F = GM1M2G = Fr2Inexpensive 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 excellent tool in providing tangible evidence of gravitational force between all objects of mass. Many articles have been written on the subject of how it works, making quantitative measurements of G, 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 to tackle these obstacles in making a qualitative set-up that will be indispensable in your physics classroom.Acknowledgements: This paper addresses requirements for PHY690: Masters’ project atSUNY-Buffalo State College under the guidance of Dr. Dan MacIsaac, and the cooperation of Timothy O’Mara.Introduction: 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) 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 high school classrooms it may seem a bit excessive and time consuming to challenge students to confirm this value through experimentation. However, the demonstration of the 1gravitational 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.Physics 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? 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 hung at the end 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. 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 2axis of rotation 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 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.Materials:string, a meter stick, two 20 oz. Soda bottles, water, three two gallon buckets, enough sand to fill the buckets, an adjustable swivel stool, a 1’x .5’ smallpiece of plexi-glass, a small mirror, laser, stand for laser, video tape, two large binder clips, scotch tape, wood glue, piano wire, large C-clamp, turn table, one 4’x 1’x 1” wooden board. six 1’x 1’x 1” wood boards, white board, cubical partition, four small blocks of wood, pen, clock, ring stand, clamp.This balance is very sensitive so it is imperative to set this up in a room with no wind currents. This is where the cubical partition comes in handy if you have on around. This helps to block any small wind currents that might be circulating around the room. Building and encasement in plexi-glass is ideal but greatly increases the cost of the apparatus.The Balance: Open up an old VHS cassette tape and unravel the recording medium and cut two lengths that would be long enough to extend from the ceiling to about chest level when standing. This will be the torsion medium for the balance. These will be sandwiched between two small blocks of wood at each end. Glue and clamp the tapes between the two pieces of wood. Find a place on the ceiling that would sturdy enough to affix one end of the tape and block assembly and hold several pounds. Drill a hole in the meter stick at the 30cm and 70cm mark in order to tie the string through it and keep it 3from sliding. The string should be roughly double that of the distance between the two holes. By placing a pen between the
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