PASCO ME-6950 User Manual

Instruction Manual and
Experiment Guide for
the PASCO scientific
Model ME-6950

PAScar with Mass

012-07361B

250g

250g

© 2000 PASCO scientific $10.00

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PAScar with Mass

Introduction

The PASCO Model ME-6950 PAScar with Mass
performs high quality motion experiments through
its low-friction design.

The PASCar with Mass has several excellent
features:

• Extremely low friction ball-bearing design pro­vides smooth motion.

• Built-in spring plunger, activated by a conve­nient trigger (button), with three positions of
launching amplitude enables the car to be
launched without using additional apparatus.

• Unique suspension system allows the wheels to
collapse inside the body of the car to prevent
damage to the internal components of the car
caused by being dropped or other misuse (such
as the car being used as a roller skate).

• Convenient holes located at the top of the end
cap on each end of the PAScar facilitate the
use of string, springs, etc.

• Hook and loop fasteners on the front of each
PAScar enable the user to perform inelastic
collision experiments without using additional
apparatus.

• The mass of the PAScar is approximately
250g. The additional mass also has an approxi­mate mass of 250g.

NOTE: For best results, measure the mass of
the car and mass bar with an accurate balance
or scale.

The spring plunger of the PAScar has three cocking
positions. Determine the one that gives you a range
that fits your situation best, taking into account the
limitations of space. Most experiments require a
range of at least 2 meters or more.

Practice launching the PAScar by placing the cart
on the floor with its cocked plunger against a wall
or a secured brick.

NOTES:

1. Before performing experiments with the
PAScar and Mass, calibrate to insure accu­rate results from your experiments. We
suggest performing Experiment #2 before
Experiment #5 and #4 before #6.

2. To insure that you do not give the cart an
initial velocity, other than that supplied by
the spring plunger, release the trigger by
tapping it with a rod or stick using a flat
edge.

3. Rolling distance can be shortened by add­ing more mass to the car.

4. For even less friction, use 1/4-inch plate
glass as surface for the car.

• Other features include a tray on top of the cart
for application of additional mass and the abil­ity of the cars to be stacked.

While performing experiments, you may find that
you get better results by making the surface over
which the car rolls more uniform and clean. One
way to achieve this is by taping a long piece of
butcher paper to the surface on which the cart rolls.

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PAScar with Mass

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Equipment

The ME-6950 PAScar with Mass includes the
following:

• (2) PAScars, 1 red, 1 blue

• (2) 250 g mass

• Instruction Manual/Experiments Guide

Additional Equipment Required

• A spool of thread

• Masses, such as the Slotted Mass Set (SE-8704)

• A pulley and clamp, such as the Super Pulley
with Clamp (ME-9448A) or the Super Pulley
(ME-9450) used with the Model ME-9376B Uni­versal Table Clamp and Model SA-9242 Pulley
Mounting Rod

• Metric ruler, such as the Metric Measuring Tape
(SE-8712A).

• Stopwatch, such as the Digital Stopwatch (SE-

8702)

• Mass balance, such as the Triple-Beam Balance
(SE-8723)

• A friction block that can fit in the car's accessory
tray (such as PASCO's Friction Block, part num­ber 003-04708)

Plunger bar

Plunger bar

release button

Accessory

tray

Additional mass

(250 g)

PAScar

(250 g)

250g

250g

2

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EQUIPMENT NEEDED:

– PAScar (ME-6950)

– Metric tape (SE-8712)

– Stopwatch (SE-8702)

Purpose

In this lab, the PAScar will be used to investigate one dimensional accelerated motion.
The car will be launched over the floor using the built-in spring plunger. The car will
“decelerate” over the floor under the combined action of rolling friction and floor
slope. You will be able to establish whether or not the acceleration of the car is con­stant. This will be done by initially assuming a constant acceleration and then by
examining the results to see if they are consistent with this assumption.

