F = GM1M2G = Fr2Please format all figures as inline.Use "Figure 1: descriptive title" above eachAlso Tim, see an interesting discussion of this expt in Feynman Physical Law Lecture 1:http://www.microsoft.com/presspass/press/2009/jul09/07-14PhysicsLecturesPR.mspxGravitation in your Classroom: Construction and Operation ofan Inexpensive Cavendish Balance 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 excellent appropriate tool in providing tangible evidence of gravitational force between two all ordinary room-scale objects of mass. HereMany articles have been written I review appropriate HS on the subject oliteraturef on design, operation, construction how it worksand, making quantitative measurements of G with an inexpensive Cavendish balance, and construction of this experiment. Plug and play computer apparatus even exists for purchase of this experiment. However, few if any have had the goal of making this experiment easy and affordable. Many problems also arise from this being a very sensitive experiment. Here is where you will find how totackle these obstacles in making a qualitative set-up that will be indispensable in your physics classroom. Tighten this last up to one sentence. The info on commercial apparatus needs to be elsewhere.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, and the cooperation ofMr. Timothy O’Mara.1Introduction: In 1798 Henry Cavendish performed a powerful experiment that measured the universal gravitational constant, G (Carlson, 1989). Actually, he intended the experiment to measure the density of the earth and succeeded (Clotfelter, 1987). He never made any mention of a gravitational constant in his reports of on the torsion balance (Clotfelter, 1987). As Clotfelter (1987) reported, a critical component of the unit of G is the newton, and “no unit of force was proposed until 1873.” (p. 213) In this para you needlessly contradict yourself and are incomplete in the discussion of thehistory. I would expand this one historical para to two, and focus on getting it right. Check the Wikipedia article for a little more guidance, include a mention of previous researchwork done by Coulomb and you need to introduce the correct phrase "torsion balance." Then go into how a torsion balance works with a figure. Comment on oscillating versus stationary balances.Figure 1: Conceptual model of a Torsion BalanceIs this figure yours? You need full copyright to it. Why the different font and weird "fig.(1)" label?Never the less, it was discovered that the experiment is a reliable way to measure the gravitational constant and is described in most textbooks this way. Of course in most highschool classrooms it may seem a bit excessive and time consuming to challenge students to confirm this value through experimentation. However, the demonstration of the gravitational force between objects of mass, other than the earth, can be accomplished with a fair amount of effort and within a class period. Moreover, the experiment can be done rather cheaply and with items available at you local hardware store.2Physics text books will tell you that everything that has mass has a gravitational attraction to every other thing that has mass. Well, this is hard to believe because the force is so small for ordinary objects that it is never noticed. The only gravitational force most people recognize is the one between an object and the Earth. But what if there was an instrument that was made so sensitive that it could detect these forces? Better still, what if this instrument could show directly that objects of relatively small mass were attracted to each other? Too chatty in tone with rhetorical questions. Please say what others have done, then what you did, what problems you found, and then suggestions for others.There is such an instrument and it is called the Cavendish balance. To understandhow this works, one must know something about torsion. It is the twisting of something by an applied torque. A torque is a force applied about an axis perpendicular to it displacement from it. Call it a twisting force. Take a thread, wire, or any other long flexible object and if it is twisted, it will tend to want to oppose this twisting force to restore its original shape. The more you twist it the more strongly it opposes this force. This is the characteristic of a torsion spring. The strength of this spring depends on several factors, one of which is length. The longer the spring, the weaker it is. If we use atorsion spring to demonstrate the gravitational forces between two small objects, we wantthe spring to be very weak thus making it very sensitive to extremely small forces. If a mass is PAST TENSE hung at theend of a string, it would be impossible to get the string to twist by approaching it with another mass because the gravitational force would always be acting upon the center of the hanging mass. There would be no moment arm. LAST IS UNCLEAR – RESTATE OR EXPUNGE 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 3rotation if it is “balanced” by an object with an identical mass and separated with a rigid object. The string hangs down attaches to the rigid object in the center and the masses balance on either end. Now the string could conceivably be PAST TENSE THROUGHOUT PLEASE twisted by an attractive force on one or both of the two objects. (See figure 1)The mass on the other end does affect the experiment, but placing another fixed mass next to it thus making the whole experiment symmetrical can offset this. Since the Gravitational force is inversely proportional to the distance between the two objects, the other two objects on the other side of the balance are sufficiently far away enough and at an angle such as to minimize the torque applied to not cause much error. REALLY UNCLEAR AND POSSIBLY WRONG. RETHINK AND RESTATE THIS LAST PARAPLEASE – I think the size of the total torque is 2*Fgrav*r; due to two masses – they BOTH
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