Ball+on+Incline-+Jonathan+Hannings+&+Jordan+Anderson

Ball on Incline
 * Title of Lab: **

Jonathan Hannings & Jordan Anderson
 * Researchers: **

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

Free body diagram picture source: [] We know that distance is equal to the intial velocity multplied by time plus one-half time acceleration times time squared. d=vit + 1/2at^2 So since the inital velocity is zero, we get this: d=1/2at^2. If we solve for t^2 we get 2(d)(a)=t^2. Newton's Second law states that the sum fo the forces is equal to the mass times acceleration. Using the above diagram we can say that mgsin θ (in the x direction) = ma (in the x direction). The mass cancels on both sides leaving us with gsinθ=a. If we place this in for acceleration, our final equation is 2(d)(gsinθ)=t^2.
 * Research: **


 * Hypothesis: ** The distance traveled down the incline is directly related to time squared using the equation t^2=2dgsin θ.

__//variables//__- time and displacement __//constants//__- gravity and angle of inclination 1) Retrieve a tennis ball, board, protractor, meter stick, and stopwatch. 2) Place the board at 10-15 degrees above the horizontal. 3) Place the meter stick on the board to measure the ball's displacement. 4) Make sure the stopwatch is reset to 0 before every trial 5) Hold the ball at a certain measurement and release. Start the timer upon release and stop it once it is at a designated finishing point. 6) Record the time on the stopwatch and repeat steps 2-6 for various displacements, making sure the board remains at the same inclination.
 * Procedure: **

Angle of inclination: 13 degrees.
 * Data: **
 * Distance traveled(cm) || Time trial 1(s) || Time trial 2(s) || Time trial 3(s) || Average Time (s) || Time Squared ||
 * 0 || 0 || 0 || 0 || 0 || 0 ||
 * 20 || .37 || .28 || .44 || .36 || .1296 ||
 * 40 || .50 || .53 || .56 || .53 || .2809 ||
 * 60 || .62 || .59 || .66 || .62 || .3844 ||
 * 80 || .70 || .78 || .75 || .74 || .5476 ||
 * 100 || .85 || 1.06 || .91 || .94 || .8836 ||
 * 120 || .94 || 1.00 || .94 || .96 || .9216 ||

**Data Analysis:**



The above graphs represent the Distance Traveled vs. Time and the Distance Traveled vs. Time Squared, respectively.

__//Line of Best Fit (Distance vs. Time Squared)//__: y=.008x-.037 This demonstrates that time squared is increasing as the distance traveled increases. //__Slope of Best Fit Line (Distance vs. Time Squared)__//: .008 The slope of the best fit line gives us acceleration. Using the equation g= 2/(slope*sin θ), our experimental g is equal to 7.71. This gives us a percent error of 21.4%. This error was likely due to human error using the protractor and the stopwatch.

Conclusion: Our data did not support our hypothesis for the experiment. Our equation does not work using our data and the graph also does not support the expected relation. To improve upon our experiment, we should take more data points at more distances and at more angles. Also, we could use photo gates to decrease human error.