PAScar with Mass

Experiment 1: Kinematics

(Average vs. Instantaneous Velocities)

Figure1.1

Theory

The car will be allowed to roll to a stop. The distance D covered and the total elapsed
time T from launch to stop will be measured and recorded. The average velocity over
this interval is given by:

D

v

=

(EQN-1):

av

T

If the acceleration of the car is constant as it rolls to a stop over the floor, then the
initial instantaneous velocity of the car at the final moment of launch is given by:

2D

T

(EQN-2):

v

= 2vav =

0

And the value of the acceleration would be given by:

v

(EQN-3):

If the acceleration and v

a = = = –

are known, then the time t1 required to cover the distance d

o

0 – v

0

t

T

2D

T

2

to some intermediate point (i.e. short of the final stopping point!) can be calculated by
applying the quadratic formula to:

(EQN-4):

d = v

+ 1/2at

0t1

2

1

Calculated values of t1 will be compared with directly measured values. The extent to
which the calculated values agree with the directly measured values is an indication of
the constancy of the acceleration of the car.

Note your theoretical values in Table 1.1.

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PAScar with Mass

Procedure

1. Once you have roughly determined the range of the cart, clearly mark a distance d that is
about half way out from the start. Measure this distance and record it at the top of Table

1.1.

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2. Using a stopwatch with a lap timer and metric tape, it is possible to determine t
for each launch. Practice this step a few times before you start recording data.

NOTE: To eliminate reaction time errors, it is very important to have the person who
launches the cart also be the timer!

3. Launch the car and record the data described in the previous step for six trials. To cock
the spring plunger, push the plunger in, and then push the plunger slightly upward to
allow one of the notches on the plunger bar to “catch” on the edge of the small metal bar
at the top of the hole. (Don’t count the trials in which the timer feels that a distraction
interfered with the measurement.) Record your best trials in Table 1.1.

4. Using the equations described in the theory section and the data recorded in the table, do
the calculations needed to complete the table.

Data Analysis

d = _______cm

Table 1.1

TheoryExperiment

Trial

t1 (sec) T (sec)

D (cm)

vo (cm/s) a (cm/s2)t1 (sec)

, T and D

1

% Diff.

1

2

3

4

5

6

Questions

1. Is there a systematic difference between the experimental and calculated values of t1? If
so, suggest possible factors that would account for this difference.

2. Can you think of a simple follow-up experiment that would allow you to determine how
much the cart’s “deceleration” was affected by floor slope?

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EQUIPMENT NEEDED:

– PAScar (ME-6950)

– Metric tape (SE-8712)

– Stopwatch (SE-8702)

Purpose

In this lab, the PAScar will be launched over the floor using the on-board spring
launcher. The car will “decelerate” over the floor under the combined action of rolling
friction and the average floor slope. To determine both the coefficient of rolling
friction µ
ments must be done. (Recall that to determine the value of two unknowns, you must
have two equations.)

Experiment 2: Coefficient of Friction

and θ, the small angle at which the floor is inclined, two separate experi-

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PAScar with Mass

Theory

UPSLOPE

Figure 2.1

DOWNSLOPE

The car will be launched several times in one direction, and then it will be launched several
times along the same course, but in the opposite direction. For example, if the first few runs
are toward the east, then the next few runs will be toward the west. See Figure 2.1. In the
direction which is slightly downslope, the acceleration of the car is given by:

(EQN-1):

a1 = + gsinθ – µrg (since cos2θ + sin2θ =1)

And the acceleration in the direction that is slightly upslope will be:

= – gsinθ – µrg

(EQN-2):

a

2

Numerical values for these accelerations can be determined by measuring both the
distance d that the car rolls before stopping and the corresponding time t. Given these
values, the acceleration can be determined from:

(EQN-3):

Having obtained numerical values for a

2d

a =

2

t

and a2, EQN-1 and EQN-2 can be simultaneously solved

1

for µr and θ.

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PAScar with Mass

Procedure

1. Place the car in its starting position and then launch it. To cock the spring plunger,
push the plunger in, and then push the plunger slightly upward to allow one of the
notches on the plunger bar to “catch” on the edge of the small metal bar at the top of
the hole. Using a stopwatch and metric tape, determine the range d and the total time
spent rolling t. Record these in Table 2.1.

2. Repeat step 1six times for each direction and enter your results in Table 2.1.

3. Using EQN-3, compute the accelerations corresponding to your data and an average
acceleration for each of the two directions.

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4. Using the results of step 3, determine µ
unknowns.

