PASCO ME-6955 User Manual
®
Instruction Manual and
Experiment Guide
012-07557C
*012-07557*
1.2 m PAScar Dynamics System
ME-6955
1.2 m PAScar Dynamics System Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
About the Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Spare Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
About the Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Experiment 1: Conservation of Momentum in Explosions . . . . . . . . . . . . . . . . . . . . . . . . 7
Experiment 2: Conservation of Momentum in Collisions . . . . . . . . . . . . . . . . . . . . . . . . . 9
Experiment 3: Simple Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Experiment 4: Oscillations on an Incline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
Experiment 5: Springs in Series and Parallel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Experiment 6: Launch Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Experiment 7: Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Experiment 8: Acceleration Down an Incline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Additional Experiment Suggestions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.2 m PAScar Dynamics System
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ME-6955
Included Equipment Quantity Replacement Part Number
1. PAScars 2 ME-6950 (set of 2 with masses)
2. Adjustable End Stops 2 ME-8971 (2-pack)
3. 1.2 m Dyna mic s Track 1 ME-9779
4. Adjustable Feet 2 ME-8972 (2-pack)
5. 250 g Stackable Cart Masses 2 ME-6756
6. Pivot Clamp 1 ME-9810
Introduction
The 1.2 m PAScar Dynamics System includes everything you need for a variety of experiments and demonstrations. You can also combine it with many other PASCO products—both traditional and computer-based—for an
even greater range of uses.
This manual contains descriptions of the included equipment, complete instructions for eight experiments, and
ten additional experiment suggestions.
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1.2 m PAScar Dynamics System About the Equipment
Track Features
1: Grooves 2: Metric scale 3: T-slot
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3
1
1
2
3
Plunger Cart
1: Push plunger in.
2: Press button to trigger.
2
Cart Features
1: Slots 2: Threaded
inserts 3: Bumpers
4: Attachment points
Cart Masses
About the Equipment
Track The 1.2 m aluminum track has two groves to guide the
wheels of carts, a metric scale for measuring cart positions, and
T-slots on both sides for attaching end stops, leveling feet and
other accessories.
Tip: The track is designed to support the weight of carts and related
apparatus. Excess weight will warp it. When you store the track, ensure
that no heavy object will be placed on top of it.
PAScars These carts run along the track on low-friction wheels.
Each cart includes a spring-loaded plunger that launches the cart off of an end stop or
another cart. Push the plunger in to the first, second, or third “click” (for a slow,
medium, or fast launch). To make the plunger pop out, press the trigger button. When
the plunger is not in use, push it all the way in to the fourth position for storage.
For elastic and inelastic collisions, both carts have hook-and-loop bumpers on one
end and magnetic bumpers on the other end. When the hook-and-loop bumpers collide, the carts stick to each other. When the magnetic bumpers collide, the carts repel
each other without touching. The magnetic bumpers also repel the magnets in the end
stops.
The top or each cart forms a tray designed to hold the included masses. The carts also
feature threaded inserts for attaching accessories and sensors, and slots for holding a
picket fence (such as PASCO part ME-9804) or the included angle indicator.
At each end are two attachment points for connecting a string or spring.
For more information, see the manual packaged with the PAScars.
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Cart Masses These masses are designed to be placed on the upper tray of a cart.
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Model No. ME-6955 Spare Parts
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1
3
4
Adjustable Feet
1: Slide tab into T-slot. 2: Tighten thumbscrew to
secure feet set. 3: Turn feet screws to level track.
4: Tighten lock nuts to secure feet screws.
1/4 1/4
1
2
3
4
Adjustable End Stop
1: Slide tab into T-slot on side of track. 2: Tighten
thumbscrew to secure end stop. 3: Magnets repel
cart’s magnetic bumper 4: Spring attachment stud
Pivot Clamp
T-slot
Adjustable Feet Attach the feet to the track as illustrated.
Turn the feet screws to level the track then tighten the lock nuts
to secure them.
For maximum stability, position the feet about 1/4 of the track
length from each end
Adjustable End Stops Attach the end stops to the track
as illustrated. The end stops contain magnets to repel the magnetic bumper of a cart. A stud is provided as an attachment
point for a spring.
Pivot Clamp Attach the pivot clamp to the T-slot of the track (as illustrated) to elevate one end of the track on a vertical rod.
Spare Parts
You can order any of the major components of the system using the part numbers
listed in the table on page 3. For an assortment of thumbscrews, square nuts, and other
small parts, order the IDS Spares Kit (ME-9823)
For help identifying a part, contact PASCO technical support (see page 27).
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1.2 m PAScar Dynamics System About the Experiments
About the Experiments
These eight experiments can be done with the equipment included in the system and
other equipment such as springs, pulleys and mass sets. See each experiment for a
specific equipment list.
1. Conservation of Momentum in Explosions (page 7): Demonstrate conservation
of momentum when two carts push off from each other.
2. Conservation of Momentum in Collisions (page 9): Demonstrate conservation
of momentum in elastic and inelastic collisions.
3. Simple Harmonic Oscillator (page 11): Study how the period of oscillation of a
system varies with its mass.
