Inexpensive Construction and Operation of Cavendish BalanceExperiment for High School DemonstrationTimothy 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 to provide tangible evidence of gravitational force between two ordinary room-scale objects. Here I review appropriate high school literature on 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 small electrostatic forces between small objects (McCormmach & Jungnickel, 1996). 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 (McCormmach & Jungnickel, 1996). Some years later, the geologist John Mitchell independently invented the torsion balance in 1783, 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 density 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 1was: 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. It is interestingthat Cavendish never made any mention of a gravitational constant in his reports on the torsion balance as it was not realized as an important idea (Clotfelter, 1987). Nevertheless, the Cavendish experiment is a reliable way to measure the gravitational constant and is described in many textbooks this way. In most high school classrooms it may seem time consuming to challenge students to confirm the value of G through experimentation. However, the demonstration of a gravitational attraction can beaccomplished 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.Physics textbooks will state that all objects that have mass are attracted to one another by a gravitational force. This may be hard for students to believe because the force is often so small for ordinary objects 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. A torque is a force applied about an axis perpendicular to its displacement from it, or simply a twisting force.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 springto 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 2offset 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 string2. 1 - wooden meter stick3. 2 - 20oz. Soda bottles4. 2.5gallons of water5. 3 - 2gallon buckets6. 1 – 20lb. bag of play sand7. 1 - adjustable swivel stool (optional)8. 1 - 30cm x 15cm piece of 1/8inch plexi-glass9. 1 - 1in square mirror10. 1 - laser pen (preferably green for visibility)11. 1 - stand for laser12. 1 - blank video tape13. 2 - large binder clips14. 1 - roll of scotch tape15. 1 - bottle of wood glue16. 1 – large 6in C-clamp17. 1 - turn table18. 1 - 4ftx 1ft x 1inch wooden boards19. 6 - 1ft x 1ft x 1inch wood boards20. 1 - white shower board cut to 3ft x 2ft21. 1 - temporary wall partition (optional)22. 4 - blocks of wood cut to 2in x 3in x 1in23. 1 - pen24 1 - clock25. 1 - ring standConstructing 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 3blocks 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 hold several pounds. Then, a hole was drilled in a meter stick at the 30cm and 70cm mark, in order to tie the string through it and keep it from sliding.Insert Figure 2: Balance Hanger Insert Figure 3: Balance Hanger DiagramThe string was cut to a length of roughly
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