1. In an experiment to determine the value of pi, a sphere is measured to have an average value of 6.37 cm for its diameter and an average value of 20.11 cm for its circumference. What is the experimental value of pi to the correct number of significant figures?
2. If the theoretical value of pi is 3.142 what is the fractional error and percent error of the experimental value found in (2)?
3. The equation of motion for an object in free fall starting from rest is y = 1Ac„2 g t^2, where g is the acceleration due to gravity. The graphical form of this equation and the data plotted in Fig. 1 is called a parabola, a polynomial of degree 2, which has the general form y = at2+bt+c , where a, b, c are constants with values a = g/2, b = 0, c = 0 respectively for the present case.
For data given in table 1 plot y vs t2. This will be the plot of y vs t' where t' = t^2 which has the general form of y = ax+b , a = g/2 and b = 0.
(a) Determine the experimental value of g from the slope of your graph.
(b) Compute the percent error of the experimental value of g determined from the graph in (a).
| Data table 1 |
|
t (s)
|
t2 (s2)
|
y (m)
|
|
0.00
|
0.00
|
0.00
|
|
0.31
|
0.10
|
0.50
|
|
0.44
|
0.19
|
1.00
|
|
0.53
|
0.28
|
1.50
|
|
0.63
|
0.40
|
2.00
|
|
0.71
|
0.50
|
2.50
|
|
0.76
|
0.58
|
3.00
|
|
0.83
|
0.69
|
3.50
|
|
0.89
|
0.79
|
4.00
|
|
0.94
|
0.88
|
4.50
|
|
1.00
|
1.00
|
5.00
|
