Free Fall Motion of a Ball Lab Report May 22, 2013 10:00 A.M Emily Muller Lab Partners: Aaron Jacobs and Janne Olson Physics 250, Section 1 Dr. Hasan Objective: The purpose of the experiment was to analyze the free fall of a ball using a variety of tools in order to calculate the acceleration due to gravity. Theory and Formulas: When an object is released from another restraining object, it is in free fall. Free fall is when the only force acting on an object is gravity. The object is only affected by the acceleration due to gravity. On earth, this value is -9.81m/s2. The important formulas for a free fall experiment are: 1: vn = (yn+1 – yn) / (tn+1 – t n) and 2: an = (vn+1 – vn) / (tn+1 – tn). Apparatuses: Meter stick, lights, dark blanket, video camera with recording tape, tripod, balls, computer, video camera cord for connecting to computer, video editing software, and VideoPoint program. Procedure: The camera was set up facing the blanket with meter sticks measuring from the floor up, two meters. The camera was placed far enough away to capture almost all of the two meters in the frame. The camera recording was turned on. For the first part of the experiment, a ball was dropped close to the meter sticks (for easy analyzing) from about two meters from the ground. For the second part of the experiment, a ball was thrown upward from as close to the ground as possible to approximately two meters. This ball was also thrown as close the meter sticks as possible. The tape of the balls being thrown/dropped was imported into a movie editing software and each of the motions was extracted to be a separate clip. This clip was then uploaded into VideoPoint and then analyzed to calculate the acceleration constant due to gravity. Observations and Data: (See graphs) Calculations: The average values of the points on each graph were calculated using the computer program. The coefficients for the line represented the calculated value for acceleration due to gravity. For Graphs 1 and 4 where position was measured, the coefficient in front of the squared term represented ½ of the acceleration due to gravity because of the equation: change in y = vot + ½ at2. In graphs 2 and 5, the velocity was measured, therefore the slope of the line, also represents the acceleration due to gravity. Lastly, in graphs 3 and 6, the acceleration was measured; therefore the average of the points represents a calculated value for the acceleration due to gravity. These values can be compared to accepted value to assess the accuracy of the experiment. Results: Graph Calculated Acceleration Value Accepted Value Percent Error 1 -5.17 m/s2 2 -10.1 m/s2 3 -10.1 m/s2 4 -5.09 m/s2 5 -10.2 m/s2 6 -10.2 m/s2 -4.9 m/s2 -9.8 m/s2 -9.8 m/s2 -4.9 m/s2 -9.8 m/s2 -9.8 m/s2 5.22% 2.97% 2.97% 3.73% 3.92% 3.92% Sources of Error: One possible source of error is the placement of the video camera. Because the camera is not moving, the frame of reference is not changing with the ball as it moves. Therefore, an angle is created between the video camera and the balls location. This could create the slight error seen in the calculated acceleration due to gravity values. Conclusion: The objective of the experiment was to calculate the acceleration value due to gravity using balls in free fall. The results of the experiment show between 2.97% and 5.22% error, which could be due to the video cameras stationary placement. Overall, the results of the experiment support the accepted value of the acceleration due to gravity as -9.8 m/s2.