exp02 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01 Fall Term 2010 Experiment 2: Uniform Circular Motion Purpose of the Experiment: The direct goal of this experiment is to study a“conical pendulum”, and apply Newton’s 2nd law to an object moving in a circular orbit. A round weight of mass m (the “mass”) is attached to a rotating shaft by a spring; you will adjust the angular velocity ω of the shaft rotation, measure the radius r m ( ω ) of the circular motion of the mass, calculate the centripetal force from F = ma and use the results to find the force constant of the spring. To simplify the analysis of your results, assume that the mass of the spring can be neglected. ω r m You will do the following things in this experiment: Measure the radius r m ( ω ) of the orbit of the mass m as a function of ω for the shaft, and interpret your measurements with a model based on two things (i) the centripetal force is F cent = ma cent = m r m ( ω ) ω 2 , and (ii) the spring obeys Hookes’ law (spring force proportional to amount of stretch). This model predicts r m ( ω ) → ∞ at a critical angular frequency, ω c , for the shaft rotation; you will observe the approach to this behavior and understand what causes it. You may find that your spring has an initial tension that must be overcome before the spring will begin to stretch. Experimental Materials: Logger Lite Software Vernier LabPro Interface Cicular Motion Apparatus/power cord Vernier Differential Voltage Probe small weight on spring Circular Motion 1 Sept. 30/Oct. 1, 2010
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Setting Up the Experiment: The apparatus includes a viewer to facilitate measuring the radius of the mass’s motion, r m ( ω ). It is a white teflon block with a black viewing tube and it slides in a slot in the top cover of the apparatus. A small nail protudes down into the slot and should be placed to engage the loop of the brass wire that has a LED taped to it; that is so the LED will move to illuminate the mass as you try to read its position. (This all works better if the room lights are dim.) Another nail protrudes into the viewing tube and can be lined up over the black stripe around the mass; the same nail also allows you to read the radius on the scale. You need to know the mass m of the round weight. The one I used had m = 8 . 5 gm; use this value for your experiment. (If you use an incorrect value for the mass, the experiment will still work normally, but the spring constant you find will be incorrect.) Attach the mass and spring to the hook on the shaft inside the box.
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