Motion Detector & Video Analysis Lab

 1. Measuring acceleration due to gravity using a motion detector.

        a) My group used the motion detector to measure the acceleration due to gravity of a falling ball.

        b) We did this by using the motion detector to track the balls motion and use that motion to plot two graphs: a velocity vs time graph and a position vs time graph. Then, we zoomed into the portion of graph that we wanted to analyze, and then applied a curve fit. Next, we obtained the equations of each curve to find the acceleration due to gravity using both curves. We found acceleration by taking the second derivative of the position function with respect to time and the first derivative of the velocity function with respect to time.

        c) We found the acceleration using the position vs time graph to be -9.644 m/s^2.

             We found the acceleration using the velocity vs time graph to be -9.568 m/s^2.

        d) The standard deviation is 0.127 m/s^2.

2. Measurement of acceleration due to gravity using video analysis.

        a) I used vernier to track the motion of a ball and measure the acceleration due to gravity.

        b) I took a video of myself dropping a ball and used Vernier's motion tracking to plot two graphs: a position vs. time graph and a velocity vs. time graph. Again, I zoomed into the portions of the graphs that I wanted to analyze, applied a curve fit, and then obtained each of the curve's respective equations. Using the equations, I found acceleration from second derivative of the position function with respect to time and the first derivative of the velocity function with respect to time.

        c) I found the acceleration using the position vs. time graph to be -10.036 m/s^2.

            I found the acceleration using the velocity vs. time graph to be -9.443 m/s^2.

        d) The standard deviation is 0.275 m/s^2.

3. Write-up on measurement variability.

        a) The percent difference that I calculated between the measurements of both experiments using                 the velocity vs. time graphs is 1.32%.

        b) Yes, both of my measurements agree with the uncertainty determined by standard deviation.

        c) The measurements that have uncertainty when using the motion detector are: change in position from external interference (such as the table or something/someone being in the way), and all of the measurements (including time, position, and velocity) stemming from human error in the setup or capture of data.

        d) The measurements that have uncertainty when using the video analysis could be: time due to the frame rate, the change in position due to a bad scale of reference, and most importantly both the velocity and position from inaccurately plotting the points on the ball.

        e) The estimated uncertainty for each of the measurements in the first and second experiments is:

                Motion Detector - +/- 0.05m  (height)  &  +/- 0.2s (time)

                Video Analysis -  +/- 0.1m (height)  &  +/- 0.3s (time)

        f) The uncertainty propagation that I calculated is:

                Motion Detector - +/- 0.052

                Video Analysis -  +/- 0.112

        g) The measurements do seem to agree with my estimated uncertainty.

        h) I believe the data taken from the motion detector experiment is way more useful compared to the data taken from video analysis. This is because almost every aspect of video analysis (plotting points on the ball, scale for reference, etc.) seems much more inaccurate in my opinion.