As/ Expt /G/ Kevin


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As/ Expt /G/ Kevin

  1. 1. How to determine the magnitude of the g?
  2. 2. Equipment required <ul><li>Meter stick/meter ruler </li></ul><ul><li>Vernier caliper </li></ul><ul><li>Carpenter’s level </li></ul><ul><li>Motion sensor </li></ul><ul><li>Dynamics track </li></ul><ul><li>Blocks, notebooks,etc to prop up the incline </li></ul><ul><li>Ring stand & clamp </li></ul>
  3. 3. Diagram of the experiment
  4. 4. Procedure <ul><li>Start by leveling the incline. Depending on how you set it up, you might want to measure and record the height of what will be the upper end of the track. When you raise the end, you can measure the height from the same location, then subtract to find h. Alternatively, you can use a vernier caliper to measure the thickness of the block, etc., that you use to prop up the track. </li></ul>
  5. 5. <ul><li>Be sure that you place the motion detector on the upper end of the incline (see the diagram above). </li></ul><ul><li>Set up the motion detector to display a graph of velocity vs. time. You can use the statistics capability of the software to calculate the slope of this graph, which, of course, is the acceleration of the cart. </li></ul>
  6. 6. <ul><li>Open the sampling options dialog, and set the detector to stop automatically after 2 seconds or so. </li></ul><ul><li>Let the cart start down the incline, then start the detector. </li></ul><ul><li>Remember that you can restrict the statistical analysis to the &quot;good part&quot; of the graph. </li></ul><ul><li>If you can't get decent data, you'll need to make some motion detector adjustments. </li></ul>
  7. 7. <ul><li>When you are ready to take acceleration data, open Graphical Analysis TM and type your acceleration and height data directly into its data table. Construct a graph of acceleration vs. height. </li></ul><ul><li>Be sure to take at least a few trials at each height so you can get a good idea of the uncertainty in the acceleration calculation. </li></ul>
  8. 8. Results <ul><li>We have made several runs at each height, it might not be necessary to add error bars to the graph. Draw the best fit regression line, and get regression statistics for the acceleration vs. height graph, assuming it looks linear. We can calculate &quot;g&quot; from the slope of this line. </li></ul>
  9. 9. Calculation <ul><li>If a is the cart's acceleration down the track, and θ is the angle that the ramp makes with the horizontal ,then from the diagram: a=g sin θ =g h/L={g/L}h </li></ul><ul><li>so a graph of a vs. h should be a straight line with slope g/L . </li></ul><ul><li>Measure the magnitude of L,according to the slop of the a vs. h diagram, we get the magnitude of the g. </li></ul>