One Dimension Motion
(In the One Dimension Motion experiment, we tried to empirically estimate the value of g (the acceleration of an object due to gravity). In order to empirically estimate this value of g, we created a set up with a slow motion camera, a stopwatch, a measuring stick, and a paper clip. We measured the distance the paperclip fell(an almost constant distance of 0.25 meters), as well as the time it took for it to fall( Tinitial and Tfinal). When formulating the experiment, we knew we had to do an experiment that would give us the variables delta T and d (change in time and distance) because we knew that those would be two unknowns from the equation we used to find the acceleration of the experiment. We also had to consider how important the accuracy of the time was(because a tenth of a second makes a big difference in this small of a drop), resulting in us including the stopwatch in frame of the stop motion camera. In order to complete the experiment, we did a single drop in a single stop motion video to make sure we were getting a result that was close to expected. We saw the time it took for the paperclip to drop the .25m and started plugging in numbers to the calculations. We started with the equation:
deltaX = Vinitial * deltaT + (1/2) * a * deltaT^2.
From there we knew we needed to rework the equation to solve for a. After reworking the equation we came up with the formula:
a = (2(deltaX - Vinitial * deltaT))/(deltaT^2)
Because we knew that Vinitial was zero, we could further simplify the equation to be:
(2deltax)/(deltaT^2) = a
After we recorded the results from the first test and saw that it was semi-near our expected result(7.13m/s^2), we decided to film 8 more drops in a single video, input the results into a spreadsheet, and utilize the spreadsheet to do the calculations for us.
Here is a picture of the Spreadsheet we created(there are a total of 10 tests, some of them are off screen:
deltaX = Vinitial * deltaT + (1/2) * a * deltaT^2.
From there we knew we needed to rework the equation to solve for a. After reworking the equation we came up with the formula:
a = (2(deltaX - Vinitial * deltaT))/(deltaT^2)
Because we knew that Vinitial was zero, we could further simplify the equation to be:
(2deltax)/(deltaT^2) = a
After we recorded the results from the first test and saw that it was semi-near our expected result(7.13m/s^2), we decided to film 8 more drops in a single video, input the results into a spreadsheet, and utilize the spreadsheet to do the calculations for us.
Here is a picture of the Spreadsheet we created(there are a total of 10 tests, some of them are off screen:
Our average result for acceleration was 9.9m/s^2 which is pretty close to the actual value of g which is 9.8m/s^2. The standard deviation of the data set was 4.66, showing how surprising it is that our wide range of values actually average to a result that is pretty close to the actual result. The percent error that we had was a mere 1.01% (using the rounded values of 9.8 and 9.9 due to the inaccurate nature of the experiment.
I think that we were very lucky to get such a small percent error because of the imprecise measurements we took. We could only really see the motion in increments of about 4 hundredths of a second. This means our deltaT had a range of almost a tenth of a second off the actual value. Also the motion of the drop was not extremely precise. The paper clip was in no way dropping a precise .25m, it varied from a little under the mark to a little over. Also the equation would never be exact due to the friction of air acting upon the paperclip.
Here is a drawing of my experiment:
I think that we were very lucky to get such a small percent error because of the imprecise measurements we took. We could only really see the motion in increments of about 4 hundredths of a second. This means our deltaT had a range of almost a tenth of a second off the actual value. Also the motion of the drop was not extremely precise. The paper clip was in no way dropping a precise .25m, it varied from a little under the mark to a little over. Also the equation would never be exact due to the friction of air acting upon the paperclip.
Here is a drawing of my experiment: