Ap Physics Lab 1 - "galileo's Dilemma"

Nick Budak 9/11/08 AP Physics per. 1

Lab Report: Galileo’s Dilemma In this lab, we were attempting to answer a question dating back to the era of Galileo – whether an object’s acceleration is more closely related to how long it has been accelerating or how far it has gone. By accelerating an object using gravity and taking measurements of distance and time, we could calculate its speed and eventually acceleration by measuring different distances. When graphing the data, we would need to compare the relationships between velocity/time and velocity/distance to determine which showed a clearer, simpler association. Going into the experiment, we knew a number of things. We already knew the relationships between distance, time and velocity: velocity was given by distance over time, and acceleration was given by increase or decrease in velocity over time. To give a greater accuracy to the velocity measurements, we used the concept of instantaneous velocity, which stood for the velocity the object attained immediately before it stopped, rather than the average velocity for the entire distance. This could be given by doubling the average velocity (a simplification). Also, the idea that objects accelerate when rolled down a plane or dropped because they are affected by gravity was a given. So, we would need to accelerate the object using gravity for different distances to measure the correlation between its velocity and time or distance traveled. Our main method for gathering data involved accelerating a golf ball down an inclined plane (the same one Galileo used). Propping up a wooden track on a chair at an angle of approximately 20 degrees, we let go of the ball at a point at the top of the track, started a timer, and stopped it when the ball reached marked distances at 25, 50, 75, 100 and 125 feet. We took five measurements at each distance, and each data point was the average of two simultaneous readings given by two different observers with a stopwatch.

After the data had been collected, the highest and lowest values from each set of points were thrown out to streamline the graph. Graphs of the data and a diagram are attached. As you can see, the graph of velocity vs. time shows a more simple linear relationship, whereas velocity vs. distance forms a curve. However, some of the later data points in the velocity vs. time graph don’t fit the line, and our best theory is that this was due to friction. Because we rolled the ball down an inclined plane, as the ball went longer and longer distances it lost more and more speed to friction. You can see this in our acceleration graph at the lower left, which should remain a linear constant, but instead decreases, which indicates that forces were slowing the ball down as it traveled farther. Another culprit may have been the sliding of our plane, which was propped up on a chair in such a way that it may have easily slid forward, decreasing the angle of incline and therefore slowing the acceleration due to gravity. Because the graph was pulled down at the end, it may have decreased the overall slope, and prevented it from going through the necessary point (0, 0). In conclusion, although our data was skewed by a couple different sources of error, we were able to scientifically show that our acceleration decreased – which means that, had we not used an inclined plane, our data probably would have fit a linear pattern for velocity vs. time. In any case, looking at the velocity vs. distance graph, which is unquestionably a curve, one is able to make the observation that time and velocity share a more simple relationship.