PASCO AP-8215A Instruction Manual With Experiment Manual And Teacher's Notes

®

Instruction Manual with

Experiment Guide and

Teachers’ Notes

012-11032C

*012-11032*

Gravitational Torsion Balance

AP-8215A

L

E

A

C

AP-8215

N

N

LA

A

ATIO

B

IT

V

N

A

IO

R

S

G

R

O

T

und.

Gro

ach to

th

Att

Ear

Note: To avoid breaking the torsion ribbon, the locking mechanism must be

fully raised on both sides when moving or transporting the Gravitational
Torsion Balance.

Note: Save the packing material from the interior of the box, and

re-install this material when moving or transporting the Gravitational
Torsion Balance.

Gravitational Torsion Balance Table of Contents

Section Page

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

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

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

Equipment Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Equipment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Initial Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Leveling the Gravitational Torsion Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Vertical Adjustment of the Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Rotational Alignment of the Pendulum Bob Arms (Zeroing). . . . . . . . . . . . . . . . . . . . . . . . 5

Setting up for the Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Measuring the Gravitational Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Overview of the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Method I: Measurement by Final Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Method II: Measurement by Equilibrium Positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Method III: Measurement by Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Transporting and Storing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Safety Precaution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

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Gravitational Torsion Balance Copyright, Warranty, and Equipment Return

Copyright, Warranty, and Equipment Return

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

Copyright Notice

The PASCO scientific 012-11032C Gravitational Torsion Balance manual is copyrighted and all rights reserved.
However, permission is granted to non-profit 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.

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:

• The packing carton must be strong enough for the item shipped.

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

• 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] (worldwide) or 800-772-8700 (US)

web:www.pasco.com

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Model No. AP-8215A Introduction

Base with leveling feet

Large

masses

Sight for

leveling

Grounding

wire

Head of

torsion ribbon

Zero adjust

knob

Mirror on

pendulum

bob

Figure 1: Assembled Gravitational
Torsion Balance, ready to begin Henry
Cavendish’s classic experiment to
determine the gravitational constant.

Newton’s Law of Universal Gravitation:

where m

1

and m2 are the masses of the
objects, r is the distance between their
centers, and G is the universal gravita­tional constant, 6.67 x 10

-11

Nm2/kg2.

FG

m

1m2

r

2

--------------

=

Introduction

The PASCO scientific AP-8215A Gravitational Torsion Balance
reprises one of the great experiments in the history of physics—the
measurement of the gravitational constant, as performed by Henry Cav­endish in 1798.

The Gravitational Torsion Balance consists of two 38.3 gram masses
suspended from a highly sensitive torsion ribbon and two 1.5 kilogram
masses that can be positioned as required. The Gravitational Torsion
Balance is oriented so the force of gravity between the small balls and
the earth is negated (the pendulum is nearly perfectly aligned vertically
and horizontally). The large masses are brought near the smaller
masses, and the gravitational force between the large and small masses
is measured by observing the twist of the torsion ribbon.

An optical lever, produced by a laser light source and a mirror affixed to
the torsion pendulum, is used to accurately measure the small twist of
the ribbon. Three methods of measurement are possible: the final
deflection method, the equilibrium method, and the acceleration
method.

A Little Background

The gravitational attraction of all objects toward the Earth is obvious.
The gravitational attraction of every object to every other object, however, is anything but obvious. Despite the
lack of direct evidence for any such attraction between everyday objects, Isaac Newton was able to deduce his
law of universal gravitation.

However, in Newton's time, every measurable example of this gravita­tional force included the Earth as one of the masses. It was therefore
impossible to measure the constant, G, without first knowing the mass of
the Earth (or vice versa).

The answer to this problem came from Henry Cavendish in 1798, when he
performed experiments with a torsion balance, measuring the gravitational
attraction between relatively small objects in the laboratory. The value he
determined for G allowed the mass and density of the Earth to be deter­mined. Cavendish's experiment was so well constructed that it was a hun­dred years before more accurate measurements were made.

012-11032C

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Gravitational Torsion Balance Equipment

Attach to

Ear

th

Ground.

G

R

A

V

IT

A

T

IO

N

A

L

TO

R

S

IO

N

B

A

L

A

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AP-8215

1.5 kg Tungsten
masses

Adapter rings

Plastic demonstration

plate

Replacement
torsion ribbon

Zero adjust

knob

Torsion ribbon

head

Aluminum plate

Leveling feet

Pendulum

mirror

Optical

grade glass

window

Large mass

swivel support

Leveling sight

2-56 x 1/8 Phillips

head screws

Figure 2: Equipment included

Equipment

Included:

Gravitational Torsion Balance Plastic Plate

Support Base with Leveling Feet Replacement Torsion Ribbon*

1.5 kg Tungsten Balls (2) 2-56 x 1/8 Phillips head screws (4)

Adapter Rings (2) Phillips screwdriver (not shown)

(*Model No. AP-8218)

Additional Required:

Laser light source (such as the PASCO OS-9171 Helium-Neon Laser)

Meter stick

2

012-11032C