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Instruction Manual
PAStrack Wheel Set
ME-6964
012-10635A
Mounting
Screw
Low-friction Wheels
Introduction
Alignment Tabs
Low-friction Wheels
Mounting Screw
The PAStrack Wheel Set consists of two wheel enclosures that mount on the bottom of any PASCO PAStrack.
Once the wheel set is mounted on the bottom of a PAStrack, the PAStrack with wheels can be used to help students better understand frames of reference. For example, a cart runs on top of the PAStrack with wheels as the
PAStrack itself moves. Using visual observation or motion sensors, students can compare the motion of the cart
relative to the moving PAStrack and relative to the “stationary” lab frame.
The PAStrack with wheels can be used on any flat surface such as a tabletop or floor. It can also be used with a
PASCO dynamics track, which reduces friction and is easily leveled or inclined. The PAStrack with wheels is
compatible with other PASCO carts, including motorized carts and fan carts.
Assembly
Each wheel enclosure has alignment tabs and a mounting screw.
The alignment tabs are designed to
fit into similarly shaped notches
on both ends of the PAStrack
approximately 11 cm from each
end.
800-772-8700 www.pasco.com
Remove
Accessory
Screw
Align Tabs
with Notches
Mounting Screw
PAStrack with wheels Suggested Activities
Remove the accessory screw from the threaded hole on the underside of the P AS track
between the notches. Align the tabs of the PAStrack Wheel Set with the notches, and
tighten the mounting screw into the threaded hole to hold the wheel set in place
against the bottom of the PAStrack.
Suggested Activities
The experiments and demonstrations described in this manual can be done with the
P AS track with wheels and other equipment listed on page 2. T o add motion sensors to
any of the activities, use the setup detailed in Activity 1: Relative Velocity.
Suggested Equipment Part Number
PAStrack with Wheels Any PAStrack plus the ME-6964
Stationary Track part of any PASCO dynamics system
Dynamics Cart ME-6951, ME-6950, ME-9430, or ME-9454
Motorized Cart ME-9781
Time Pulse Accessory ME-9496
Fan Cart or Fan Accessory ME-9485 or ME-9491
Sail Part of ME-9485, or use a piece of cardboard
Compact Cart Mass (250 g) ME-6755 or similar
Rotational Inertia Set ME-9774
Motion Sensors (qty. 2) CI-6742 or PS-2103
Some of these activities also call for stands or blocks to position sensors and incline
the track.
Activity 1: Relative Velocity
In this experiment, you will use two motion sensors to measure the velocities of the
PAStrack with wheels and a motorized cart in the lab reference frame. From these
measurements, you will calculate the velocity of the cart in the PAStrack with wheel’s
reference frame.
Equipment Setup
1. Set up two motion sensors as pictured to measure the velocities of the motorized
cart and PAStrack with wheels
Note that the motion sensor is mounted to allow the PAS track with wheels to pass
under it. The sensor’s position and angle are adjusted so it detects only the cart,
not the PAStrack with wheels. (The support piece in the picture is the CI-6692
2
NOTE: The illustrations
show a PASCO Relative
Motion Track in place of
the PAS track with wheels.
All of the setups and procedures are the same for
the PAStrack with wheels.
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Model No. ME-6964 Suggested Activities
Dynamics Track Mount; a similar arrangement can be achieved with a rod stand,
right-angle clamp, and horizontal support rod.)
2. Plug the Time Pulse Accessory into the EXT. INPUT jack on the Motorized Cart.
3. Set the switch on the cart to ON (Batt.), and turn speed knob to maximum (f ull
clockwise).
4. Set the rotary switch on the Time Pulse Accessory to position 3, the variable-time
setting.
5. Place the cart at one end of the PAStrack with wheels and press the START but-
ton on the Time Pulse Accessory; after a two second delay the cart will drive for
a few seconds and stop automatically. Adjust the variable-time knob so that the
cart drives nearly the full length of the PAStrack with wheels without falling off
the end. (It is not necessary to let the PAStrack with wheels move freely for this
step.)
6. Set the sample rates of both sensors to 20 Hz. Record some trial data runs and
adjust the positions and angles of the sensors to get clear position and velocity
data.
Calculations Setup
For more information about creating calculations in DataStudio, click the Calculate button, then
press F1 (Windows) or the Help key (Mac).
