Ball+on+Incline+-+Lekha+Vuppalapati+and+Ji-Won+Park


 * Title of Lab: Ball on Incline **


 * Researchers: Lekha Vuppalapati and Ji-Won Park **


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


 * Research: **



Newton's Second Law mg·sinθ=ma g·sinθ=a

Kinematics Δx= Vi*t + 1/2*a*t2 There is no initial velocity: Δx= 1/2*a*t2 Solving for t2 : t2 = 2*Δx/a

t 2 = 2*Δx/( g·sinθ)

t <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">2 = 2*Δx/( g·sinθ) <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">As the distance the ball rolls increases, so does the time it takes, leaving a square root curve. <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">As a result, the equation above creates a linear relationship between the time and the distance travelled.
 * <span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 14pt;">Hypothesis: **

<span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 12pt;">tennis ball, incline, meter stick, stopwatch, textbooks, and protractor
 * <span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 14pt;">Materials: **

<span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 12pt;">Constant: angle of inclination, gravity <span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 12pt;">Variables: time, displacement
 * <span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 14pt;">Procedure: **
 * 1) <span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 12pt;">Adjust incline by adding textbooks underneath so incline is at 11° and make sure it stays constant throughout the entire experiment.
 * 2) <span style="background-color: #ffffff; font-family: Arial,sans-serif; font-size: 10pt;">Place the ball at the same starting point from where the displacement will be measured.
 * 3) <span style="background-color: #ffffff; font-family: Arial,sans-serif; font-size: 10pt;">Measure the displacement for where you'll stop your time.
 * 4) <span style="background-color: #ffffff; font-family: Arial,sans-serif; font-size: 10pt;">Find the time it takes for your ball to reach the end point from its starting point.
 * 5) <span style="background-color: #ffffff; font-family: Arial,sans-serif; font-size: 10pt;">Record both the displacement and time.
 * 6) <span style="background-color: #ffffff; font-family: Arial,sans-serif; font-size: 10pt;">Repeat steps 3-5 for various displacements.


 * <span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 14pt;">Data: **
 * = <span style="font-family: 'Times New Roman',serif; font-size: 16px;"> Δx (cm) ||= time (s) ||= t^2 (s^2) ||
 * = 20 ||= 0.5 ||= 0.25 ||
 * = 30 ||= 0.7 ||= 0.49 ||
 * = 40 ||= 0.9 ||= 0.81 ||
 * = 50 ||= 1.0 ||= 1.00 ||
 * = 60 ||= 1.2 ||= 1.44 ||
 * = 70 ||= 1.2 ||= 1.44 ||
 * = 80 ||= 1.2 ||= 1.44 ||
 * = 90 ||= 1.4 ||= 1.96 ||
 * = 100 ||= 1.5 ||= 2.25 ||
 * = 110 ||= 1.6 ||= 2.56 ||
 * = 120 ||= 1.7 ||= 2.89 ||
 * = 130 ||= 1.7 ||= 2.89 ||

<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">
 * <span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: 14pt;">Data Analysis: **

The original graph of Displacement vs Time resembles a square root curve.
This graph of Displacement vs. Time^2 has a linear line of best fit. The equation of this line is y=2.127x. The slope of this line is 0.0221, and the y intercept is at (0, 0). The time squared vs. displacement graph has a slope of 2.127 s^2/m, and using the equation g= 2/(slope*sin θ),we find the experimental g is equal to 4.93 m/s^2. Error could have come from an imprecise measurement of the angle. Error also could have come from delayed time of starting and stopping the stopwatch, and the lack of trials to confirm our hypothesis.

Our hypothesis was not supported by the experiment. Though there was a positive linear relationship between time squared and distance, our experimental value for g was 4.93 m/s^2: there was a percent error of 49.7% which isn't a clear. The person timing could have a more consistent starting and stopping reaction time to not have delays and have more accurate readings of time. This experiment could also be improved by using technology that could give more precise readings for the time and, as well as reading the angle measure more accurately, and lastly carrying out multiple trials to data to further support our hypothesis.
 * Conclusion: **