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Physics 105 lab 3 answer key with data
Typology: Lab Reports
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Goal: The purpose of this experiment is to analyze the motion of a freely falling object and determine the value of g , the acceleration due to gravity. Background: Free fall is described in your textbook. A metal ball is suspended at y = 0 m above a sensor pad that registers the impact after the ball is dropped. We expect that the falling distance y and elapsed time t will be related by y = – ( g / 2 ) t^2. We also expect the vertical velocity to be related to the elapsed time t as v y = – g t. In both equations, the parameter g is the acceleration due to gravity. Task 1: Determine the uncertainty in the time measurements. First, practice releasing the larger of the two balls until you have consistent time results. Position the ball 0.50 m above the sensor pad and measure the time of fall for five consecutive trials to determine the uncertainty of the computer-controlled time measurement. What is the typical uncertainty as determined by the percent difference between the smallest and largest times? Are all four displayed digits useful and how do you know? Task 2: Measure the vertical displacement and the time of fall. Measure the time of fall for the larger ball for fifteen different initial heights between –0.05 m and –0.75 m in 0.05 m increments. A suitable table could look like the one below. Note columns 3 and 4 will be used for a later task. Pad position y [m] Time of fall t [s] t^2 [s^2 ] Velocity Vy [m/s]
- 0.05 0.100 0.01 x - 0.10 0.143 0.02 -1. - 0.15 0.178 0.031 -1. - 0.20 0.210 0.044 -2. - 0.25 0.225 0.051 -2. - 0.30 0.250 0.062 -2. - 0.35 0.260 0.067 -2. - 0.40 0.285 0.081 -2. - 0.45 0.310 0.096 -2. - 0.50 0.320 0.10 -4. - 0.55 0.334 0.11 -3. - 0.60 0.352 0.12 -3. - 0.65 0.362 0.13 -3. - 0.70 0.378 0.14 -3. - 0.75 0.392 0.15 x Task 3: Compare the time of fall for balls of different mass.
Task 7: Compute the velocity v y as a function of time t. Take the heights y and the times t in the table and use them to compute velocities. For example, the velocity at time t 7 (corresponding to the seventh data point) can be obtained using the formula. Here, the difference ( y 8 – y 6 ) is computed from the two neighboring position values (sixth and eighth measurements) and similarly for the time difference ( t 8 – t 6 ). Compute the velocities v y for all values of t (except for the first and last one) and insert the 13 data values into the fourth column. Task 8: Graph the velocity v y as a function of time t. Use the data points ( t , v y) and create Graph III by plotting the velocity v y as a function of the time t. Find the best fit straight line through all the data points and determine its slope mIII. According to v y = – g t , what should the value of the slope mIII be? According to mIII, what is the predicted value of g? Calculate the percent error between the measured value of g and its predicted value. Lab Report: Prepare a report that includes your data sheet, three graphs, and answers to the questions raised in the instructions.