Tim Hughes690 Abstract & OutlineJuly 31, 2007Cavendish BalanceThe 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 thisexperiment. 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.I. IntroductionII. Constructiona. Materialsb. Settingc. Assemblyd. OperationIII. Pitfallsa. Windb. mirror and laser beam placementc. finding optimum torsionIV. Math required to make calculationsV. Links and ReferencesDr. MacIsaac,Any questions or comments would be greatly appreciated.~Tim HughesIn 1798 Henry Cavendish performed a powerful experiment in order to measure the universal gravitational constant, G. 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 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 withitems available at you local hardware store.So what is a Cavendish balance? It’s the coolest thing! You know how they say in physics 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 we 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 showdirectly that objects of relatively small mass were attracted to each other? There is such an instrument and it is called the Cavendish balance. How does it work? Well first, one must know something about torsion. It is the twisting of something by an applied torque. Torque? Yes, a force applied about an axis perpendicular to it displacement from it. Let’s just call it a twisting force. Take a thread, wire, or any other long flexible object and you will find that if you twist it, it will tend to want to oppose this twisting force to restore it’soriginal 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. So what! Well, if we use a torsion spring to 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. Ah ha! So how do we make two masses twist a spring? This is where it gets interesting. If you hang a mass 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. Don’t know what I’m talking about? Well, we can offset the mass from the axis of rotation if we “balance” the mass with an identical mass and separate the two with a rigid object. The string hangs down attaches to the rigid object in the center and the masses balance oneither end. Now the string could conceivably be twisted by an attractive force on one or both of the two objects! What about the mass on the other end? Doesn’t this affect the experiment? Of course it does, but this can be offset by placing another fixed mass next to it thus making the whole experiment symmetrical. 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.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. 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 from sliding. The string should be roughly double that ofthe distance between the two holes. By placing a pen between the hanging VHS tapes, this makes a convenient place to hang the string from which the meter stick is attached. Glue a 1” square mirror on the 50cm mark of the meter stick. Using string, hang two full 20oz. Soda bottles from the ends of the meter stick so it balances The Brake and Stand for the Stationary Masses:Lay the 4’ board flat on top of the stool so it balances. Set the turn table and the two gallon bucket on top of the board and stool. Clamp the board and turntable to the
View Full Document
Unlocking...