One-Dimensional Motion Lab: Finding 'g'
The purpose of this lab was to calculate an experimental value for the acceleration due to gravity, g. To complete this lab, we were given 250mm rulers and any supplies we had on-hand. We ended up using the timer on a phone, the ruler, and a pencil. We were also given a set of one-dimensional motion equations for constant acceleration. In designing our experiment, we had to figure out a way to obtain values for all variables in one of the motion equations except for a, which we would then solve for (we designed our experiment using a dropped object, since the acceleration of a falling object equals g). We determined that the equation ∆x=u•∆t+0.5•a•∆t^2 would be the most useful, as we would only have to know the distance traveled, the time of motion, and the initial velocity of a dropped object in order to calculate its acceleration.
For our experimental setup (see picture in top left), we took a cell phone stopwatch and placed it next to the ruler, which we stood vertically. We then dropped a pencil in front of the ruler and filmed the stopwatch and pencil together in slow motion. In that way, we could see the approximate time required for the ruler to travel 250mm, and we knew that the initial velocity (u in the equation) was 0 since it was dropped from rest, so we were able to calculate a. Since our times were never perfectly accurate, we conducted ten trials of the experiment and used the average of the ten results as our experimental value for g. In the top right is an example of the videos we took in our experiments.
Our lab results are below.
For our experimental setup (see picture in top left), we took a cell phone stopwatch and placed it next to the ruler, which we stood vertically. We then dropped a pencil in front of the ruler and filmed the stopwatch and pencil together in slow motion. In that way, we could see the approximate time required for the ruler to travel 250mm, and we knew that the initial velocity (u in the equation) was 0 since it was dropped from rest, so we were able to calculate a. Since our times were never perfectly accurate, we conducted ten trials of the experiment and used the average of the ten results as our experimental value for g. In the top right is an example of the videos we took in our experiments.
Our lab results are below.
True acceleration due to gravity: 9.80665m/s^2
Experimental acceleration due to gravity: 11.14m/s^2
Percent Error: 14%
Standard deviation: 2.58m/s^2
Experimental acceleration due to gravity: 11.14m/s^2
Percent Error: 14%
Standard deviation: 2.58m/s^2
It's easy to see from our results that we had a pretty large margin of error. A very large probable cause of this error was the fact that the camera we used didn't have an extremely high frame rate, so that the recorded time was off by ±0.03 seconds for each test. That doesn't seem like much, but compared to the short time of the motion, it may have significantly skewed our results. In addition, our calculations assumed that the distance traveled was exactly 250mm, but it may have varied by as much as ±5mm. With these in mind, one can estimate that the observed acceleration should have been off by a factor of 1.3 in either direction (observed values should have ranged from 7.48m/s^2 to 13.3m/s^2 in any given test), which is consistent with the spread of the various tests.