MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01T Fall Term 2004 Experiment 04: Uniform Circular Motion Purpose of the Experiment: The direct goal of this experiment is to study a“conical pendulum” like the one in your homework assignment this week. A fishing sinker (the “mass”) is attached to a rotating shaft by a spring and you will adjust the angular velocity of the shaft rotation, and measure the radius rm of the circular motion of the mass, calculate the centripetal force, and use the res ults 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. ωrmYou s hould learn at least the following things from this experiment: • An experimental verification of the force required to produce centripetal acceleration. • This system has an instability at a critical angular frequency, ωC , for the shaft rotation; you will observe the approach to this instability and understand what causes it. • You will get more experience in analyzing your measurements to find properties you may want to know (the spring force constant) and you may find that the spring has a property (pre-tension) that we have not discussed before. Setting Up the Experiment: The apparatus includes a viewer to facilitate measuring the radius of the mass’s motion, rm. It is a w hite 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 ro om lights are off.) 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. Circular Motion 1 September 29, 2004First you need to know the mass mm of the fishing sinker. The one I used had mm = 9.3 gm, but you should ask your instructor for the right mass for your apparatus (most of them seem to have a mm = 8.5 gm.) Next, attach the mass and spring to the hook on the shaft inside the box. Before you turn on the apparatus, you should measure r0, which is the value that rm would have if the spring were not stretched at all. Stand the box on its side and hold the counterweight and the shaft so that the spring and mass hang down along the scale. Use the viewer to measure the value of r0 = rm(ω = 0) when the mass is hanging still; you can use r0 to calculate how much the spring stretches when it is rotating. Next connect the apparatus to its 12V power supply via the connector on the side. You should replace the side cover to the box before you turn on the motor. The lead sinker moves at fairly high speed and would give a nasty whack to your finger if it were hit by it. Turn on the circular motion apparatus and try different speeds to see how it behaves. You will use DataStudio to measure the rotation period, T , of the mass, and from that calculate the angular rotation frequency ω = 2π/T . rmAs the motor rotates, a magnet in the counterweight triggers a reed relay on the top cover of the box and makes a voltage pulse every time the magnet passes under it. A voltage sensor should be connected from the ScienceWorkshop 750 interface to the two banana jacks that are farthest away from the speed control knob. In DataStudio drag a voltage sensor to the appropriate input on the 750 interface; double-click the voltage sensor and set it to low sensitivity and a sample rate of 5000 Hz in the window that opens. Set the sampling options (either from the “Experiment” main pull-down menu or the“Options” button of the “Experiment Setup” window) to “none” for both automatic start and stop. After that, DataStudio will make measurements continuously when you click the start button. To display the voltage pulses, drag the Voltage in the “Data” window to the Scope icon in the “Display” window. That will open up a scope display. Set it to 1 V/div on the vertical scale and 20 ms/div on the horizontal (time) scale. The � symbol to the left of the ms/div label on the x-axis reduces the time to sweep a division (increases the sweep rate) and the � symbol does the opposite. Slide up the trigger level symbol Δ on the y-axis of the graph to about 0.5V; this will give a more stable scope pattern. You should see voltage pulses like this on the scope display after you click the Start button. Circular Motion 2 September 29, 2004Making Measurements: Measure the radius rm(ω) of the mass’s circular motion for three different angular velocities to give values of rm between 5 and 10 cm. Allow the speed to stabilize before you make your measurement. To find the rotation period on the scope display, you may find it helpful to click on the single trace button at the top of the display graph and use the smart tool. For each measurement you need to determine rm(ω) and the rotational period T . Your goal is to complete a table like the one below for ω = 0 and for three or four values of ω > 0. The values for T and rm (shown in bold type) should be entered as you do the experiment; all the other values will be calculated from them when you do the analysis. T rm ω ΔX mmrmω2 ∞ 4.8 cm 0 s−1 0 m 0 N 0.095 s 6.0 cm 66.1 s−1 0.012 m 2.44 N 0.074 s 7.2 cm 84.9 s−1 0.024 m 4.83 N 0.060 s 10.3 cm 105 s−1 0.055 m 10.5 N The table contains the values I measured, but you may have a different spring and fishing sinker mass and so may get something quite different. You calculate ω = 2π/T and find the amount ΔX the spring stretched using ΔX = rm − r0. Circular Motion 3 September 29, 2004A note about gravity: if you have been think-ing as you read this, you should wonder why I am not considering the effect of gravity. Because of gravity, the spring and mass will hang down at some angle θ, as shown exaggerated at the right. T he spring and mass will actually sweep out a conical path inside the box; that’s why this apparatus is often called a conical pendulum. rmrsθIf you ignore the mass of the spring and simply analyze a free
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