Swinging+Ball-+Peter+Choi,+Danielle+Myers,+and+Tyler+Myers

Title of Lab: Swinging Ball Lab

Researchers: Peter Choi, Danielle Myers, and Tyler Myers

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

Research: http://nobilis.nobles.edu/tcl/doku.php?id=courses:science:physics:ap_physics:ballistic_pendulum_ay13

Since gravity is a conservative force and is the only force acting on the ball, we can say total mechanical energy is constant throughout the system. E1 (energy of ball at starting point) = E2 (energy of ball at its lowest point) mgh = (1/2)mv 2 gh = (1/2)v 2

To find h, we can use our trigonometric functions, where cos(theta) = (L-h)/L L cos(theta) = L-h h = L - Lcos(theta)

If we plug this value for h into our original equation we get g[(L - Lcos(theta)] = (1/2)v 2 2g[(L - Lcos(theta)] = v 2 v 2 = 2gL - 2gLcos(theta) v 2 = -2gLcos(theta) + 2gL

Hypothesis: Velocity squared will have an inversely proportional linear relationship with cos(theta) according with the equation v 2 = -2gLcos(theta) + 2gL

Procedure: Materials: stand, string, ball, wooden protractor, photo gates 1. Set up the stand with a string and ball attached to the wooden protractor. 2. Set up the photo gates at the base of the stand and measure the distance between them. 3. Determine the angle the ball makes with the respect to the vertical and record the angle in the data table. 4. Release the ball and record the time it takes to pass through the photo gates. 5. Repeat steps 3-4 at various angles. 6. Divide the distance by the time to get the velocity at its lowest point.

Data:



Data Analysis: vf2=-2gLcos θ+2gL y=-38.8234x+39.2854 Although we could not find the theoretical slope since we forgot to measure the length of the string, our experimental slope and y-intercept being are equal in value (with slope being negative) as they should be according to our equation. If we set 2gL to either our slope or y intercept, we can get a rough estimate of the length of the string as 2.0m. This measurement seems unrealistically long, so we probably made mistakes in our measurements. Error in the experiment may have come from imperfect measurement of the angle from which the ball was dropped and the inability to perfectly drop the ball from its starting point.

Conclusion: Considering the string length we found using our data is highly unreasonable, our hypothesis is not supported by the experiment. The data does shows a negative linear relationship with the numerical values of the slop and y-intercept being similar, but some error in the experiment made these the absolute values of these two numbers much higher than they should be. To improve our experiment, we could find a better way to measure the velocity of the swinging ball at its lowest point. Our method did not technically calculate the velocity of the ball its absolute lowest point, but rather the average velocity of the ball at its lowest points.