Swinging+Ball+-+Anish+Sahasrabudhe,+Daniel+Hicks

Title of Lab: Swinging Ball.

Researchers: Anish Sahasrabudhe, Daniel Hicks

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

Research: (http://www.education.com/study-help/article/simple-pendulums/)

Constants: L=Radius(length of the string)

Variables:- Angle, velocity at lowest point, time. Due to the law of conservation of energy, the initial energy is equal to the final energy. Using the equation mgh= 1/2mV f 2 we can find the final velocity of the ball. In order to find the value of h, we used the diagram above which incorporates the cosine of the angle and the length of the string in order to find it. The masses on both side of the equation cancel left so g(L-Lcos ** Θ ** )=1/2V f 2. Solving for V f 2 leaves the equation as: V f 2 = -2gLcos ** Θ ** + 2gL.

Hypothesis: The velocity of the ball at its lowest point and cosine of an angle have a linear relationship.The greater the angle with the vertical, the faster speed the ball has at its lowest point.

Procedure: Materials: Stand, screws, sphere, time gates, string, wooden protractor. 1. Attach the protractor and then the string to the stand. 2. Set up the time gates at a distance of 0.07m such that the lowest point of the pendulum is in the center. 3. Select the interval setting on both of the time gates. 3. Holding the ball at 5 degrees from the vertical, release it such that it passes through the time gates without hitting them. 4. Increase the angle in 5 degree increments and record the times for each angle. Data:
 * Angle( in degrees) || Time(s) || Velocity(m/s) ||
 * 5 || .2789 || .25 ||
 * 10 || .1345 || .52 ||
 * 15 || .0716 || .98 ||
 * 20 || .0611 || 1.14 ||
 * 25 || .0461 || 1.52 ||
 * 30 || .0372 || 1.88 ||
 * 35 || .0339 || 2.06 ||
 * 40 || .0264 || 2.65 ||
 * 45 || .0245 || 2.86 ||
 * 50 || .0216 || 3.24 ||
 * 55 || .0201 || 3.48 ||
 * 60 || .0183 || 3.83 ||


 * cos** Θ ** || velocity^2 ||
 * 1 || 0 ||
 * .99619 || .0625 ||
 * .98481 || .2704 ||
 * .96593 || .9604 ||
 * .93969 || 1.3225 ||
 * .90631 || 2.3104 ||
 * .86603 || 3.5344 ||
 * .81915 || 4.2436 ||
 * .76604 || 7.0225 ||
 * .70711 || 8.1796 ||
 * .64279 || 10.498 ||
 * .57358 || 12.11 ||
 * .5 || 14.669 ||

Data Analysis: The slope of the line of best fit of the graph is -29.133 m^2/s^2cos ** Θ **and the y-intercept is 28.901, which means that when cos equals zero, that should be the velocity. Using the equation V f 2 = -2gLcos ** Θ ** + 2gL, we can find what the theoretical slope is equal to -2gL. Using that slope equation, the theoretically the slope is equal to -17.64 but our slope was -29.133 which gives us a 65% experimental error.

Conclusion: Based on our data, our hypothesis was not accepted because of such a high percent of error. This error could be due to mistakes in reading measurements, the ball hitting the time gates as it passes through it,incorrect angle measurements, and how the ball was released. In order to improve the error, a better way to release the ball should be used so the ball can travel on a straight path and be at the exact desired angle.