012-05750A Instruction Manual and 1/95 Experiment Guide for the PASCO scientific Model SE-9633B GRAVITATIONAL TORSION BALANCE © 1995 PASCO scientific $10.00 better 10101 Foothills Blvd. • P.O. Box 619011 • Roseville, CA 95678-9011 USA ways to Phone (916) 786-3800 • FAX (916) 786-8905 • email: [email protected] teach physics 012-05750A Gravitational Torsion Balance Table of Contents Section Page Copyright, Warranty, and Equipment Return................................................... ii Introduction ...................................................................................................... 1 A Little Background ......................................................................................... 1 Equipment......................................................................................................... 2 Setup .............................................................................................................. 3 Measuring the Gravitational Constant .............................................................. 5 Method I: Measurement by Final Deflection ....................................... 6 Method II: Measurement by Equilibrium Positions ............................. 8 Method III: Measurement by Acceleration .......................................... 9 Replacing the Torsion Band ........................................................................... 11 i Gravitational Torsion Balance 012-05750A Copyright, Warranty and Equipment Return Please—Feel free to duplicate this manual subject to the copyright restrictions below. Copyright Notice Equipment Return The PASCO scientific Model SE-9633B Gravitational Should the product have to be returned to PASCO Torsion Balance manual is copyrighted and all rights scientific for any reason, notify PASCO scientific by reserved. However, permission is granted to nonprofit letter, phone, or fax BEFORE returning the product. educational institutions for reproduction of any part of Upon notification, the return authorization and this manual providing the reproductions are used only for their laboratories and are not sold for profit. shipping instructions will be promptly issued. Reproduction under any other circumstances, without ä the written consent of PASCO scientific, is prohibited. NOTE: NO EQUIPMENT WILL BE ACCEPTED FOR RETURN WITHOUT AN Limited Warranty AUTHORIZATION FROM PASCO. PASCO scientific warrants this product to be free from defects in materials and workmanship for a When returning equipment for repair, the units period of one year from the date of shipment to the must be packed properly. Carriers will not accept customer. PASCO will repair or replace, at its option, responsibility for damage caused by improper any part of the product which is deemed to be defec- packing. To be certain the unit will not be tive in material or workmanship. This warranty does damaged in shipment, observe the following rules: not cover damage to the product caused by abuse or improper use. Determination of whether a product ➀ The packing carton must be strong enough for the failure is the result of a manufacturing defect or item shipped. improper use by the customer shall be made solely by PASCO scientific. Responsibility for the return of ➁ Make certain there are at least two inches of equipment for warranty repair belongs to the cus- packing material between any point on the tomer. Equipment must be properly packed to prevent apparatus and the inside walls of the carton. damage and shipped postage or freight prepaid. ➂ Make certain that the packing material cannot shift (Damage caused by improper packing of the equip- in the box or become compressed, allowing the ment for return shipment will not be covered by the instrument come in contact with the packing warranty.) Shipping costs for returning the equip- carton. ment, after repair, will be paid by PASCO scientific. Address: PASCO scientific 10101 Foothills Blvd. Roseville, CA 95747-7100 Phone: (916) 786-3800 FAX: (916) 786-3292 email: [email protected] web: www.pasco.com ii 012-05750A Gravitational Torsion Balance Introduction The PASCO scientific SE-9633B Gravitational Torsion Balance reprises one of the great experiments in the his- tory of physics—the measurement of the gravitational constant, as performed by Henry Cavendish in 1798. The torsion balance (see Figure 1) consists of two 15 gram masses suspended from a highly sensitive torsion band, and two 1.5 kilogram masses that can be positioned as required. The torsion constant of the band is deter- mined by observing the period of oscillation of the tor- torsion band mirror sion balance, which is approximately 10 minutes. The large masses are then brought near the smaller masses and the gravitational force is measured by observing the twist of the torsion band. To accurately measure the small twist of the band, an op- tical lever is used, consisting of a laser or other light 1.5 kilogram source (not included) and a mirror affixed to the torsion mass 15 gram band. Three methods of measurement are possible. The mass acceleration method requires only about 5 minutes of