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Calculating acceleration using Experimental equation

  1. Feb 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the y intercept and slope of the linearization equation of the graph. Find an experimental equation. From this and the theoretical equation given in the introduction, determine the acceleration on the object.

    Context: I recorded data for the distance vs velocity of an object. With that distance, I plotted it a graph and found the linearization equation to it.

    2. Relevant equations
    The theoretical equation relating distance and velocity:
    v = [itex]\sqrt{2a}[/itex]Δx1/2

    3. The attempt at a solution
    I found the log10 x = log10 y and x = lny graphs of my data.
    The log10 x = log10 y graph has the best R2 value, so I will use this in finding my experimental equation.
    According to excel, the linearization equation is
    y = .5018x - .1117
    with R2 being .9999
    According to my question, I have to convert this to an experimental equation.
    Experimental equation for power function is: y = bxm

    What I don't know how to do is, 1. Converting it to an experimental equation and 2. Finding the acceleration of the object.

    My attempt at converting:
    y = 10-.1117*x.5018

    As to determining the acceleration of the glider from this using the experimental and theoretical equation, I have no idea how.
     
  2. jcsd
  3. Feb 20, 2012 #2

    Redbelly98

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    Welcome to Physics Forums.

    The idea is to compare the equations:
    [tex]\begin{align}
    v & = \sqrt{2a} \cdot \Delta x^{1/2} \\
    \text{and} &\\
    y & = 10^{-.1117} \cdot x^{.5018}
    \end{align}[/tex]
    From looking at those two equations, it is evident that
    [tex]\sqrt{2a} = \text{ _____?}[/tex]
     
  4. Feb 20, 2012 #3
    Thank you for responding!

    Alright, comparing the two equations:
    I set both equations equal to each other.

    [itex]\sqrt{2a}[/itex] = 10-.1117 • x.5018/x1/2

    [itex]\sqrt{2a}[/itex] = .773215 x.0018

    squaring both sides

    2a = .597861 x.0036

    dividing by 2

    a = .298931 x.0036

    I still don't understand. I have a value for a, but it is dependent on x. What does this mean? Isn't acceleration a constant?
     
  5. Feb 20, 2012 #4
    When you are plotting data, and obtain a fit, you will get a list of parameters.
    In your case, you plotted y=b*xm and obtained values for b and m,b = 10-0.1117 and m = 0.508.
    Your next step is to compare your data (b and m) to the expected values ([itex]\sqrt{2a}[/itex] and 1/2).
    The important part of this is to recognize that you are not comparing the experimental equation b*xm to the theoretical [itex]\sqrt{2a}[/itex]*x1/2, but b to [itex]\sqrt{2a}[/itex] and m to 1/2.
     
  6. Feb 20, 2012 #5
    How do I compare b to [itex]\sqrt{2a}[/itex] and m to 1/2 and find a? What do you mean by compare?
     
  7. Feb 20, 2012 #6

    Redbelly98

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    Yes, acceleration should be a constant.

    The fact that your best fit line gives x.5018 instead of x.5000 can be attributed to experimental error. So x.5018 is essentially (approximately) equal to x1/2, and you may treat them as canceling out where you had x.5018/x1/2 in your work.

    EDIT: you may ignore the rest of this post, it is probably just going to confuse the issue...

    Or looked at another way ...

    Assuming you are using meters for x and m/s for v, I would bet that your x-values are mostly somewhere between 0.1 m and 10 m. How would this change the value of a in

    a = .298931 x.0036 ?​

    I.e., what is 10.0036, and what is 0.1.0036?
     
    Last edited: Feb 20, 2012
  8. Feb 20, 2012 #7

    Redbelly98

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    He means:

    1. Compare b to [itex]\sqrt{2a}[/itex]

    and

    2. Compare m to 1/2

    So there are two separate, independent comparisons to make.

    Also, this all assumes consistent length and time units for x, v, and a. For example meters and seconds everywhere (or cm and seconds would work too).
     
  9. Feb 20, 2012 #8
    Yes, in that case x is very close to 1. So my a is .298931, which is an acceptable result. Thank you!
     
  10. Feb 20, 2012 #9
    The value of a does not depend on x.
    When I said compare, i mean set equal to each other.
    Like Redbelly98 said, 1/2 is pretty close to .5018, probably within your experimental error, so you get 1/2≈.5018
    The important part is that you set [itex]\sqrt{2a}=10^{-.1117}[/itex] and solve for a.
    No need to assume x is 1 or close to 1 or any other value.
     
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