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Uniformly Accelerated Motion

Uniformly Accelerated Motion - Uniformly Accelerated Motion...

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Uniformly Accelerated Motion Author: Colleen Doorhy Partners: Brittany Denning and Barbara Hoskins PY 211 Sec 220 TA: Eli Owens Performed: September 18, 2007 Submitted: September 25, 2007

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I. Introduction A. Objective: The purpose of this experiment was to determine the speed or acceleration of gravity by measuring various positions of a freely falling object as a function of time or by measuring how long it takes a freely falling object to travel a fixed distance. In this experiment, the position of a falling body as a function of the time elapsed since it was released was measured and used to find the velocity and acceleration and then from that the acceleration of the object due to gravity can be determined. B. Theory: The laws of physics can determine the speed of a falling object and the time it takes to fall by knowing the height from which it is dropped. For each second that an object falls, its speed increases by 9.8 m/s. For convenience, the downward direction is positive and the displacement is that direction by y . The air resistance was neglected, so the body is “free falling”, therefore the acceleration, a , is constant. Using the values found for y and t , the average time, average velocity and average acceleration of the object can be calculated. The variable y stands for position and the variable t stands for time. The average velocity is found by using the change in position over the change in time: t y v avg = (1) The equations below are the average velocity during the time interval between the instants t 1 and t 2, and similarly, during the next time interval (between the instants t 2 and t 3 ): 1 2 1 2 12 t t y y t y v - - = = (2) 2 3 2 3 23 t t y y t y v - - = = (3) In calculating average acceleration, the average time can be found by: 2 i f avg t t t + = (4) Shown below is how to calculate the average time between the interval, 1 t and 2 t and the interval 2 t and 3 t : 2 1 2 12 t t t + = (5)
2 3 23 t t t + = (6) The value found for 12 v is the instantaneous velocity at 12 t and the value found for 23 v is the instantaneous velocity at t 23. After calculating the average velocity the average acceleration can be calculated using the average velocities and using the average times. The formula for average acceleration is: t v a avg = (7) Using these instantaneous velocities and the average times t 12 and t 23 , the average acceleration can be calculated: 12 23 12 23 t t v v t v a avg - - = = (8) The percent error equation is used to calculate a difference between an accepted value and a calculated value in a percentage form: 100 exp % - = actual erimental actual error (9) -OR- 100 * 2 / 1 % B A B A diff - - = (10) II. Methods and Materials A. Equipment: A “picket fence”, also known as Plexiglas or Lucite, is a piece of clear acrylic with equally spaced black bands (shown in Figure 1 below). Fig 1 the “picket fence”

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Uniformly Accelerated Motion - Uniformly Accelerated Motion...

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