shown in Figure 3 so the
two halves of the clip will separate, leaving an opening through which
the cord is threaded. The cord is inserted into the end opposite the pointed end of the clip. The cord should be
looped back through the clip as shown in Figure 4. Then the Cord Clip can be used in the bridge, using the
attachment screw to tighten the clip shut. To adjust the cord tension, loosen the screw and pull on the cord to the
desired tension and then tighten the screw.
Attaching the Road Bed
To attach the blue road bed to the cross-members
of a bridge, first connect the road bed clips to the
underside of the road bed by twisting the clip into
the slot so the edges of the slot capture the clip (see
Figure 7).
Slide the clip in the slot a short distance to align it
with the cross member of the bridge.
Using the Road Bed Coupler
Each end of the coupler is inserted into the slot
on the bottom of the Road Bed to join two Road
Beds together (see Figure 8).
Attaching the Starter Bracket
The main purpose of the starter bracket is to
align the Mini-car wheels with the ridges in the
road bed when the car is placed on the road bed.
In general, install the starter bracket at the end of
the road bed.
Figure 2: Lateral bracing
Cord
Cord
Tensioning
Clip
Figure 3: Hold half of
the cord lock so the
two halves separate
Figure 4: Loop the
cord back through the
cord lock
Figure 5: The cord
goes around the
screw hole
Figure 6: The cord lock is
ready to be attached to the
structure using a screw
Figure 7: Attach road bed clip to road bed
Figure 8: Use the coupler to
connect road beds
Coupler
Road Bed

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Bridge Set Adding Load Cells
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To attach the starter bracket to the road bed, squeeze the
spring metal clip and insert the clip into the slot on the bot-
tom of the road bed, then release the clip (See Figure 9).
Place the mini-car between the sides of the starter bracket
to align the wheels with the ridges on the road bed (see the
figure below).
Using the Mini-car
The ridges in the road bed guide the Mini-car wheels. The supplied mass (approximately 200 g) can be set in the
recess in the Mini-car to give the car more mass. If smaller masses are desired, use the Mass and Hanger Set
(PASCO Model ME-8979).
The photogate flag fits into the slot on the side of the Mini-car. As the car passes through a photogate, the infra-
red beam is blocked twice by the flag. To find the speed of the car, measure the distance between the leading
edges of the flag (approximately 1 cm) and measure the time between the events when the infrared beam is
blocked.
The Accessory Photogate with Stand (PASCO Model ME-9204B) is useful as a free-standing photogate.
Adding Load Cells
To measure the compression and tension forces in individ-
ual members, add load cells (PASCO Model PS-2199) to
any PASCO Structure. Replace a beam with two shorter
beams and a load cell.
#5 beam = load cell + two #3 beams
#4 beam = load cell + two #2 beams
#3 beam = load cell + two #1 beams
Use thumbscrews to attach two beams to a load cell as shown in Figure 10.
When using load cells, assemble your structure with the screws loose. This will simplify the analysis by ensuring
that the members experience only tension and compression without moments.
See the instructions that came with the load cells for details about how to connect the load cells to an interface or
datalogger and collect data.
metal
clip
Road Bed
Starter
Bracket
Figure 9: Attaching the starter bracket to the
track (end view)
Mini-car
Starter Bracket
Mini-car
Figure 10: A load celll combined with two #2 beams is
the same length as a #4 beam

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Model No. ME-6991 Properties of I-beams
7
Example: Bridge with Load Cells
The bridge shown in Figure 11 incorporates six load
cells to measure the tension or compression in various
members. A hanging mass is used to apply load. The
mass is adjusted so that the compression in one of the
legs is 1.0 N. Compression is registered as a positive
value and tension as a negative value.
If the screws are loose, the theoretical analysis of the
bridge can be carried out by assuming that the net force
at each node is zero. Thus, the vertical component of compression in the left-most diagonal member must be 1 N
(to oppose the force applied by the leg). The horizontal component must also be 1 N since the member is at a 45°
angle. The predicted resultant force is:
The actual measured force confirms the theory.
Calibration of Load Cells.
Load cells are factory calibrated; however, you can
recalibrate them in software or on the datalogger. See
the documentation for your software or datalogger for
instructionsWhen calibrating a load cell, it is necessary
to apply a known load. Assemble the fixture shown in
Figure 12 to support the load cell. Hold or clamp the
fixture at the edge of a table and hang a mass from it as
shown. Note that the hanging mass applies tension to
the load cell; therefore the known force that you enter
into the software or datalogger should be a negative
value. For example, if the mass is 1.0 kg, the applied
force is -9.8 N.
Properties of I-beams
This demonstration shows the difference between
the X and Y bending moments of an I-beam.
Simple Triangles
Most structures are made of isosceles right trian-
gles as shown in Figure 14
.
Figure 11: Bridge with load cells
1.0 N
21.0 N 2
+1.4 N=
Figure 12: Calibration fixture
Figure 13: Bending an I-Beam
#4
#4
#5
#4
#3
#3
#3
#2
#2
#2
#1
#1
Figure 14: (Left) A triangle made from a #5 beam and two #4 beams.
(Right) Combinations of beams to make triangles.

