PASCO ME-9430 User Manual

Instruction Manual and
Experiment Guide for
the PASCO scientific
Model ME-9430

Dynamics Cart with Mass

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Dynamics Cart

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Copyright, Warranty and Equipment Return

Please—Feel free to duplicate this manual
subject to the copyright restrictions below.

Copyright Notice

The PASCO scientific Model ME-9430 Dynamics Cart
with Mass Manual is copyrighted and all rights reserved.

However, permission is granted to non-profit educational
institutions for reproduction of any part of this manual,
providing the reproductions are used only for their
laboratories and are not sold for profit. Reproduction
under any other circumstances, without the written
consent of PASCO scientific, is prohibited.

Limited Warranty

PASCO scientific warrants this product to be free from
defects in materials and workmanship for a period of one
year from the date of shipment to the customer. PASCO
will repair or replace, at its option, any part of the product
which is deemed to be defective in material or workman­ship. This warranty does not cover damage to the product
caused by abuse or improper use. Determination of
whether a product failure is the result of a manufacturing
defect or improper use by the customer shall be made
solely by PASCO scientific. Responsibility for the return
of equipment for warranty repair belongs to the customer.
Equipment must be properly packed to prevent damage
and shipped postage or freight prepaid. (Damage caused
by improper packing of the equipment for return shipment
will not be covered by the warranty.) Shipping costs for
returning the equipment, after repair, will be paid by
PASCO scientific.

Equipment Return

If this product requires return to PASCO scientific, for
whatever reason, notify PASCO scientific by letter or
phone BEFORE returning the product. Upon notification,
the return authorization and shipping instructions will be
promptly issued.

NOTE: NO EQUIPMENT WILL BE ACCEPTED
FOR RETURN WITHOUT AN AUTHORIZA­TION.

When returning equipment for repair, the units must be
properly packed. Carriers will not accept responsibility
for damage caused by improper packing. To be certain
the unit will not be damaged in shipment, observe the
following rules:

1. The carton must be strong enough for the item
shipped.

2. Make certain there is at least two inches of packing
material between any point on the apparatus and the
inside walls of the carton.

3. Make certain that the packing material can not shift in
the box, or become compressed, thus letting the instru­ment come in contact with the edge of the box.

Address: PASCO scientific

10101 Foothills Blvd.

Credits

This manual authored by: Scott K. Perry

This manual edited by: Dave Griffith

Roseville, CA 95678-9011

Phone: [phone]

FAX: [phone]

Email: [e-mail]

Web: www.pasco.com

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012-04840E

Dynamics Cart

Table of Contents

Section Page

Copyright, Warranty, Equipment Return, and Credits . . . . . . . . . . . . . . . . . . i

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Experiment 1: Kinematics (Average vs. Instantaneous Velocities) . . . . . . . 3

Experiment 2: Coefficient of Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Experiment 3: Newton's Second Law (Predicting Accelerations) . . . . . . . . 7

Experiment 4: Cart Calibration (Measuring the Spring Constant) . . . . . . . 11

Experiment 5: Rackets, Bats and "Sweet Spots" . . . . . . . . . . . . . . . . . . . . . 15

Experiment 6: Sliding Friction and Conservation of Energy . . . . . . . . . . . 19

Appendix (Replacing Parts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

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012-04840E

Dynamics Cart

Introduction

The PASCO Model ME-9430 Dynamics Cart with
Mass performs high quality motion experiments
through its low-friction design.

The PASCO Dynamics Cart has several excellent
features:

• An extremely low friction ball-bearing design pro­vides smooth motion.

• A built-in spring plunger, activated by a conve­nient trigger (button) located on the front end cap,
with three positions of launching amplitude, en­ables the cart to be launched without using addi­tional apparatus.

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

• Rugged construction on the cart-body and end­caps prevents damage to the cart and the environ­ment during high-impact situations.

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

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

• The mass of the Dynamics Cart is approximately
500g. The additional mass also has an approxi­mate mass of 500g.

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

• Other features include: rounded corners on molded
plastic end caps for durability, a tray on top of the
cart for application of additional mass, and the
ability of the carts to be stacked.

