You will measure the acceleration of gravity by dropping a picket fence through a photogate. The...

 

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You will measure the acceleration of gravity by dropping a picket fence through a photogate. The leading edges of the black stripes are 0.050m apart. As the fence accelerates, the gate will record shorter time periods between stripes. From this information, it will compute the velocity of the picket fence. For your calculations you will get a table with the measured time and velocity data, as well as the graph velocity vs time. The procedure consists in the following steps a) Prepare software and hold the picket fence above the photogate as shown in Figure 1. (Be sure that the picket fence has a soft, foam pad to land on.) Figure 1. Picket fence and photogate b) Click "record" on the display, then release the picket fence. c) After the picket fence lands, click "stop". Picket fence must not hit the gate d) Use the velocity vs time in Table 1 to calculate the acceleration of the picket fence due to gravity using the following equation v(t+At)-v(t) a(t)=lim- where a(to) is the acceleration evaluated at time = to At is the increment of time. v(to+At) is the velocity evaluated at time = t+At v(to) is the velocity evaluated at time = to To get an approximation of the acceleration use a(to) (v(to+At) - v(to))/At Table 1. Time and speed data. time v [m/s] 0 1.12 0.039 1.51 0.069 1.81 0.095 2.06 0.119 2.27 0.140 2.49 Results Determine the acceleration due to gravity using consecutive data and then use the first and final data. data v(to+At) v(to) [m/s] Table 2. Determined values of the acceleration of the picket fence due to gravity. Acceleration [m/s] At [s] 1-2 0.039 2-3 0.030 3-4 0.026 4-5 0.024 5-6 0.021 1-6 0.140 Show a sample of your calculations You will measure the acceleration of gravity by dropping a picket fence through a photogate. The leading edges of the black stripes are 0.050m apart. As the fence accelerates, the gate will record shorter time periods between stripes. From this information, it will compute the velocity of the picket fence. For your calculations you will get a table with the measured time and velocity data, as well as the graph velocity vs time. The procedure consists in the following steps a) Prepare software and hold the picket fence above the photogate as shown in Figure 1. (Be sure that the picket fence has a soft, foam pad to land on.) Figure 1. Picket fence and photogate b) Click "record" on the display, then release the picket fence. c) After the picket fence lands, click "stop". Picket fence must not hit the gate d) Use the velocity vs time in Table 1 to calculate the acceleration of the picket fence due to gravity using the following equation v(t+At)-v(t) a(t)=lim- where a(to) is the acceleration evaluated at time = to At is the increment of time. v(to+At) is the velocity evaluated at time = t+At v(to) is the velocity evaluated at time = to To get an approximation of the acceleration use a(to) (v(to+At) - v(to))/At Table 1. Time and speed data. time v [m/s] 0 1.12 0.039 1.51 0.069 1.81 0.095 2.06 0.119 2.27 0.140 2.49 Results Determine the acceleration due to gravity using consecutive data and then use the first and final data. data v(to+At) v(to) [m/s] Table 2. Determined values of the acceleration of the picket fence due to gravity. Acceleration [m/s] At [s] 1-2 0.039 2-3 0.030 3-4 0.026 4-5 0.024 5-6 0.021 1-6 0.140 Show a sample of your calculations