I have completed the data table and the graphs, but I’m stuck on the calculations for the questions. Can anyone please help and explain the steps I should take? Thank you! Also the `y is being used in place of a y with a line over it to indicate the mean of y.
The data table located in the Lab Report Assistant shows data taken in a free-fall experiment.Measurements were made of the distance of fall (y) at each of the four precisely measured times. From this data, perform the following operations:
|
Time, t (s) |
Dist. y (m) |
Dist. y (m) |
Dist. y (m) |
Dist. y (m) |
Dist. y (m) |
` y |
? |
t^2 |
|
0 |
0 |
0 |
0 |
0 |
0 |
– |
0 |
0 |
|
0.5 |
1 |
1.4 |
1.1 |
1.4 |
1.5 |
1.28 |
0.177012241 |
0.25 |
|
0.75 |
2.6 |
3.2 |
2.8 |
2.5 |
3.1 |
2.84 |
0.248997992 |
0.5625 |
|
1 |
4.8 |
4.4 |
5.1 |
4.7 |
4.8 |
4.76 |
0.224499443 |
1 |
|
1.25 |
8.2 |
7.9 |
7.5 |
8.1 |
7.4 |
7.82 |
0.318747549 |
1.5625 |
1. Complete the table.
2. Plot a graph `y versus t (plot t on the x-axis or abscissa).
3. Plot a graph `y versus t2 (plot t2 on the x-axis). The equation of motion for an object in free fall starting from rest is y = 1?2 gt2, where g is the acceleration due to gravity. This is the equation of a parabola, which has the general form y = ax2.
4. Determine the slope of the line and compute an experimental value of g from the slope value. Remember, the slope of this graph represents 1?2 g. (The equations I got from the spreadsheet by doing a polynomial trendline. For y vs t – y=4.9838x^2 – 0.041x. For y vs t^2 – y=0.1164x^2 + 4.7937x)
5. Compute the percent error of the experimental value of g determined from the graph in step 4. (Accepted value of g = 9.8 m/s2).