1. Since the sensors are facing in opposite directions, it is necessary to
create a calculation that reverses the velocity measurement of the
right-hand sensor; that way both sensors will register movement from
left to right as positive. In DataStudio, create the calculation
V
= −V
track
where V is the measured velocity.
2. Create a second calculation for the velocity of the cart relative to the
PAStrack with wheels:
V
= V
cart
− V
track
where V
V
track
is the measurement made by the left-hand sensor and
cart
is the previous calculation.
rel
3. (This step is optional.) If you plan to use this arrangement of sensors for other
experiments in which you will compare the positions of the cart and
PAStrack with wheels, create a calculation to transform the position
measurement made by the right-hand sensor:
=0.5− x
x
where x
measured
track
is the measurement made directly by the right-hand
measured
sensor. The number 0.5 is the difference (in meters) between the
length of the PAStrack with wheels and the distance between the
sensors, which may be different in your setup. This calculation will make the
readings from both sensor identical when the back of the cart is even with the left
end of the PAStrack with wheels.
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3
PAStrack with wheels Suggested Activities
Procedure
Record data as the cart runs from left to right across the PAStrack with wheels, which
is free to move on the stationary track.
Analysis
V
1. Look at a graph of
versus time. Note that it takes a short time for the motor-
rel
ized cart to get up to speed, then it travels at a constant velocity relative to the
PAStrack with wheels.
2. Compare
rel
to V
. Why is the cart’s velocity higher in the PAStrack with
cart
V
wheels’ reference frame than in the lab reference frame?
3. Record another data run, but this time hold the PAStrack with wheels so it does
not move. Compare
from this run to V
cart
from the first run. Why are they the
rel
V
same?
Further Study
Clip a motion sensor to the end of the PAStrack with
wheels as pictured. In this configuration, the sensor
makes a direct measurement of the cart’s velocity in
the PAStrack with wheels’ reference frame.
Hold the sensor’s cord so that it does not prevent the PAStrack with wheels from
moving freely. Record data with this setup as the cart runs across the PAStrack with
wheels.
V
How does this direct measurement of
compare to the original measurement?
rel
Activity 2: Center of Mass
In this experiment, the motorized cart will run the length of the PAS track with wheels
and stop automatically while the PAStrack with wheels is free to move on a stationary
track. You will measure the initial and final positions of both objects and calculate
how the center of mass of the cart-track system changes.
Setup
To simplify the theory behind this experiment, the cart and PAStrack with wheels
should be considered an isolated system. To make this possible, use the following
steps to incline the stationary track so that a component of the gravitational force cancels the frictional force between the PAStrack with wheels and the stationary track.
1. Follow steps 2 through 5 on page 3 to connect and adjust the Time Pulse Acces-
sory and motorized cart.
2. Level the stationary track.
3. Place the PAStrack with wheels on
the stationary track and place the cart
at the left end of the PAStrack with
wheels. Press START on the Time Pulse Accessory and allow the cart to drive
across the track from left to right as the track moves in the opposite direction.
Note that when the cart stops running, the cart-track system continues to move to
the right. The force that caused this movement was the friction between the PAStrack with wheels and the stationary track.
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Model No. ME-6964 Suggested Activities
4. Raise the right end of the stationary track slightly and repeat step 3. The
cart-track system should now move to the right slower after the cart stops running. Adjust the incline of the track and repeat step 3 until the cart-track system
stops when the cart stops running.
You should find that cart-track system remains stationary if you hold it and let go
very carefully (because static friction is higher than kinetic friction), and it will
travel at a constant velocity if you nudge it to left (because the component of
gravity parallel to the track cancels the friction).
1
Procedure
1. Place the PAStrack with wheels on the stationary track and place the cart at the
left end of the PAStrack with wheels. Using tape, mark:
• the position of the cart on the PAStrack with wheels,
• the position of the cart on the stationary track, and
1
Another way to counteract friction is to attach a
small mass hanging on a
string over a pulley.
Adjust the mass so that
the system stops when
the cart stops running, or
use a photogate to monitor the speed of the pulley, and adjust the mass
so that it moves at a constant velocity when you
nudge the track.
• the position of the PAStrack with wheels on the stationary track.
2. Press START on the Time Pulse Accessory and allow the cart to drive across the
track from left to right as the track moves in the opposite direction.
