Lab 4. Free Fall Motion (1) (2)

a. The velocity vs. time graph followed a positive, linear relationship. As the time increased, so did the velocity. This is related to the position vs. time graph, because as the position changes over time the velocity increases. 1. Inspect your velocity graph. How would the associated acceleration vs . time graph look? Sketch your prediction on paper. Now change the upper graph to acceleration vs. time. To do this, click the y-axis label and select Acceleration. Comment on any differences . You may want to rescale the graphs so that the acceleration axis begins at zero. a. I originally sketched the acceleration vs. time graph to look like a horizontal straight line, since acceleration on the object is constant over time. This prediction was confirmed after running the experiment again after changing the y-axis to acceleration, and the graph displayed a horizontal straight line at about 9.8 m/s^2, the accepted value of acceleration of an object in free fall. 1. Use the Statistics tool and the acceleration graph to find the average acceleration. How does this compare with the acceleration value for the same drop, determined from the slope of the velocity graph? a. An average acceleration of 9.68 was obtained, which corresponds to the acceleration obtained on the velocity vs. time graph. In fact, it is the same value as the 6th trial in our experiment. 1. Use the position vs . time graph and a parabolic fit to determine g. How close is this value of g to the one calculated g Ave ? a. When the parabolic fit was applied an equation of 4.8466x^2+1.4153x+-1.5874*10^-5, was obtained. i. f’(x)= (96932x+14153)/10000 ii. f’’(x)= 24233/2500= 9.69 b. When taking the second derivative of this equation we derived an acceleration of 9.69m/s^2, which is very similar to the values obtained in the experiment. 1. Would dropping the Picket Fence from higher above the Photogate change any of the parameters you measured? Try it. a. No, no matter where the fence was dropped from the acceleration remains constant on the object at around 9.8 m/s^2. Results and Discussion: It was found after conducting six trials that the average acceleration of the picket fence was about 9.74248 m/s^2, which is supported by the accepted value of acceleration which is 9.8 m/s^2. There was a 1.29% uncertainty, and the accepted value of acceleration (9.8 m/s^2) fell within the range of experimental values which was 8.48 to 11. Conclusions: It was determined that acceleration on an object in free fall is constant at about 9.8 m/s^2, and does not depend on the height at which the object was dropped.