Ball+on+Incline-+Saie+Ganoo+&+Nick+Gant

Title of Lab: Ball on Incline

Researchers: Saie Ganoo and Nick Gant

Research Question: How does the time it takes for a tennis ball to roll down an incline relate to the distance it travels?

Research: The kinematics equation that relates distance and time is d = vit + (1/2)at^2 Since we are releasing the ball, the initial velocity will be 0, giving us d = (1/2)at^2 If we use algebra to solve for t we get t^2 = 2d/a

 If we assume that friction is negligible since the ball is rolling, force of mgsin(theta) = ma divide the mass from both sides and we get gsin(theta) = a

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Hypothesis: The total distance covered is related to the time squared with the equation t^2 = 2d/(gsin(theta)

Materials: tennis ball, wooden incline, meter sticks, stopwatch, platforms, protractor, recording tools

Procedure:
 * 1) Adjust platforms so incline is at (20)°.
 * 2) Placed meter sticks along wooden incline to ensure precise measurement and to prevent the ball from falling off the incline.
 * 3) Release ball at a recorded distance on incline and time how long it takes to cross said distance.
 * 4) Repeat with various distances while checking to make sure there is a constant angle of inclination.
 * 5) <span style="font-family: 'Times New Roman',Times,serif;">Graph data.

<span style="font-family: 'Times New Roman',Times,serif;">Data:

<span style="font-family: 'Times New Roman',Times,serif;">Data Analysis: <span style="font-family: 'Times New Roman',Times,serif;">
 * <span style="font-family: 'Times New Roman',Times,serif;">Time (seconds) || <span style="font-family: 'Times New Roman',Times,serif;">Distance (meters) ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.7 || <span style="font-family: 'Times New Roman',Times,serif;">1.6 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.6 || <span style="font-family: 'Times New Roman',Times,serif;">1.5 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.6 || <span style="font-family: 'Times New Roman',Times,serif;">1.4 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.5 || <span style="font-family: 'Times New Roman',Times,serif;">1.3 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.4 || <span style="font-family: 'Times New Roman',Times,serif;">1.2 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.3 || <span style="font-family: 'Times New Roman',Times,serif;">1.1 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.2 || <span style="font-family: 'Times New Roman',Times,serif;">.70 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">1.1 || <span style="font-family: 'Times New Roman',Times,serif;">.60 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">0.94 || <span style="font-family: 'Times New Roman',Times,serif;">.50 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">0.88 || <span style="font-family: 'Times New Roman',Times,serif;">.40 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">0.69 || <span style="font-family: 'Times New Roman',Times,serif;">.30 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">0.62 || <span style="font-family: 'Times New Roman',Times,serif;">.20 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">0.41 || <span style="font-family: 'Times New Roman',Times,serif;">.10 ||
 * <span style="font-family: 'Times New Roman',Times,serif;">0.00 || <span style="font-family: 'Times New Roman',Times,serif;">0.00 ||

<span style="font-family: 'Times New Roman',Times,serif;"> Seeing a square root curve, we decided to square the time in order to receive a linear function.

<span style="font-family: 'Times New Roman',Times,serif;">

Since the data shows a square root function, we decided to square time in order to give us a linear relationship The slope was 1.6 m/s. We found this out by using the points: (1.8, 3.0) and (0.40, 0.75) Using the equation g= 2/(slope*sin θ), we find the experimental g is equal to 3.66, which gives us a percent error of 63% Clearly our experiment was not very accurate, so the following are some possible sources of error: <span style="font-family: 'Times New Roman',Times,serif;">Our data was slightly skewed due to <span style="font-family: 'Times New Roman',Times,serif;">possible miscalculations of the distance and if we ever started the timer too late or stopped it too early The y-intercept at 0 represents 0(cm) distance achieved in 0 seconds.

<span style="font-family: 'Times New Roman',Times,serif;">Conclusion: <span style="font-family: 'Times New Roman',Times,serif;">This experiment supported our hypothesis that the distance is proportionally related to time squared in a graph of a square root curve. <span style="font-family: 'Times New Roman',Times,serif;"> This probably caused the slight upward shift of the graph from the square root curve it should have been. In the future, we could find more data points, which would help fill the gap that is occurring in the middle of the graph. Furthermore, this experiment could be tried with different sized balls as well as inclines with different surfaces to expand on this experiment.