3. After the cart stops, measure:
• ∆x
• ∆x
• ∆x
cart-track
cart
track
, the displacement of the cart on the PAStrack with wheels;
, the displacement of the cart on the stationary track;
, the displacement of the PAStrack with wheels on the stationary
track.
Analysis
1. What is the relationship between ∆x
(Hint: do ∆x
cart
and ∆x
they be combined to equal ∆x
have the same sign or opposite signs? How should
track
cart-track
cart-track
?)
cart
, and ∆x
track
?
, ∆x
2. The change in position of the center of mass of the cart-track system is
1
---- -
∆x
cm
where M is the m ass of the system, m
mass of the PAStrack with wheels. Measure the masses and calculate . Did
m
cart∆xcartmtrack∆xtrack
M
+()=
is the mass of the cart, and m
cart
∆x
the system’s center of mass change significantly?
track
cm
is the
3. Add a 250 g mass to the cart and repeat the experiment. Move the mass from the
cart to the track (as pictured) and repeat the experiment again.
In the three cases, what variables change? What variables do not change
significantly?
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5
PAStrack with wheels Suggested Activities
Activity 3: Fan Cart
Use this demonstration to compare the behavior of the fan cart to that of the motorized cart in the previous activities. Before starting the fan cart each time, predict how
the fan cart and P AS track with wheels will move relative to the stationary track and to
each other.
1. Place the PAStrack with wheels on a level stationary track.
2
2. Place a fan cart on the PAStrack with wheels. Turn on the fan.
What happens?
3. Attach a sail to the PAStrack with wheels so the air from the fan blows onto the
3
Now what happens?
sail.
Activity 4: The Slingshot Effect
In an elastic collision between a moving object and a much more massive stationary
object (a tennis ball bouncing off a wall, for instance), the speed of the smaller object
after the collision is equal to its speed before. The interaction that occurs when a
space probe “slingshots” around a planet can be thought of as a similar elastic collision. How do engineers use this technique to increase the speed of a space probe?
(Hint: consider the interaction in the planet’s frame of reference and in the Earth’s
frame of reference.)
2
If you have a Time
Pulse Accessory , use it to
make the fan run for a
second or two before
stopping.
3
The picture shows the
sail included with Fan
Cart model ME-9485
attached with a binder
clip. You can also use a
piece of cardboard.
In this experiment, you will observe an elastic collision between a “planet” (the PAStrack with wheels) and a “space probe” (a freely moving cart).
Setup
1. Turn a dynamics cart upside down and use a rubber band secure it at one end of
the PAStrack with wheels, with the magnet-equipped end of the cart pointing
toward the center. This cart will be the bumper that the other cart collides with.
2. Place the P A Strack with wheels on a 2.2 m dynamics track, on a long tabletop, or
on the floor.
3. Position a motorized cart, as pictured, to push the PAStrack with wheels.
4. Place the other dynamics cart right-side up on the PAStrack with wheels with the
magnet end pointing toward the upside-down cart.
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Model No. ME-6964 Suggested Activities
5. Attach a motion sensor to the end of the PAStrack with wheels to record the
velocity of the cart relative to the PAStrack with wheels.
Procedure
Start data collection, then start the motorized cart and observe what happens.
Analysis
1. Before looking at the motion-sensor data, consider the motion of the cart in the
lab reference frame. Did the cart’s speed after the collision appear to be greater
than, less than, or equal to its speed before the collision?
2. Now consider the motion of the cart as measured by the motion sensor. In the
sensor’s reference frame, was the cart’ s speed after the collision greater than, less
than, or equal to its speed before the collision?
Activity 5: Inclined Plane
When you release the PAStrack with wheels on an inclined plane, it undergoes constant acceleration. When you hold the PAStrack with wheels still and release a
dynamics cart on top of it, the cart undergoes the same constant acceleration. What
happens when both the PAStrack with wheels and dynamics cart are released
together?
1. Stack a dynamics cart
on the PAStrack with
wheels on an inclined
stationary track (as pictured), but don’t release
them yet.
2. Predict how the cart will move relative to the PAStrack with wheels and relative
to the stationary track.
3. Release them. Was your prediction correct?
4. For comparison, stack the cart on the PAStrack with wheels on a level stationary
track. Predict what will happen when you pull the PAStrack with wheels so that it
accelerates. Try it. How does the cart move relative to the stationary track? How
does it move relative to the PAStrack with wheels?