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Bridge Set Trusses
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Trusses
Kingpost Truss
Figure 13 shows a simple king-
post truss made from #5 and #4
beams. Use a hanging mass to
apply a load.
Lay the kingpost truss on the
table to comare its horizontal
and vertical stiffness.
To build a three-dimen-
sional structure, connect
two trusses with #4 beams
(Figure 14)..
Add cross bracing to
increase stiffness
Queenpost Truss
To make a queenpost truss, separate the kingpost truss in the middle and
add a square section.
Legs can be added to any
truss or bridge (Figure 15).
#4 #4
#4
#5
#5
Figure 13: A simple
kingpost truss
Figure 14: (Left) A three-dimensional kingpost truss structure.
(Right) Kingpost truss with cross bracing
#4
#4 #4
#4 #4
#4
#5
#5
Figure 15: (Left) Queenpost truss. (Right) Queenpost truss with legs.

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Model No. ME-6991
9
Roof Truss.
Use #4 and #5 beams to
build a simple roof truss or
a roof truss structure with
legs
Common Truss Bridges
Warren Bridge
The Warren Bridge (Figure 17) is a simple type of
bridge consisting of a series of triangles. However, a
simple Warren Bridge is not practical for supporting a
deck (road bed). Vertical members can be added to
support the deck. Additional verticals can support an
upper deck.
To make a free-standing bridge, begin by laying out
one side of the bridge on a table. Then build the other
side of the bridge. Join the two sides of the bridge
attaching the floor beams and the top cross beams.
Use additional members as piers to support the
bridge. (Figure 18).
.
Different Scales
It is possible to build bridges of two different scales. In
Figure 19 is a Warren with Verticals built to two differ-
ent scales.
#4 #4
#4
#4
#4 #4
#5
#5
#5
Figure 16: Roof truss
#4
#5
#3
#3
#3
#4
Figure 17: (Top) Warren Bridge. (Middle) Warren with
deck verticals. (Bottom) Warren with verticals.
#4
#3
#3
#3
#4
#5
Figure 18: (Left) Free-standing Warren. (Right) Free-standing Warren with deck verticals
#3
#4
#4
#5
Figure 19: Smaller and Larger Scale Warren with Verticals

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Bridge Set Warren Bridge
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In spanning a particular distance, why wouldn’t you use
the smaller scale bridge and add more panels? An exami-
nation of the forces in the memebers of each size bridge
will give the answer. If the smaller and larger bridges
have the same number of panels and experience the same
load, the forces in any member of the smaller bridge is
the same as the same member in the larger bridge. Each
additional panel is submitted to larger forces. This can be
explored using load cells. See the section on Measure-
ment of Static and Dynamic Loads
Figures 20 through 23 show additional common types of bridges. Investigate how the forces in these bridges dif-
fer from the Warren..
Figure 20: (Top) Pratt. (Bottom) Howe
#4
#5
#3
#3
Figure 21: Free-standing Howe
#5 Cord
#4
#3
#3
#4 #5
#2
#3
Figure 22: Waddell “A” Truss Bridge
Figure 23: Deck Truss Bridge
(Connect the sides with #3 or #4 beams.)

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Model No. ME-6991 Measuring Bridge Deflection Under Load
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Measuring Bridge Deflection Under Load
Because the members are made of plastic, it is easy to show bending in a bridge using
relatively small loads.
Using a Motion Sensor
In Figure 24, the bridge is loaded by hanging a weight (Large Slotted Mass Set, PASCO Model ME-7566) from
the center of the bridge. A Motion Sensor (PS-2103) is placed on the floor and pointed up toward the bottom of
the weight hanger. A PASPORT inteface (in this case, the Xplorer GLX, PS-2002) is used to record the amount
of mass and the distance to the bottom of the weight hanger. A graph of the deflection as a function of the load is
shown next to Figure 24.
Hint: For the GLX, set the Motion Sensor sample rate to 50 Hz. In the Sensor Setup window, change the
‘Reduce/Smooth Averaging’ from ‘Off’ to ‘5 points’.
Using Load Cells
Figure 25 shows two bridges of the same type but dfferernt scale. For a given load the deflection is different.
Also note that the forces in some of the members are being measured using load cells to discover the difference
caused by the size of the bridge.
NOTE: Do not attempt to
load the bridge to the
point of breaking.
Figure 24: (Left) Deflection of bridge under
load. (Above) Displacement vs. Mass plotted
using PASCO’s DataStudio software
Figure 25: (Above) Same load for different scale bridges.
(Right) Displacement vs. mass

