Galileo's Dilemma

Colwyn Fritze-Moor Medley Period 4 Physics

Galileo's Dilemma For the first experiment in physics we're going to take it back a few steps. Back to the days of Galileo and the question as to whether velocity is more closely related to the distance it has traveled or the amount of time it has been traveling. It is a good experiment to start with as it orients the class with physics and how the year is going to go. The way we are going to do this is very basic: drop a golf ball and time how long it takes to hit the ground. Simple? Well, for the most part it is. Although, there are things we already know and have to take into consideration before diving into this lab. The first of which is: human error or limitations. As a human, it is impossible to time exactly how long it takes for the golf ball to hit the ground. For instance, the average human response time is somewhere around 250 milliseconds, or .25 seconds. This means our timing will most likely be skewed. We also know the relationships between velocity, distance and time. Considering we are gathering information on time and distance, there will be two equations we will use. One will be getting the average velocity. That equation is: Distance divided by time equals average velocity (d/t = Vavg). The other equation is a simple variant of this; it is used to acquire the velocity that the golf ball is traveling at the very end of the distance it has traveled. That equation is: two times the distance divided by time equals the instantaneous velocity (2d/t = Vint). To elaborate, if you had a ball that went 2 meters in .6 seconds, it's average velocity would be 3.3 m/s (2/.6 = Vavg). But it's instantaneous velocity would be 6.7 (2*2/.6 = Vint). It pretty simple and easy to understand. To start off the experiment I grabbed a metre stick, a stopwatch and a few golf balls. I then measured out 1 metre on the wall and dropped the ball from that height. When I dropped the ball I had two people start their stopwatches and stop them when the ball hit the ground. I recorded that in my notebook under the height and time it took. After that I dropped any outliers from the equation and averaged the numbers. I did this for 1, 2, 2.5, 3 and 5.5 metres. For each height I recorded 20 numbers (5 from two people and 10 from another) and used those for the average. I figured out the velocity and then put it on a graph and found the line of best fit. The two graphs I had were velocity vs. time and velocity vs. distance. Those two graphs are attached to this report and you can see a clear relationship emerging between velocity and time. Admittedly it does look like velocity vs. time is a parabola, but after considering the classes graphs as

well as my own I decided that it was just human error. The y-intercept of the graphs is also very important. The velocity vs. time graph goes almost directly through (0,0), which is the origin. Inversely the graph of velocity vs. distance was nowhere near (0,0), it's actually around 4! This leads me to believe that there is a more direct correlation between velocity and time. This is because that when the graph starts at (0,0) the ball actually started at a stand still. On the distance vs. velocity graph it starts the ball at about 4m/s; which it obviously did not. I also excluded a point from this process because it was an outlier all on its own. I have marked that on the graph clearly. To conclude, this was a clunky lab; but it does provide an understanding of basic physics. There is so much room for human error (0.25 seconds), so that our results cannot be viewed as entirely accurate. But, I still think that, as a class, we were able to show a better connection between velocity and time as compared to velocity and distance. It is a much more linear graph and shows that acceleration is consistent over time. With distance it just covers more distance faster; which is another way of saying it accelerated over time. About 13 m/s/s or 13 metres per second per second. That basically means that for every second that passes its velocity adds another 13 m/s. For example: After one second it will be going 13 m/s, after 2 seconds it will be 26 m/s, etc... That is quite fast, but it is an answer none-the-less. In the duel between time and distance it seems time has come out on top for this lab. I could be entirely wrong and missed something, but I'm pretty confident about this one: Time and velocity have a direct, linear relationship with each other.