Swinging+Ball-Ji-Won+Park,Graydon+Yoder,+Liam+Flaherty


 * Title of Lab: ** Swinging Ball

**Researchers**: Liam Flaherty, Ji-Won Park, Graydon Ellis Yoder


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

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 * Research: ** According to the Law of Conservation of Energy, mgh = (1/2)mv 2 . From this you can derive v 2 = -2gcos(theta) + 2gL


 * Hypothesis: ** The speed and angle of the swinging ball are related by the equation v 2 = -2gcos(theta) + 2gL.

Constant: mass of ball, distance between photogates, gravity, length of string (0.8m) Variables: time, speed, angle 1. Set up a wooden post with: angle measuring tool, a string, and a wooden ball. 2. Place a photogate on both sides of the pole, measure the distance between the laser points. 3. Connect the wooden ball and the string with the distance from the ball to the connecting point being 0.7 meters. 4. Pull the string/ball out to an angle θ. 5. Set timer to "interval". 6. Release ball. 7. Record time it takes for the ball to pass through the two photogates. 8. Reset timer. 9. Repeats steps 4-8 for various θ measurements.
 * Procedure: **

**Data:**

Angle o - Time (s) 0 o - 0.0 5 o - 0.1883 10 o - 0.0973 15 o - 0.633 20 o - 0.0475 25 o - 0.0387 30 o - 0.0323 35 o - 0.0283 40 o - 0.0252 45 o - 0.0224 50 o - 0.0203 55 o - 0.0188 60 o - 0.0174


 * Data Analysis: **

The graph of Speed^2 vs cosθ has a linear line of best fit. The equation of this line is y= -20.03x + 20.12. The slope of this line is -20.03 and the y intercept is at 20.12 m 2 /s 2 . This means that when cosθ is 0, the predicted speed of the ball would be 20.12 m 2 /s 2. The x-intercept is at (1,0), which makes sense. Since cosθ when θ = 0 is 1, that means the ball has no velocity since there is no angle to give it any gravitational potential energy. Basically, the ball is just hanging off the end of the string. The expected slope is, using the equation -2gl, -15.304. This is a 23 percent error. Error could have come from imprecise measurement of the angle. Error also could have come from how the ball was released (if it was pushed a little or if it was caught on our fingertips for a fraction of a second).

Although the graph shows a close correlation between the data, the large amount of error shows that our hypothesis was not supported by the experiment. Error could have come from imprecise measurement of the angle. Error also could have come from how the ball was released (if it was pushed a little or if it was caught on our fingertips for a fraction of a second). Error for the expected slope could have come from imprecise measurement of the string. A release system would improve this experiment by decreasing the chance of error in the ball's release, as well as ensuring the angle at which the ball is dropped is precise.
 * Conclusion: **