PASCO SE-9719 User Manual

Includes

Teacher's Notes

and

Typical

Experiment Results

Instruction Manual and
Experiment Guide for

012-07192A

07/99

the

PASCO scientific

Model SE-9719

DISCOVER DENSITY SET

© 1999 PASCO scientific $7.50

Discover Density Set 012–07192A

012–07192A Discover Density Set

Table of Contents

Section Page

Copyright, Warranty, and Equipment Return............................................................................... ii

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

Equipment ................................................................................................................................. 2

Actitivies ................................................................................................................................... 3

The Speed of Sound (Pre-lab) .............................................................................................. 3

Finding an Equation Relating Mass and Volume ................................................................ 5

The Mass of Fluorite Octahedra (Pre-lab) ............................................................................ 7

Finding an Equation Relating Mass and Diameter of Tranparent Plastic Spheres ........... 13

Discovering a Mathematical Equation That Describes Experimental Data (Pre-lab) ....... 1 4

Finding an Equation Relating Mass to Length and Diameter of Black Plastic Cylinders 1 7

Specfications for the Parts ....................................................................................................... 1 9

Teacher’s Notes ...................................................................................................................... 21

Technical Support ....................................................................................................Back Cover

i

Discover Density Set 012-07192A

Copyright, Warranty , and Equipment Return

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

Copyright Notice

The PASCO scientific 012-07192A Discover
Density manual is copyrighted and all rights
reserved. However, permission is granted to non­profit educational institutions for reproduction of
any part of the 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 the 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. The
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.

Credits

Author: Jim Housley
Editor: Sunny Bishop

Equipment Return

Should the product have to be returned to PASCO
scientific for any reason, notify PASCO scientific by
letter, phone, or fax 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 FROM PASCO.

When returning equipment for repair, the units
must be packed properly. 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:

➀ The packing carton must be strong enough for the

item shipped.

➁ Make certain there are at least two inches of

packing material between any point on the
apparatus and the inside walls of the carton.

➂ Make certain that the packing material cannot shift

in the box or become compressed, allowing the
instrument come in contact with the packing
carton.

Address: PASCO scientific

10101 Foothills Blvd.
Roseville, CA 95747-7100

Phone: [phone]
FAX: [phone]
e-mail: [e-mail]
Web site: www.pasco.com

ii

012–07192A Discover Density Set

Introduction

The PASCO SE-9719 Discover Density Set provides materials and activities to
guide students through some basic graphical analysis techniques.

In each case, an example is worked out, with explanations, and then the
student is asked to perform a similar analysis based on the materials in the set.

In the first analysis, students discover the concept as a mathematical constant
relating measurements of a particular substance.

Then they are asked to discover experimentally an equation that predicts the
mass of spheres of unknown, but constant, composition, based on their
diameter.

Finally, they are lead to develop an equation in three variables that predicts the
mass of cylinders of unknown, but constant, composition, based on
measurements of their diameter and length.

The only mathematical formula students are expected to know is that for slope.
If they recall special volume formulas for spheres and cylinders, they are asked
not to use this information in the development of their equations. After
graphical analysis yields the desired equations, students can use volume
formulas and tabulated density data to verify the correctness of the equations
they have discovered experimentally.

Other Uses

Because the items in the set are machined to close tolerances, and dimensions
and masses are given in the teacher’s guide, the set may be used for other
purposes, such as a traditional density set, or as items to test students’ ability to
make accurate measurements, etc.

1

Discover Density Set 012–07192A

Equipment

Included:

• PASCO SE-9719 Discover Density Set

Figure 1

Contents of the SE-9719 Discover Density Set

2

012–07192A Discover Density Set

Activities

The Speed

of Sound

(pre-lab)

Introduction

This sample problem presents you with experimental data, and then leads you
through a process to obtain an equation that relates the data. A similar problem
based on the materials in this set is left for you to do, based on the same
process. The method is then extended to more complex situations.

A lightning bolt struck the earth, and upon seeing it, a number of observers
started timing, using stopwatches. The observers each stopped their watches
when they heard the thunder. The times recorded, and the distances of the
observers from the point the lightning struck are recorded in the table. The
variables have arbitrarily been labeled x and y:

x y
time distance
(s) (km)

3.7 1.2

5.2 1.8

8.3 2.8

12.1 4.1

14.9 5.1

Figure 2

Graph of Speed of
Sound data

When this data is graphed, a straight line can be drawn that closely
approximates the pattern of the data. We may assume that there are errors in
the data caused by factors such as random differences in human reaction time
in actuating the stopwatches, and inaccuracies of an unpredictable nature in
measuring the distances. Such errors may be the reason that the points do not
all fall exactly on the line.

3

Discover Density Set 012–07192A

In algebra, the formula for a graph such as above is often given by:

y = m x + b,

where y is the variable on the vertical axis,

x is the variable on the horizontal axis,
b is the point on the vertical axis where the line intersects, and
m is the slope of the line.

The slope is found by marking two points on the line, and dividing the
difference in y-coordinates (called the rise) by the difference in x-coordinates
(the run).

Since all parts of a straight line have the same slope, the slope is a constant for
this experiment.

For this data, b is zero, and m is 2.0 km / 6.0 s = 0.33 km/s

Notice that dimensional units are part of the rise and of the run. The slope is
found in this case by dividing a distance by a time. You should recognize this
as the formula for speed.

The algebra equation y = m x + b may be translated into an equation
appropriate to this situation by replacing the algebra symbols with the variables
in the problem.

Thus, distance = speed * time, a very familiar equation!

The speed in this case is the speed of sound, and is in agreement with
published data, considering uncertainty.

This example is intended as a simple illustration of how numerical data from
an experiment is transformed from a table to a graph to a meaningful equation.

4

012–07192A Discover Density Set

Finding an

Equation

Relating

Mass and

Volume

Introduction

In this activity you are given four rectangular solid metal pieces, and four
similar plastic pieces. You are asked to take data, organize it, graph it, and
create equations relating the mass and volume of each of the two kinds of
material. A minimum of instructions are given. You should study and follow
the example titled “The Speed of Sound” which preceded this task.

Materials required

The materials needed are in compartments AB1, AB2, C1, and C2.

Procedure

1. Create a table to record the length, width, and height, volume, and mass of

the four metal pieces from compartment AB1, and a similar table for the
four gray plastic pieces from compartment AB2.

2. Record the length, width, and height in centimeters. If you are using a

metric ruler, estimate to the nearest 0.01 cm when finding these
dimensions. Use the rules regarding significant figures or other
appropriate methods of expressing uncertainty.

3. Consider the volume to be the independent variable, and the mass to be

the dependent variable when graphing the data. Prepare a graph that
shows the data for all eight objects, labeling your data points for the metal
pieces with circles, and the data points for the gray plastic pieces with
squares.

4. Draw a best-fit line for the data from the metal pieces, and another for the

data from the grey plastic pieces. If straight lines passing through the
origin do not represent the data well, recheck your measurements and
calculations for any data points that do not fit the pattern.

5. Calculate the slope of each line, and include dimensional units as part of

your calculations. Show your calculations, and use significant figures or
another appropriate expression of uncertainty.

6. Although each item had its own mass and volume, the slope of the line for

the metal pieces is constant. The metal pieces are all aluminum, and the
slope is termed the density of aluminum. Find a published value for the
density of aluminum, and compare to your value. Does your value agree
within the limits of uncertainty?

7. The gray plastic is polyvinyl chloride, or PVC. Its published density is

1.36 to 1.40 g/cm
uncertainty?

3

. Does your value agree within the limits of

5