ob- servation, and produces results accurate to within 15%. "A" base With an observation time of up to 45 minutes, the final- deflection method can be used, producing results that are accurate to within 10%. The method of equilibrium posi- tion requires the longest time of 90 plus minutes, but the results are accurate to within 5%. Figure 1: The Gravitational Torsion Balance A Little Background The gravitational attraction of all objects toward the However, in Newton's time every measurable example of Earth is obvious. The gravitational attraction of every this gravitational force included the Earth as one of the object to every other object, however, is anything but ob- masses. It was therefore impossible to measure the con- vious. Despite the lack of direct evidence for any such stant, G, without first knowing the mass of the Earth (or attraction between everyday objects, Isaac Newton was vice versa). able to deduce his law of universal gravitation: The answer to this problem came from Henry Cavendish in 1798, when he performed experiments with a torsion Gm1m2 F= balance, measuring the gravitational attraction between R2 relatively small objects in the laboratory. The value he where m1 and m2 are the masses of the objects, R is the determined for G allowed the mass and density of the distance between them, and G is a constant. Earth to be determined. Cavendish's experiment was so well constructed that it was a hundred years before more accurate measurements were made. 1 Gravitational Torsion Balance 012-05750A Equipment casing d zero-adjust head torsion head retaining screw (DO NOT UNSCREW) b0 zero-adjust small lead ball lock screw (m1) L0 large lead ball (m2) (To measure b0 = L0/2, measure L0 with a caliper gauge.) Torsion Balance Geometry torsion band alignment holes mirror casing small mass lever arm large mass swivel support locking screws mounting rod for lever arm large mass height adjustment "A" base leveling screws (2) Figure 2: Setting Up the Gravitational Torsion Balance 2 012-05750A Gravitational Torsion Balance Equipment Parameters (see Figure 2 insert—Torsion Balance Geometry) • Small lead balls • Period of Oscillation of System: Mass: 0.015 kg (m ) 2 T = approximately 10 minutes Radius: 7.5 mm Distance to torsion axis: d = 50 mm • Logarithmic damping decrement: D = approximately 0.7 • Large lead balls • Torsion Band Mass: 1.5 kg (m1) Radius: 32 mm Material: Bronze Length: 26 cm • Distance from the center of mass of the large ball to Cross-section: 0.01 mm x 0.15 mm the center of mass of the small ball when the large Torsion Constant 8.5 * 10 –9 N*m/rad ball is against the casing glass and the small ball is in the center position within the casing: b = 46.5 mm Setup ➤ IMPORTANT NOTES Initial Setup • The Gravitational Torsion Balance is a delicate ➀ Remove the "A" base from its box. Place the "A" instrument. We recommend you set it up in a rela- base on a flat, stable table, and adjust the leveling tively secure area where it is safe from accidents screws until the tripod is approximately level. and from those who don’t fully appreciate delicate ➁ Carefully remove the torsion balance, the large mass instruments. swivel support and the height adjust collar from the • The first time you set up the torsion balance, do so box. Slide the swivel support on the mounting rod. in a place where you can leave it for at least one Then slide the height adjust collar against the swivel day before attempting measurements. This allows support and secure it with the phillips head screw. time for the slight elongation of the torsion band ➂ which will occur initially. Insert the assembled mounting rod into the tripod and secure it in place with the other hinge-handled bolt. • Mount the torsion balance in a position so that the ➃ mirror on the torsion wire faces a wall or screen at Place the two 1.5 kg lead balls on the swivel support, least 5 meters away. as shown. 3 Gravitational Torsion Balance 012-05750A Leveling the Torsion Balance Using an Incandescent Light Source ➀ Unlock the small mass lever arm by loosening the ➀ Mount a metric scale on a wall at least 5 meters away locking screws that are located at the bottom of the from the torsion balance, facing the mirror. casing. ➁ Stretch a thin thread over the aperture of your light ➁ Adjust the leveling screws of the "A" base until the source, to use as a focusing aid (a piece of tape half torsion band is suspended precisely in the center axis covering the aperture will also work). of the torsion band alignment holes. ➂ Place the light source so the aperture is approximately Setting Up the Light Source 30 cm away from the mirror and so the light source is tilted up at an angle and pointing toward the mirror. An optical lever is used to accurately measure the small angle of twist of the torsion band. The torsion balance is ➃ Adjust the distance and angle of the light source until designed to be used with an incandescent light source, as you get a sharp image of the thread on the scale that the mirror mounted to the torsion wire is a spherical mir- you mounted on the wall. ror with a 30 cm focal length.