Determining g: Evaluating Methods of Measuring Acceleration

Please ignore the bouncing title. Like seriously. It’s not even proper HTML.

What’s the Big Idea‽

How does gravity affect the motion of objects? The force of gravity is consistently affecting everything on our planet, but its effect becomes even more apparent in falling objects. Gravity causes all objects to undergo a constant acceleration of 9.8 m/s²—but how can we calculate this value (notated as g) using only our knowledge of kinematics? 

We completed two different labs to find out and then determined which method was better.

Procedure

The first lab was the Picket Fence Free Fall lab, which required a photogate, a LabQuest, and, of course, a picket fence (which is a thick, transparent strip of plastic with black rectangles evenly space apart). There were also some additionally materials such as the stand and the cloth to make for a soft landing. The resulting setup looked like this:

Once everything was connected, we dropped the picket fence as indicated by the diagram. One of our trials looked like this:

Notice the quadratic curve in the distance-vs.-time graph, a hallmark of constant acceleration. The velocity-vs.-time graph is linear, because the velocity increased at a constant rate. We repeated the procedure several times to get the following composite graph:

Each trial resulted in similar graphs that matched the first.

Now, on to the second lab: the Ball Toss lab! The materials were simple: a ball, a motion detector, and once again, a Vernier LabQuest.

The procedure, like the materials, was also simple: just hold the ball in front of the motion detector, throw it up, and catch it before it hits the motion detector. However, I found this to be rather clumsy because it was difficult to throw the ball straight up and have it return to the starting position. Our most successful trial yielded the following graph:

Like the first lab, we can see the quadratic curve in the first graph and the linear one in the second—giving us insight into how gravity affects an object. The velocity graphs of both experiments happen to be particular insightful—notice the value for m. The first experiment yields a value of 9.666 and the second experiment yields a value of -8.953. Though the signs of these values aren’t important, their magnitudes are. Roughly speaking, they match the Earth’s value of acceleration due to gravity—9.8 m/s² downwards.

Takeaways

If you haven’t realized it yet, we performed these experiments on Earth. Meaning our predicted values for the acceleration due to gravity were fairly accurate, however more so in the Picket Fence Free Fall lab. These predicted values are the criteria by which we are judging the two labs.

There are a couple reasons why I think the first experiment resulted a value closer to the one we were looking for. This concerns accuracy and precision. Accuracy is generally associated with systemic error, whereas precision is generally associated with random error. We were able to eliminate much more (but certainly not all) systemic and random error in the Picket Fence Free Fall lab, meaning our value of 9.666 was was both more accurate and more precise than the one we got in the Ball Toss lab. We were able to repeat the first experiment multiple times without changing the result very much, which ultimately allowed us to average our data (minimizing random error and increasing precision). Furthermore, dropping the picket fence was much less awkward and clumsy than throwing the ball up, which explains the difference in accuracy (the first experiment was affected by less systemic error than the second lab).

Ultimately, I felt that the tools (i.e. the photogate and the motion detector) were both fairly reliable and not a major source of error in either experiment.

And for gravity? Well, we were able to visualize its affects on an object in free fall graphically, as well as roughly determine its value based on our knowledge of kinematics.