The Construction and Operation of an Inexpensive Cavendish Balance Experiment for High School Demonstration of Gravitational Force.Timothy W. Hughes Jr., Physics Department, State University of New York – Buffalo State College 1300 Elmwood Avenue, Buffalo, New York 14222 <[email protected]>Abstract: The Cavendish balance is an appropriate tool that can be used to provide tangible evidence of gravitational force between two ordinary room-scale objects. Here Ireview appropriate literature on regarding high school design, operation, construction and, quantitative measurements of G with an inexpensive Cavendish balance. Characteristic problems and possible solutions for this type of apparatus are also discussed.Acknowledgements: This paper addresses requirements for PHY690: Masters’ project atSUNY-Buffalo State College under the guidance of Dr. Dan MacIsaac. I acknowledge the significant assistance of Mr. Timothy O’Mara.Introduction: Before Henry Cavendish performed his powerful experiment in 1798, the apparatus he used was simply called a torsion balance (Clotfelter, 1987). The torsion pendulum was invented in 1777 by a French physicist named Charles-Augustin de Coulomb (McCormmach & Jungnickel, 1996). Coulomb’s intentions for his famous experiment were to measure the electrostatic forces between small objects (ibid.). Though the torsion balance had quite a different function from describing gravitational forces, Coulomb’s studies laid the ground work in analyzing the data taken from it, regardless of the force being measured (ibid.). Some years later, in 1973, the geologist John Mitchell independently invented the torsion balance with the intention of measuring the density of Earth (Thorpe, 1921). Not much was known about the solar system at that time, but it was clear that if the mass and 1density of the earth was known, it would be possible to calculate the rest of the bodies in the system as well (Clotfelter, 1987). Mitchell’s idea was: if one could measure the force between two ordinary objects of known mass and size, and compare it with the force of gravity between one of the masses and Earth, a proportion could be used to solve for the unknown mass and density (Thorpe, 1921). Mitchell never lived to see his work completed and eventually the apparatus was passed down to Henry Cavendish who used Mitchell’s experiment to measure the density of the earth (Thorpe, 1921). It has since been found that this experiment is a very reliable way to calculate an important constant in nature, the gravitational constant, G. Cavendish never made any mention of a gravitational constant in his reports on the torsion balance as it was not then realized as an important idea by Geologists (Clotfelter, 1987). Nevertheless, the Cavendish experiment is a reliable way to measure the gravitational constant and is described in many textbooks. In most high school classrooms it may seem time consuming to challenge students to confirm the value of G through experimentation. However, the simple demonstration of a gravitational attraction can be accomplished with a fair amount of effort and within a class period. Moreover, the experiment can be done affordably and with items available at most hardware stores for approximately 100 dollars or less.Textbooks commonly cite that all objects that have mass are attracted to one another by a gravitational force (Knight, 1997). This may be hard for students to believe because the force is too small for ordinary sized objects so that it is never noticed. The only gravitational force most students recognize is the one between an object and the Earth. A torsion balance is a piece of equipment that makes this force not only measurable, but also visually apparent.Torsion is the twisting of something due to an applied torque (Knight, 1997). A torque is a force applied about an axis perpendicular to its displacement from it, or simplya twisting force (ibid.). A thread, wire, or any other long flexible object, if it is twisted, will elastically oppose this twisting force to restore its original shape. Increasingly twisting a spring will increase the apposing elastic force directly. A torsion springs strength depends on several factors, one of which is length. Thelonger the spring, the weaker its torsional constant will become. If we use a torsion spring2to demonstrate the gravitational forces between two small objects, we want the spring to be very weak thus making it very sensitive to extremely small forces. The mass must be offset from the axis of rotation for there to be any torque. Since a string is not rigid, we cannot expect to put a bend in the string at a right angle to achieve this. The mass can be offset from the axis of rotation if it is “balanced” by an object with an identical mass and separated with a rigid object. The string is attached to the rigid object in the center and the masses balance on either end. Now the string can be twisted by an attractive force on one or both of the two objects. Insert Figure 1: Torsion Balance DiagramParts List:1. 1 - 2m length of string ($2.00)2. 1 - wooden meter stick3. 2 - 20oz. Soda bottles ($2.00)4. 2.5gallons of water5. 3 - 2gallon buckets ($6.00)6. 1 – 20lb. bag of play sand ($8.00)7. 1 - adjustable swivel stool (optional)8. 1 - 30cm x 15cm piece of 1/8inch plexi-glass ($5.00)9. 1 - 1in square mirror10. 1 - laser pen (preferably green for visibility) ($10.00)11. 1 - stand for laser12. 1 - blank video tape ($1.00)13. 2 - large binder clips14. 1 - roll of scotch tape15. 1 - bottle of wood glue (2.00)16. 1 – large 6in C-clamp17. 1 - turn table (optional)18. 1 - 4ftx 1ft x 1inch wooden boards ($10.00)19. 6 - 1ft x 1ft x 1inch wooden boards ($5.00)20. 1 - white shower board cut to 3ft x 2ft ($5.00)21. 1 - temporary wall partition (optional)22. 4 - blocks of wood cut to 2in x 3in x 1in (scrap)23. 1 - pen24 1 - clock25. 1 - ring stand3Constructing the Balance: Two lengths of VHS tape were cut that were long enough to extend from the ceiling support to about chest level. The tapes acted as the torsion medium, or the spring, for the balance. The tapes were sandwiched between two small blocks of wood at each end, and were glued and clamped. A place on the ceiling was found that was sturdy enough to affix one end of the tape and block assembly and supporttwo pounds. Then, a hole was drilled in a meter stick at the 30cm and 70cm mark, in order to tie the string
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