Conservation+of+Energy

Logger Pro is my friend. This was the main part of the analysis of the ball's velocity.

-10.403m/s for instantaneous velocity for P1  12.891 m/s for instantaneous velocity for P2  1.304 m was the height of the ball from the origin. The PE was set to 0 at the origin, so the P2 did not have PE, however P1 did, and it used 1.304 as the height. 

Conservation of Energy keep in mind that the mass cancels out in this problem: KE1 + PE1 = KE2 1/2 mvi^2 + mgyi = 1/2 mvf^2 ½ vi^2 + gyi = ½ vf^2 <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;"><span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 130%;">½ * -10.403^2 + 9.8*1.304 = ½ * 12.891^2 <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;"><span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 130%;">54.11 + 12.7792= 83.09 <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;"><span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 130%;">66.89 = 83.09 <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;"><span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 130%;">((66.89 – 83.09)/83.09))*100 = 19.5% error PE of the spring was not used in this problem because the ball was thrown at such a small speed and the tention of the strings were very tight. There was no noticable x value for the elongation of spring in the racket to take data, so it was considered neglegable. <span style="color: #ff0000; font-family: Impact,Charcoal,sans-serif; font-size: 150%;">It can be seen with this data and work, that conservation of energy can be proven through tennis! With a simple hit of the ball after it was thrown, a video can prove that this is possible. Using Logger Pro, the video was analyzed for the y position, as well as the velocities in order to have the data to work out this problem. Conservation of energy was used to prove that P1=P2. Although there was a 19.5% error in this experiment, it was largely due to the video analysis program. Some of the positions of the ball were very hard to see at times and were strung across two seperate locations because of the camera quality, however it was mostly accurate. Also, since instantaneous velocity was used in this proof, one data point was used, and may have been a bit different or skewed from the actual value at that time. One data point is not always the most accurate way when dealing with only a certain amount of frames per second on a camera. In conclusion however, conservation of energy can indeed be proven in tennis, as seen above in the tables of data and the work done, so get out there and start playin' some CRAZY AWESOME TENNIS!!

<span style="color: #ff0000; font-family: Impact,Charcoal,sans-serif; font-size: 150%;">Sources < Click here for the sources we used