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Graphing acceleration versus theta to find gravity

  1. Aug 22, 2011 #1
    1. The problem statement, all variables and given/known data

    using the equation a = g*sin(theta) where theta is in degrees

    how do i find g using the slope from a graph plotting acceleration versus theta? (i have acceleration on the y axis versus theta on the x axis)

    2. Relevant equations

    a = g*sin(theta) where theta is in degrees

    3. The attempt at a solution

    i was able to set it up as slope = y/x = a / theta = [g*sin(theta)] / theta
    but im totally stumped on how to use it since theta is changing but the slope and g are constant...
     
  2. jcsd
  3. Aug 22, 2011 #2

    gneill

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    Staff: Mentor

    What is the general equation for a line passing through the origin in the X-Y plane?
     
  4. Aug 22, 2011 #3
    the question is to find g, i already HAVE the slope if thats what youre getting at. i need to use the value i have for the slope to find g
     
  5. Aug 22, 2011 #4

    gneill

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    It's not quite what I'm getting at :smile:

    What's the general form?
     
  6. Aug 22, 2011 #5
    is standard form alright?

    y = mx + b
     
  7. Aug 22, 2011 #6

    gneill

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    Okay, since the line will pass through the origin, b = 0 and you have just y = m*x. Now, let's identify each of the terms of your acceleration equation with the the standard form:

    a --> y
    m --> g {this is what you're trying to find}
    x --> sin(θ)

    So, if you were to plot a on the y-axis, and sin(θ) on the x-axis...
     
  8. Aug 22, 2011 #7
    the line doesnt pass through the origin though it starts at a positive value for b right above the origin
     
  9. Aug 22, 2011 #8

    gneill

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    If you're plotting from collected experimental data, there's bound to be some offset due to human error, systematic error, or random error in the collection process. Some small amount of friction, for example, could bias the results.

    How large is the offset compared to the range of data?
     
  10. Aug 22, 2011 #9
    the data was given to us, its a exercise to help us learn how to use excel. by offset do you mean the R^2 value? its pretty close to 1. so do i just ignore the value for b and say the slope is the value for gravity? (thats why im having such trouble i have no way to check my answer because they could be assigning the value for gravity to be anything as far as i know so im not sure if im supposed to manipulate formulas somehow to obtain 9.81 or if my value for "m" can be used for "g" even though i have a positive value for b)
     
  11. Aug 22, 2011 #10

    gneill

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    Since I haven't seen the data or a full description of the problem or experiment its supposed to represent, there's not much I can comment on with any certainty. It could be that if friction is involved a straight line fit to the data will be problematical. Friction will have the most effect at small incline angles when normal force is maximal.
     
  12. Aug 22, 2011 #11
    neither have i really. we're given a table of data including theta and "a=gsin(theta)" and we're told to use excel to obtain the slope to find g
     
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