Ball+on+Incline+-+Peter+Choi+and+Joey+He

Title of Lab: Ball on Incline

Researchers: Peter Choi, Joey He

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

Research: Using the equation from the cart on incline lab, mgsin θ, and Newton's Second Law, we found that the ball's acceleration equals gsin θ. And using the kinematic equations, we can find that the displacement of the ball equals 1/2*gsinθ*t^2.

F = ma mgsinθ = ma a = gsinθ

Δx = vit + 1/2at^2 = 1/2*(gsinθ*t^2)



http://www.physics247.com/physics-homework-help/slope.php

Hypothesis: As the distance the ball rolls increases, so does the time it takes to roll down. The time can be related to the distance in a square root curve. This can be represented by the equation 1/2 *gsin θ* t^2. Since the angle of our incline is constant at 12, the equation is written as 1/2 *gsin12* t^2. When t is written as a function of displacement, it is sqrt((2 Δx)/(gsin12))=t

Procedure: __Variables__: Time, displacement __Constants__: Angle of inclination, gravity

Materials: Incline board, tennis ball, meter stick, protractor, stopwatch 1) Set the incline board to an angle between 10 and 15 degrees above the horizontal. 2) Measure the angle and make sure it stays constant throughout the experiment. 3) Place your ball a measured displacement from where you'll stop your time. 4) Find the time it takes for your ball to reach the end point from its starting point. 5) Record both the displacement and time. 6) Repeat steps 3-5 for various displacements.

Data: Angle of Inclination = 12 degrees

Data Analysis: The time vs displacement graph shows a square root curve.

By squaring the time, we can see that the displacement is directly related to the time squared.

The time squared vs displacement graph has a slope of 1.50 s^2/m, and using the equation g= 2/(slope^2*sin θ), we find the experimental g is equal to 4.27m/s^2. According to the line of best fit, the y-intercept is -0.0065 s^2. In theory, the y-intercept should be at 0. Also, g should be about 9.81m/s^2, so we had a 56.5% error. This large disparity between the recorded value and predicted value is probably due to inaccuracy when timing and the limited precision of the meter stick used to measure displacement. A better timing device and a more precise distance measuring tool would produce a value much closer to the predicted value.

Conclusion: S ince our graph did not pass through (0,0) it is probably not very accurate. The lack of values also reduces confidence in our results. Combined with how large our percent error was for the value of g, we can infer that the results are inconclusive, do not support our hypothesis, and further testing is needed.