Let's 'g'!

Did you know that the value of \(g\) differs on one's geographic location, and even one's altitude? For years, many people try to measure the value of \(g\) equal to its accepted, or standard value (which is \(9.80665\ \text{m}/\text{s}^2\) or simply \(9.80\ \text{m}/\text{s}^2\)). Sadly (or is it?), according to my high school textbook (which, sadly, I cannot refer to at this point because I forgot the title, etc.), you can only measure this value when you are in Ottawa, Canada. Yes, the value of \(g\) we all love and memorize is actually a hoax - in reality. In truth, when scientists calculated the value of \(g\) they assumed that the Earth was spherical, and from there, applied Newton's Universal Law of Gravitation, plugged in the values, and came out the value we all know. However, we know from reading or in class, that the Earth is not spherical, so it means that since it has different radii at different points, therefore the value of \(g\) would differ for different places.

In this particular experiment, we approximated the value of \(g\) in UP Diliman - more specifically, in NIP. We used two methods of approximation, but using one main item. We approximated this value through the use of digital interface known as Vernier LabQuest. This device is composed of one main handheld device and a group sensors you can use to do physics experiments with. In this particular one, we used the Motion Detector, and the Photogate, with something called the Picket Fence.

Figure 1: The Materials Used in the First Part of the Experiment

In the first part of the experiment, we used the Motion Detector, and a ball. Our target was to toss the ball directly up above the Motion Detector multiple times for 5 seconds for 10 trials. Thanks to the materials we used, the interface of Vernier LabQuest plotted the \(y\)-displacement and velocity of the ball in that 5 seconds. What we needed to do now is to zoom in into one of the plotted \(y\)-displacement graph, and from there get a quadratic fit to get the value of \(g\) according to the said plot. At the same time, we zoom in to the most linear part of the plotted velocity of the ball, and from there get a linear fit to still get the value of \(g\). As stated earlier, we did this 10 times.

Figure 2: The Materials Used in the Second Part of the Experiment

In the second part of the experiment, we used the Photogate Sensor, and the Picket Fence. The Picket Face, as shown in Figure 2, is a glass piece filled with black and clear bands. For this part of the experiment, we drop the Picket Fence near or at the top of the Photogate Sensor, and similar with the first part of the experiment, analyse the linear and quadratic fit of the velocity of the picket fence and \(y\)-displacement of the Fence respectively. Doing this, we were also able to approximate the value of \(g\).

Collating the data, and calculating for the mean and standard deviation of the values of \(g\) measured in the two parts, we were able to give the best approximate for the value of \(g\) in NIP, found in UP Diliman. In that area, \(g=9.35749\pm0.387\ \text{m}/\text{s}^2\), or in three significant figures, \(g=9.36\pm0.39\ \text{m}/\text{s}^2\).

Most probably, this may be the wrong, or possibly, not the accurate value of \(g\) in the area. If that were true, then one of the possible reasons of inaccuracies is the sensor itself. There are times when the sensor would not respond or give us faulty readings, maybe due to its limitations. So as it is really precise (gives results up to four decimal places!), its ability to measure the things it can measure may also be faulty at times. At the same time, probably, the handling of the materials can affect the detection of motion. Therefore, many of these things can really affect the reading given by the device, and will, in effect, affect the data our group gathers.