Swinging+ball-+Tyler+Naughton,+Saie+Ganoo+and+Sanjana+Sreenath

Title of Lab: Swinging Ball lab

Researchers: Tyler Naughton, Saie Ganoo and Sanjana Sreenath

Research Question: How does the initial angle with the vertical relate to the speed of ball at its lowest point?

Research: Law of conservation of mechanical energy (initial)Energy=(final)Energy mg(hi)=(1/2)m(vf)^2.................. (1) The potential energy is converted to kinetic energy and then back to potential energy. http://www.physicsclassroom.com/mmedia/energy/pe.cfm the height of the ball = L - L cos( theta) plugging h into 1: g[(L - Lcos(theta)] = (1/2)v^2 2g[(L - Lcos(theta)] = v^2 v^2 = 2gL - 2gLcos(theta) v^2= -2gLcos(theta) + 2gL y=mx+b

Hypothesis: The cosine of the angle between the string and the stand is directly proportional to the velocity squared.

Materials: String, Ball with hole for rope in it, stand, screw, wooden protractor that has a small hole to be screwed in, photogate

Procedure: 1. Place the stand on a flat surface. 2. Screw in the wooden Protractor at the top of the stand and tie the string with the ball to it ( to shorten the length of the string swing the string either clockwise or counterclockwise one path directly behind the screw). 3. Unpack the laser sensor kit with both sensors connected to the control panel and power cord in. 4. Set the laser sensor to input and hit either A or B (Not Both), and which ever sensor you chose place it in the farthest from the direction you are going to release the ball. 5. Straighten the string with the angle of choice 6. Release the ball and once it is released hit the start button and stop when the button passes the laser sensor that you chose earlier. 7. Record your data. 8. Repeat your previous angle again for constancy and record your data. 9. Repeat steps 5-8 until you feel you have enough data points.

Data:
 * Angle from where ball was dropped (degrees) ||  ||
 * 10 || .0720 ||
 * 10 || .0676 ||
 * 20 || .0314 ||
 * 20 || .0341 ||
 * 30 || .0275 ||
 * 30 || .0221 ||
 * 40 || .0167 ||
 * 40 || .0200 ||
 * 50 || .0138 ||
 * 50 || .0131 ||
 * 60 || .0123 ||
 * 60 || .0116 ||

Speed= width of the object/ time =Diameter of the ball/ time
 * angle with vertical (theta)(degrees) || cos theta || Avg. time(s) || velocity (m/s) || v^2(M^2/s^2) ||
 * 10 || .984 || .0698 || .447 || .199 ||
 * 20 || .939 || .0328 || .951 || .904 ||
 * 30 || .866 || .0496 || 1.13 || 1.28 ||
 * 40 || .766 || .0184 || 1.695 || 2.87 ||
 * 50 || .642 || .0135 || 2.31 || 5.34 ||
 * 60 || .5 || .0119 || 2.62 || 6.86 ||

Data Analysis: NOTE: GRAPH WOULDN'T ALLOW ANY ADDITIONAL CHANGES, BUT VELOCITY SQUARED IS IN (m^2/s^2) units

The graph indicates a negative association between cosine theta and v^2. The slope is negative and the best fit line has a y-intercept of 7.7291m^2/s^2 (this is 2gL). This suggests that as the cosine of the angle approaches 0, the velocity squared approaches 7.7291 m^2/s^2. The best fit line has a slope of -1.3772m^2/s^2/cos theta. This slope represents -2gL. We noted some possible s ources of error: lack of multiple trials, did not measure the length of the string, and incorrect measurement of the angle itself. We couldn't calculate the percentage error, because we didn't know the actual length. We calculated experimentally the length to be .38 meters from the y-intercept, however this doesn't match with the length when calculated from the slope. For our hypothesis to be supported by this experiment, the slope and the y intercept would have to be opposites. However this is not the case, and if it is, there is a high percentage of error.

Conclusion: The data does not support our hypothesis stating that the cosine of the angle between the string and the stand is directly proportional to the velocity squared since the y-intercept and the slope are not additive inverses. The experiment can be further improved by conducting multiple trials and possibly performing the experiment again with a different object or a more comprehensive range of angles. We should have also calculated the length of the string.