4. Oscillations on an Incline (page 14): Study the oscillation of a cart attached to a
spring on an inclined track.
5. Springs in Series and Parallel (page 17): Examine how springs combined in
different ways affect the period of oscillation of a cart.
6. Launch Speed (page 19): Show qualitatively how the final speed of the plunger
cart depends on its mass and the initial compression of the plunger spring.
7. Newton’s Second Law (page 20): Show quantitatively how the acceleration of a
cart is related its mass and net force.
8. Acceleration Down an Incline (page 22): Determine the strength of earth’s
gravity (g) by measuring the acceleration of a cart on an inclined track.
Additional Experiment Su ggestion s (page 25): Many of these suggestions are variations on the above experiments. Some require additional carts.
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Model No. ME-6955 Experiment 1: Conservation of Momentum in Explosions
pm1v1m2v
2
–0==
v
1
v
2
---- -
m
1
m
2
------
=
v
1
v
2
---- -
x
1
t
-------- -
x
2
t
-------- -
-------------- -
x
1
x
2
-------- -
==
x
1
x
2
-------- -
m
1
m
2
------
=
Experiment 1: Conservation of Momentum in Explosions
Required Equipment from Dynamics System
Track with Feet and End Stops
(2) PAScars
Collision Cart
Cart Masses
Other Required Equipment Suggested Model Number
Mass set ME-9348
Purpose
The purpose of this experiment is to demonstrate conservation of momentum with
two carts pushing away from each other.
Theory
When two carts push away from each other (and there is no net force on the system),
the total momentum is conserved. If the system is initially at rest, the final momentum
of the two carts must be equal in magnitude and opposite in direction to each other so
the resulting total momentum of the system is zero:
Therefore, the ratio of the final speeds of the carts is equal to the ratio of the masses of
the carts.
T o simpli fy this experiment, the starti ng point for the carts at rest is chosen so that the
two carts will reach the ends of the track simultaneously. The speed, which is the distance divided by the time, can be determined by measuring the distance traveled since
the time traveled by each cart is the same.
Thus the ratio of the distances is equal to the ratio of the masses:
Procedure
1. Instal the feet on the track and level it. Install one end stop at each end with the
magnetic sides facing away from the carts.
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1.2 m PAScar Dynamics SystemExperiment 1: Conservation of Momentum in Explosions
Figure 1.1
2. For each of the cases in Table 1.1, place the two carts against each other with the
plunger of one cart latched in the third position and touching the other cart (see
Figure 1.1). Push the plunger of the other cart all the way in to its storage position.
3. Tap the plunger release button and watch the two carts move to the ends of the
track. Experiment with different starting positions until the two carts reach the
ends of the track at the same time. Measure the masses of the carts. Record the
masses and the starting position in Table 1.1.
Table 1.1: Results
Additional
Mass on
Cart 1
00
500 g 0
1000 g 0
500 250
Additional
Mass on
Cart 2
m
1
m
2
Starting
Position
x
1
Data Analysis
1. For each of the cases, calculate the distances traveled from the starting position to
the end of the track. Record the result in Table 1.1.
2. Calculate the ratio of the distances traveled and record in the table.
3. Calculate the ratio of the masses and record in the table.
Questions
1. Does the ratio of the distances equal the ratio of the masses in each of the cases?
In other words, is momentum conserved?
x
2
x1/x
2
m2/m
1
2. When carts of unequal masses push away from each other, which cart has more
momentum?
3. When the carts of unequal masses push away from each other, which cart has
more kinetic energy?
4. Is the starting position dependent on which cart has the plunger? Why?
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Model No. ME-6955 Experiment 2: Conservation of Momentum in Collisions
Experiment 2: Conservation of Momentum in Collisions
Required Equipment from Dynamics System
Track with Feet
(2) PAScars
Other Required Equipment
Paper (for drawing diagrams)
Purpose
The purpose of this experiment is to qualitatively explore conservation of momentum
for elastic and inelastic collisions.
Theory
When two carts collide with each other, the total momentum of both carts is conserved regardless of the type of collision.
An elastic collision is one in which the carts bounce off each other with no loss of
kinetic energy . In this experiment, magnetic bumpers are used to minimize the energy
losses due to friction during the collision. In reality, this “elastic” collision is slightly
inelastic.
A completely inelastic collision is one in which the carts hit and stick to each other . In
this experiment, this is accomplished with the hook-and-loop bumpers on the carts.
Part I: Elastic Collisions
Figure 2.1
1. Instal the feet on the track and level it.
2. Orient the two carts on the track so their magnetic bumpers are toward each
other.
3. Test cases A1 through A3 and B1 through B3 described below. Draw two dia-
grams (one for before the collision and one for after the collision) for each case.
In every diagram, show a velocity vector for each cart with a length that approximately represents the relative speed of the cart.
A. Carts with Equal Mass
Case A1: Place one cart at rest in the middle of the track. Give the other cart an initial
velocity toward the cart at rest.
Case A2: Start the carts with one at each end of the track. Give each cart approximately the same velocity toward each other.
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