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

The spring plunger of the Dynamics Cart 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. To cock the spring
plunger, push the plunger in, and then push the plunger
upward slightly 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.

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

NOTE:

1. Before performing experiments with the Dy­namics Cart and Mass, they should be cali­brated to insure accurate results from your ex­periments. It is suggested to perform Experi­ment #2 before Experiment #5 and #4 before
#6.

2. To ensure 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 cart.

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

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Dynamics Cart

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Equipment

The ME-9430 Dynamics Cart with Mass includes
the following:

• (1) Dynamics Cart

• (1) 500g Mass

• Instruction Manual/Experiments Guide

Additional Equipment Required:

• A spool of thread

• Masses, such as PASCO's Slotted Mass Set (SE-

8704)

• A pulley and clamp, such as PASCO's Super Pul­ley with Clamp (ME-9448) or Super Pulley (ME-

9450) used with Model ME-9376A Universal
Table Clamp and Model SA-9242 Pulley Mount­ing Rod

• Metric Ruler, such as PASCO's Metric Measuring
Tape (SE-8712) and 30cm/12in. Ruler (SE-8731)

• Stopwatch, such as PASCO's Digital Stopwatch
(SE-8702)

• Mass balance, such as PASCO's Triple-Beam Bal­ance (SE-8723)

• A friction block that can fit in the cart's accessory
tray (i.e. PASCO part number 003-04708)

Dynamics Cart

(500 g ± 20 g)

Plunger Bar

Knob

Plunger Bar

Release

Plunger Bar

Accessory

Tray

Additional Mass

(500 g ± 20 g)

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Dynamics Cart

Experiment 1: Kinematics

(Average vs. Instantaneous Velocities)

EQUIPMENT NEEDED:

– Dynamics Cart (ME-9430)

– Metric tape (SE-8712)

– Stopwatch (SE-8702)

Purpose

In this lab, the Dynamics Cart will be used to investigate one dimensional accelerated
motion. You will launch the cart over the floor using the built-in spring plunger. The cart
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 cart 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.

Theory

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

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

And the value of the acceleration would be given by:

D

v

= (EQN–1)

av

T

v

= 2vav = (EQN–2)

0

2D

T

Figure 1.1

v

If the acceleration and v

∆

a = = = – (EQN–3)

∆

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

o

t

0 – v

T

0

2D

T

2

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

2

1

(EQN–4)

Calculated values of t

d = v

will be compared with directly measured values. The extent to which

1

+ 1/2at

0t1

the calculated values agree with the directly measured values is an indication of the con­stancy of the acceleration of the cart.

Note your theoretical values in Table 1.1.

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Dynamics Cart

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, you can determine t

, T and D for each

1

launch. Practice this step a few times before you start recording data.

NOTE: To eliminate reaction time errors, have the person who launches the cart also be the
timer!

3. Launch the cart 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. (NOTE: If the timer feels that a distraction interfered with the measurement, don't count
that trial.) 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

Trial

Experiment

t1 (sec) T (sec) D (cm)

vo (cm/s)

a (cm/s2)

Theory

t1 (sec)

1

% Diff.

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:

– Dynamics Cart (ME-9430)

– Metric tape (SE-8712)

– Stopwatch (SE-8702)

Purpose

In this lab, the Dynamics Cart will be launched over the floor using the on-board spring
launcher. The cart 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
and θ, the small angle at which the floor is inclined, two separate experiments must be done.
(Recall that to determine the value of two unknowns, you must have two equations.)

Dynamics Cart

Experiment 2: Coefficient of Friction

r

Theory

UPSLOPE

Figure 2.1

DOWNSLOPE

The cart 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 down-slope, the acceleration of the cart is given by:

a1 = + gsinθ – µrg (EQN-1) (since cosθ = 1)

And the acceleration in the direction that is slightly up-slope will be:

a

= – gsinθ – µrg (EQN-2)

2

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

2d

a = (EQN-3)

2

t

Having obtained numerical values for a1 and a2, EQN-1 and EQN-2 can be solved
simultaneously for µr and θ.

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