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T^2 vs L determining g?

  1. Nov 14, 2006 #1
    Okay this is the last question of the lab and I don't get it
    Basically its a lab where we find how amplitude, bob mass, and length affects the period T for each time.

    Our finding was that length affects the period a lot. I did a bunch of graphs and tables and answered all the questions but don't know how I derive this


    the question is "From your graph of T^2 vs. L
    determine a value for g."

    T here is the period in seconds and L is the length of the string in cm. Now I do have to graph and it looks pretty normal to me.


    The slope is 0.03900 and the r is 0.9947
    now I dont think this would help much at all
    (unless its r-slope haha...)

    I have to find g from this graph and calculate the percent of error
    I know how to calculate the percent of error but I don't know how I can find g from this graph


    the points are for x which is length

    50
    60
    70
    80
    90
    100

    and for T^2 i have

    2.2831
    2.4586
    2.89
    3.3562
    3.7288



    My first guess was i need to find an equation for this relationship and then
    use the formula 4pi^2/g x L = T^2 but I don't know what to do?

    plug in what for L? someone please help!
     
  2. jcsd
  3. Nov 14, 2006 #2

    nrqed

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    As you said, the equation is [itex] T^2 = {4 \pi2 \over g} L [/itex] . So if you plot T^2 vs L, you should get a straight line. The slope of this line will be equal to what?
     
  4. Nov 14, 2006 #3
    wait I don't get it a lot.
    so for the x-axis I get all the L (from 50~100) and then just leave it.
    for the y, I should use [itex] T^2 = {4 \pi2 \over g} L [/itex] and then subsitute all the L from the x data. that would gimme T^2
    but I don't think this is right because I'm getting 4.028 as my slope
     
  5. Nov 14, 2006 #4

    nrqed

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    :confused: You measured the period for different values of L, right? Just plot your measured values of T^2 versus L. Then use theory to determine what the slope should be equal to. Theory will give you a relation between the slope of this graph and the value of g. Once you measure the slope on your graph you will be able to determine g from your data.
     
  6. Nov 14, 2006 #5
    ok so the slope of my line of T^2 vs L is 0.0390.

    since 4pi^2/g=slope g should be 4pi^2/slope...


    so the predicted g is 4pi^2/ 0.0390

    and this gives me 1012.267... what is wrong?
     
    Last edited: Nov 14, 2006
  7. Nov 14, 2006 #6

    nrqed

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    What is the uncertainty? this is not far from the expected value of about 981 cm/s^2!
     
  8. Nov 14, 2006 #7
    yes haha thanks i forgot that its in cm haha

    just to confirm, tthe % error would be 1- (980/1012.267) right?
     
    Last edited: Nov 14, 2006
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