5. Why does the system behave differently when the acceleration of the PAStrack
with wheels is caused by your hand compared to when the acceleration is caused
by gravity?
Activity 6: Rotational Inertia
1. Stack a solid disk and
a ring on the PAStrack
with wheels on a level
stationary track. Predict what will happen
when you pull the
PAStrack with wheels
so that it accelerates.
Try it. How do the disk and ring move relative to each other? How do they move
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7
PAStrack with wheels Suggested Activities
relative to the stationary track? How do they move relative to the P A Strack with
wheels?
2. Incline the stationary track. Place the disk and ring on the PAStrack with wheels
and hold them on the stationary track. Predict what will happen when you release
the disk, ring, and PAStrack with wheels all together.
3. Release them. How do the disk and ring move relative to each other? How do
they move relative to the stationary track? How do they move relative to the
PAStrack with wheels?
4. Why does the system behave differently when the acceleration of the PAStrack
with wheels is caused by your hand compared to when the acceleration is caused
by gravity?
Notes and Sample Data
Activity 1: Relative Velocity
In the first run (left),
was positive, V
cart
was negative, and V
track
was equal to their
rel
V
difference.
When the P AStrack with wheels was held still (center),
was equal to V
cart
from the
rel
V
original data run.
V
The direct measurement of
wheels (right), was also equal to
made with the sensor attached to the PAStrack with
rel
V
from the first run. Note that the cart was adjusted
rel
to run for slightly less time since it had to start 15 cm away from the sensor.
Activity 2: Center of Mass
As shown in this graph (acquired
using two motion sensors), the
distances traveled by the PAStrack with wheels and the motorized cart are different, but the
center of mass of the cart-track
system remains nearly stationary.
Activity 3: Fan Cart
Without the sail, the fan cart moves and the PAStrack with wheels remains stationary.
Unlike in the experiment with the motorized cart, the center of mass of the cart-track
system does not remain constant because this system is not isolated; the fan cart interacts with the air surrounding the apparatus.
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Model No. ME-6964 Maintenance and Replacement Parts
When the sail is attached to the PAStrack with wheels, the cart and PAStrack with
wheels move in opposite directions.
Activity 4: The Slingshot Effect
The cart was visually observed to be
nearly stationary (relative to the observer)
before the collision and moving to the left
faster than the PAStrack with wheels after
the collision. The data (right), collected by
a motion sensor attached to the PAStrack
with wheels, show that the speeds before
and after the collision were approximately
equal.
Activity 5: Inclined Plane
When the cart and PAStrack with wheels are released together on the inclined plane,
the cart does not move relative to the PA Strack with wheels; both accelerate at the
same rate. When the level PAStrack with wheels is accelerated by hand, the cart
remains stationary in the lab frame.
Activity 6: Rotational Inertia
When the PAStrack with wheels is accelerated by hand, the disk and ring both move
to the right, but the ring moves farther.
When the disk, ring, and PAStrack with wheels are all released on an inclined plane,
they all accelerate at the same rate. Since the round objects do not move relative to the
PAStrack with wheels on which they are resting, they do roll and their respective rotational inertias are not important.
Maintenance and Replacement Parts
The PAStrack with wheels is not designed to withstand abuse such as being dropped
or stood on. Excess weight or shock may cause damage.
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PAStrack with wheels Specifications
Auth
If it becomes necessary to replace the wheels, use the PAScar/GOcar Replacement
Axles (ME-6957, 4-pack), which consist of wheels and axles.
Keeps the wheel bearings away from sources of dust, such as chalk. If the bearings
become contaminated with dust, clear them with compressed air.
Specifications
Approximate Dimensions (L×W×H) 6.2 × 8.2 × 5.4 cm
Mass (each) Approximately 0.055 kg
Compatible Equipment Other PASCO carts and tracks
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) 786-3292
Web: www.pasco.com
Email: support@pasco.com
Limited Warranty
For a description of the product warranty, see the PASCO catalog.
Copyright
The PASCO scientific 012-10635A PAStrack Wheel 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 prohibited.
Trademarks
PASCO, PASCO scientific, and DataStudio 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. Windows is a registered trademark of Microsoft Corporation in the United States and/or other countries. Mac is a trademark of Apple Computer, Inc., registered in
the U.S. and other countries.
ors:Jon Hanks
10
Alec Ogston
Revised by: Dave Griffith
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