Finding gravity through experimental data

  1. 1. The problem statement, all variables and given/known data
    Experimentally measured time of fall
    vs. distance for a freely falling object
    Distance, x (m) Time, t (s)
    0.1 0.148
    0.2 0.196
    0.3 0.244
    0.4 0.290
    0.5 0.315
    0.6 0.352
    0.7 0.385
    0.8 0.403
    0.9 0.429
    1.0 0.451
    Let the mathematical model be: x = 0.5gt^2 and assume that x = 0 at t = 0 :
    a. In the light of what you learnt in problem 1.1 (parts a and b) and the form of the equation
    x = 0.5gt^2 , discuss (without calculations) two different methods that can be used to find g, the
    acceleration due to gravity, from a straight line graph representation. In each method, indicate
    explicitly the vertical variable, horizontal variable, slope, and intercept. Draw sketches.
    b. Find a numerical estimate for g based on the above table, using the EXCEL program?



    2. Relevant equations

    x = 0.5gt^2

    3. The attempt at a solution


    I know that the value of g is 9.81 m/s^2 but this is asking how to show it through experimental data and graph. I think maybe taking the ln of both sides to change this into y=mx+b form might help but am unsure. Also, I thing g would be the constant in the equation if it was changed to y = mx + b form therefore it'd be the slope value.
     
  2. jcsd
  3. Gib Z

    Gib Z 3,348
    Homework Helper

    It gives you the values of x and t, you have the equation that relates them. Solve for g.
     
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