Trial

First Direction

d (cm) t (sec)

cm

a ( )

s

1

2

3

4

5

6

and θ by algebraically solving for the two

r

Table 2.1

Second Direction

Trial

2

d (cm) t (sec)

1

2

3

4

5

6

cm

a ( )

2

s

Average Acceleration = __________

cm

2

s

Average Acceleration = __________

Data Analysis

Coefficient of rolling friction = ________________ Floor Angle = ________________

Questions

1. Can you think of another way to determine the acceleration of the car? If you have

time, try it!

2. How large is the effect of floor slope compared to that of rolling friction?

6

cm

s

2

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PAScar with Mass

Experiment 3: Newton's Second Law

(Predicting Accelerations)

EQUIPMENT NEEDED:

– PAScar (ME-6950)

– Pulley and pulley clamp (ME-9448)

– Mass set (SE-8704)

– Stopwatch (SE-8702)

– String

– Paper clips

– Block (to act as bumper)

– Balance (SE-8723 or equiv.)

Purpose

In this lab, a small mass m will be connected to the PAScar by a string as shown in Figure

3.1. The string will pass over a pulley at the table’s edge so that as the mass falls the car
will be accelerated over the table’s surface. As long as the string is not too elastic and
there is no slack in it, both the falling mass and the PAScar will have the same accelera­tion. The resulting acceleration of this system will be experimentally determined and this
value will be compared to the acceleration predicted by Newton’s Second Law.

Theory

Bumper

block

Paper clips

Trigger

Figure 3.1

The car will be released from rest and allowed to accelerate over a distance d. Using a
stopwatch, you will determine how long it takes, on average, for the car to move through
the distance d. An experimental value for the car’s acceleration a can be determined
from:

1

d = at

2

2

which leads to: a = (Experimental Value)

2d

t

2

Assuming that the tabletop is truly horizontal (i.e. level), Newton’s Second Law ( F = ma)
predicts that the acceleration of this system will be:

F

M

net

TOTAL

a = or

a = ( ) g (Theoretical Value)

M

m

TOTAL

Procedure

1. Set up the pulley, car, and a bumper of some sort to prevent the car from hitting the
pulley at the end of its run. Add the following masses to the bed of the car: 10 g, 50 g,
500 g and two 20-gram masses.

2. Carefully level the table until the car has no particular tendency to drift or accelerate in
either direction along its run.

3. Put a loop in one end of the string and place this loop over the spring-release trigger on
the PAScar. Drape the string over the pulley. Adjust the pulley so the string is level.

4. Adjust the length of the string so that the longest arrangement of masses that you intend
to use will not hit the floor before the car has reached the end of its run. Put a loop in this
end of the string.

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PAScar with Mass

NOTE: The car’s acceleration falls to zero when the falling mass hits the floor.

5. Hang enough paper clips onto the dangling loop in the string until the car will just
continue to move without apparent acceleration when barely nudged. This small added
mass will compensate for friction in the system and will be ignored in the following
calculations. The paper clips will remain attached to the loop throughout the experi­ment!

6. Move a 10 gram mass from the bed of the car to the hanging loop and pull the car back
to a clearly marked starting point. Determine the distance d that the car will move from
the starting point to the bumper block and record this distance at the top of Table 3.1.

NOTE: The total mass of the system will remain constant throughout the experiment.

7. Practice releasing the car being careful not to give it any push or pull as you do so. The
best way to do this is to press your finger into the table in front of the car thereby
blocking its movement. Quickly pull your finger away in the direction that the car wants
to move. At the instant you pull your finger away, start your stopwatch. Stop your
stopwatch at the instant the car arrives at the bumper. To eliminate reaction time errors,
it is best that the person who releases the car also does the timing!

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8. Determine the average time for the car to move through the distance d, having been
released from rest. Record the average of the four time trials in which you have the
most confidence in Table 3.1. Repeat for all of the masses given in the data table.

9. Excluding the pulley, determine the total mass of your system, M

(car, added

Total

masses, string) and record at the top of Table 3.1. (It will be close to 1100 grams, but
you might want to check it on a balance.)

10. Fill in the table using your data and the equations given in the Theory section.

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