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Bridge Set Bridge Challenges for Students
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Bridge Challenges for Students
Perhaps the best way for students to learn about bridges is to give them a task to accomplish wth limited
resources by any means possible. Here are two suggestions to challenge your students.
Span a Gap
Give each group a set of plastic, half of a Bridge Set or a Truss Set. The goal is to span a gap of 60 cm. Then find
the member with the greatest compression and change the design of the bridge to minimize the maximum com-
pression.
Least Deflection Under Load
Give each group a Bridge Set. The goal is to span a given distance with a bridge that has the least deflection
under load. The bridge is loaded with a particular load that the bridge must be able to bear. The bridge that has
the least defection is the winner.
Measuring Static and Dynamic Loading
Static Load
Apply a static load to the bridge by hanging a
hooked mass from one of the floor beams and
insert load cells into the structure as shown in
Figure 26. Loosen all the screws in the struc-
ture so the members are resting on their pins.
This will eliminate any extra moments due to
the screws and the tension and compression
readings will agree with the calculated values.
Dynamic Load
With the load cells inserted as shown in Figure 27, push the Mini-car with its extra mass across the bridge. Zero
the load cells before the measurement. Examine which members are under tension or compression.
Figure 26: Measuring a Static Load
Figure 27: (Above) Recording the forecs measured by the load cells as
the car traverses the bridge. (Right) DataStudio plot of load cell data

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Model No. ME-6991 Bridges That Require Two or More Bridge Sets
13
Bridges That Require Two or More Bridge Sets
Note that the Tied Arch Bridge is constructed
using the I-beams sideways for the arched part of
the bridge. Since the I-beams bend more in this
orientation they form a curve. The beams used in
this manner will take a set and be permanently
bent.
Figure 28: Tied Arch Bridge
Figure 29: Long Warren Bridge
#5
#3
#3
#4
Figure 30: Subdivided Warren Bridge
#3
#3
#4
#4
#5

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Bridge Set Dynamics Track
14
Dynamics Track
The Bridge Set can be used to construct dynam-
ics systems for studying motion. A straight track
can be constructed as shown in Figure 31.
Stretching a rubber band across two vertical
posts at the end of the track makes a good
bumper.
Measurement
Motion Sensor
The motion of the Mini-car can be measured
using a Motion Sensor (PS-2103). See Figure
32. Provided that the Motion Sensor is closer
than 15 cm to the rubber band, the Motion Sen-
sor will not “see” the rubber band and will
only register the position of the Mini-car.
Photogate with Pulley
If a mass hanging over a pulley is used to accelerate
the Mini-car, a Photogate can be used with the pulley
to measure the rotation of the pulley. The Photo-
gate/Pulley System (ME-6838) and the Table Clamp
(ME-8995) are available separately from PASCO. See
Figure 33.
Ramp and Photogate
A ramp is shown in Figure 34 with a Photo-
gate (ME-9204B) to measure the speed of the
Mini-car at the bottom of the ramp during a
“Conservation of Energy” experiment. The
Mini-car is supplied with a photogate flag that
blocks the Photogate’s infrared beam.
Rollercoaster Design
Challenges
Valley Design Challenge
Design a valley at the bottom of
which the Mini-car is going the
fastest possible without having
the Mini-car leave the track at
any point on the track. See fig-
ure 35.
Figure 31: Straight Dynamics Track
Rubber
band
Figure 32: Using a Motion Sensor with a Track
Figure 33: Using a Photogate with Pulley
Figure 34: Ramp with Photogate
Figure 35: Valley Design
#5
#5
#5
#4
#4
#4

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Model No. ME-6991 Rollercoaster Design Challenges
15
Loop Design Challenge
Design a rollercoaster loop such that the Mini-car makes it around the loop. Measure the forces on the track at the
bottom and the top of the loop and make the force zero at the top of the loop. See Figure 36.
Ski Jump Design Challenge
Design a ramp that will launch the Mini-car as far as possible
away from the edge of the table. See Figure 37.
Figure 36: Loop Design
Figure 37: Ski Jump Design

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Bridge Set Rollercoaster Design Challenges
16
Technical Support
For assistance with any PASCO product, contact PASCO at:
For more information about the Bridge Set and the latest revision of this Instruction Manual, visit:
www.pasco.com/go?ME-6991
Limited Warranty For a description of the product warranty, see the PASCO catalog. Copyright The PASCO scientific
012-10656B Bridge Set 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 prohib-
ited. 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. Patents Pending The
following PASCO products have patents pendng:
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95747-7100
Phone: [phone] (worldwide)
800-772-8700 (U.S.)
Fax: [phone]
Web: www.pasco.com
Email: [email protected]
ME-6983 Structures Cast Beam Set ME-6991 Bridge Set ME-6996 Cord Lock Spares
ME-6985 Flexible I-Beam Set ME-6992A Advanced Structures Set ME-6997 Round Connector Spares
ME-6987 Flat Beams Set ME-6993 Truss Set Members ME-6998 Axle Spares
ME-6989 Physics Structures Set ME-6994 Truss Set Screws ME-6999A Angle Connector Spares
ME-6990 Truss Set ME-6995 Road Bed Spares ME-7000 High School Physics Structures Set
PS-2198 Load Cell Amplifier PS-2204 Displacement Sensor
PS-2199 Load Cell and Amplifier Set PS-2205 Dual Load Cell Amplifier
PS-2200 100 N Load Cell PS-2206 Load Cell and Dual Amplifier Set
PS-2201 5 N Load Cell