Swinging+Ball-+Charlie+Morris,+Kevin+Sarfani

= = __** Title of Lab: **__ Conservation of Energy Inquiry Lab- Swinging Ball

Charlie Morris, Kevin Sarfani, Raul Ramirez
 * __ Researchers: __**

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

__** Research: **__ We used the distance between the photogates divided by the time it took the ball to swing to find the velocity. The initial energy will equal the final energy -> E f = E i (½)mv f 2 +mgh f = (½)mv i 2 +mgh i

Since h f =0 and v i =0, the equation can be simplified to (½)mv f 2 = mgh i

We find that h i is equal to L - L cos θ, and substitute it into the equation for h i

(½)mv f 2 = mg( L - L cos θ)

The masses divide out. It can be rewritten as v f 2 =2 g( L - L cos θ)

Constants: Length of string, g ravity, mass of sphere Variable: Angle (independent), time, speed of sphere at lowest point (dependent)

__** Hypothesis: **__ The initial angle with the vertical has a linear relationship with the speed of the swinging ball at its lowest point, shown by the equation v f 2 =2 g( L - L cos θ)


 * __ Materials __**
 * 1) pendulum
 * 2) photogates
 * 3) string
 * 4) ball
 * 5) meterstick
 * 6) stand


 * __Procedure:__**
 * 1) set up the pendulum and stand
 * 2) set up the photogates
 * 3) adjust the meterstick so that the distance could be measure between photogate
 * 4) swing the ball
 * 5) repeat step 4 with different angles to measure the time it takes to reach the final spot

__** Data: **__


 * ~ Angle θ ||~  Cos θ ||~  Speed (m/s) ||~ Speed^2 (m^2/s^2) ||
 * > 5 ||> 0.996 ||> 0.2674 ||> 0.0715 ||
 * > 10 ||> 0.985 ||> 0.4985 ||> 0.2485 ||
 * > 15 ||> 0.966 ||> 0.7548 ||> 0.5697 ||
 * > 20 ||> 0.94 ||> 1.0059 ||> 1.0118 ||
 * > 25 ||> 0.906 ||> 1.2241 ||> 1.4984 ||
 * > 30 ||> 0.866 ||> 1.4556 ||> 2.1187 ||
 * > 35 ||> 0.819 ||> 1.8273 ||> 3.339 ||
 * > 40 ||> 0.766 ||> 2.0239 ||> 4.0962 ||
 * > 45 ||> 0.707 ||> 2.1345 ||> 4.5561 ||
 * > 50 ||> 0.643 ||> 2.3738 ||> 5.6349 ||
 * > 55 ||> 0.574 ||> 2.6458 ||> 7.0003 ||
 * > 60 ||> 0.5 ||> 2.8222 ||> 7.9648 ||
 * > 60 ||> 0.5 ||> 2.8222 ||> 7.9648 ||

__** Data Analysis: **__ __** Conclusion: **__ Our data supports the hypothesis, since there is a linear relationship. Our slope was -16.09 m^2s^2 and y intercept of 16.1m^2s^2. We can improve this experiment by carrying out multiple trials with different angles since we were limited to angle measures. our percentage error is 8% and thats mainly due to lack of precision and limited to angles

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