3-1-17: Finding "g" through free fall

1.Title: Finding "g" Using Free-Fall
   Name: Ray Arellano
   Lab Partners: David Hwang & Jesus Hernandez
   Date: 3/1/17
2. In this experiment, we are going to use distance, time, and a velocity in order to calculate "g", the acceleration of free-falling objects on Earth due to gravity.
3. In order to measure "g" we had to measure the distance of an object experiencing free-fall. The apparatus we used allowed us to know when the object had reach certain distances. Compiling this information on Excel helped my group develop a Position Vs Time graph and a Velocity Vs Time graph. In the end, we took the derivative of the equation of our Velocity Vs Time graph in order to discover what our experimental value of "g" was.
4.

 

This image shows the apparatus used for this experiment. This machine holds an object that is ready to fall and has a strip of paper stretched along the path of the object's descent. Sparks are generated every 1/60th of a second; these sparks mark the paper and allow us to understand where and how far the object traveled for a certain amount of time. 

 

This is the strip of paper that was marked by the sparks.Next to it was a 2-meter stick that we used to collect measurements; we took the first mark on the paper to be the initial position and measured the distances between each mark that followed. 

5.The excel sheet we used to hold our data was saved in an incorrect format and cannot be displayed. However, I personally took pictures of the graphs that correspond to our data                                        6.

This is our Position vs Time graph. It displays where the object was as time progressed.

 Above is our Velocity vs Time graph. The equation for such a graph could be obtained by taking the first derivative of the position function.
8. Based on the function "y = 961.71x + 66.551" (our velocity function in the above picture), we calculated "g" to be 9.6171 m/s^2 by taking the derivative of "y" with respect to "x". The absolute difference between 9.8 m/s^2 (the accepted value of "g") and our experimental "g" is -0.1829 m/s^2. Sources of error for this experiment include the interpretation of the marks on the strip of paper. My group assumed that only the darkest marks were the most meaningful marks; we believed that the other marks were a result of sparks coming to an end. Also, air resistance could have slowed down the object that was falling, causing its acceleration towards the ground to be smaller than the expected value of 9.8 m/s^2. Our measurements with the 2-meter stick could also have been flawed; the marks on the stick are small enough to make errors while reading it. If this was so, the velocity of the object could have been faster or slower at certain times. When taking into account all of these sources of error, it becomes understandable why our experimental value of "g" does not match the accepted value of "g".