Tim Hughes 690 Abstract Outline July 31 2007 Cavendish Balance 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 I Introduction II Construction III a Materials b Setting c Assembly d Operation Pitfalls a Wind b mirror and laser beam placement c finding optimum torsion IV Math required to make calculations V Links and References Dr MacIsaac Any questions or comments would be greatly appreciated Tim Hughes In 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 with items 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 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 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 s 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 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 on either 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 small piece 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 of the 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 stool for safety In order to keep things symmetrical place three square wooden boards flat at each end to raise the two buckets that will be placed at each end At this moment slide the whole assembly
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