Acceleration Due To Gravity of a Falling Golf Ball

<<I will put the picture of the falling golf ball in here once I get it from the school server.>>

Abstract:

A golf ball was dropped from a standing height and tracked by a strobe light flashing every 1/15^th of a second. The experiment was recorded by a digital camera whose the picture yielded a diagram showing the location of the ball at different intervals in time. By using the time deduced from the flashes of the strobe light and the distance the ball had fallen at that point, the acceleration of the golf ball due to gravity was determined to be 10 m/s² through graphing a distance versus time graph and subsequently, a velocity versus time graph.

            The purpose of this lab was to determine the acceleration of an object due to gravity. This was done through tracking a golf ball during a fall of approximately 100 cm.

                The first step in this experiment was setting a strobe light to flash at the rate of 900 flashes per minute, or one flash each ¹/₁₅^th of a second. A digital camera was set to take a picture of the golf ball falling, with its shutter open for two seconds. Every time the strobe light would flash, it would show the golf ball in a different location on its downward path, and the digital camera was able to record each position in the duration of the fall because its shutter remained open the whole time.

                Thus, the strobe light was turned on and aimed at the golf ball, being held by another person. The camera operator pushed the button on the camera to set it going, and after four beeps and a fifth imagined beep, the ball was dropped, and the strobe followed it on its descent. (The ball had to be caught at the bottom so it didn’t bounce back into the picture.) The resulting photograph was of a golf ball shown eight times alongside of a ruler taped on the wall to use later for the measurements.

                Now that we had a picture of the golf ball’s descent, we had to graph its descent. This was done on a distance versus time graph. Along the x-axis of the graph were the points for time, showing the ¹/₁₅^ths of a second. The y-axis represented the distance traveled, in meters. To determine each of these points:

• Time was determined from the flashes. Because the strobe light flashed every 1/15^th of a second, it showed a picture of the golf ball every 1/15^th of a second. Hence, each image of the golf ball was a consecutive 1/15^th of a second (i.e. the first image of the ball occurred at 1/15^th of a second, the 2^nd at 2/15^ths, and so on).
• Distance was a little harder to determine. The first step was determining the scale of the picture. By measuring the distance with a real ruler of 10 centimeters on the photographed ruler, we found a scale: 1 cm in the picture was equal to 5.56 cm in reality. The distance between the initial position (0) and the first image of the ball was 0.5 cm, so in reality it was 2.78 cm, or .0278 meters. Thus, the first point on our graph was (¹/₁₅ , 0 .0278).  The y-coordinate for each point was the total distance traveled at that point in time, not the distance from point (x) to point (x+1), i.e. the y-coordinate of point 2 was .07784, not .05004.

We now had a graph of distance versus time of the falling golf ball. Distance divided by time is velocity, so this graph was of the velocity of the falling golf ball.

                The next step was determining the acceleration of the golf ball, which in this case was due to gravity, because it was simply let go of, not thrown, from the zero point. To find the acceleration, we made a graph of velocity versus time, since velocity divided by time equals acceleration.

                Because of the said fact that velocity divided by time equals acceleration, we determined that the slopes of the points on the velocity graph would equal acceleration. (Slope equals rise over run, y over x, or, in our case, distance over time.) By making little right triangles around each mini-slope, we could find the height and base of each right triangle, and divide them to get the slope of the hypotenuse of the triangle, which was the acceleration.

                These accelerations were plotted on a new graph against time, with time remaining the value of the x-axis and the acceleration becoming the y-axis values. Next, a line of best fit was graphed (NOT a line connecting all of the points like in the distance versus time graph). The slope of the line of best fit was the acceleration due to gravity for our data set.

                To find the slope of the line of best fit, three points were chosen on the line arbitrarily (these weren’t points from the original data set). Using any point-slope formula, the slope was determined to be 10 m/s².