Video Project Final Analysis

Over the course of this video project, we set out to analyze the real life application of two physics topics we have learned throughout the year in class. We analyzed both simple harmonic motion as well as projectile motion, with the projectile being Cam’s body. As Cam was on the swing, he was subject to simple harmonic motion, with the swing acting as a simple pendulum. From this motion, we withdrew several different aspects of the pendulum, including period, frequency, angular frequency, and amplitude. After completing half of a period of the pendulum’s motion, Cam then exited the swing and underwent projectile motion. From this motion, we withdrew even more information, including: x and y position, velocity, acceleration, and different forms of energy. We found through the course of this project that the techniques we learned in class still apply to real-world situations, yet with some error involved. It was particularly interesting to notice how all of the different information coincided with each other. For example, when potential energy was at a minimum in Cam’s motion, his kinetic energy was then at a maximum. Although this video analysis was not done in an ideal “physics” world, the data obtained from the video was still quite valid. Furthermore, the analysis we ended up obtaining from this data allowed us to analyze not just one form of motion- we were able to demonstrate both SHM and projectile motion.

Pendulum Motion Analysis

For the first part of the motion in this video, Cam’s body is moving on the swing in simple harmonic motion. Therefore, the system can be treated as a simple pendulum, with the swing having a length of 2.197 meters.  From the analysis of the y-position vs time graph for the time while on the swing, the amplitude drawn from the data is 0.67135 meters. Furthermore, the angular frequency drawn from this system is equal to the square root of gravity over the length, giving us an angular frequency of 0.473 radians/second. Cam’s body leaves the swing at the leftmost point in the swing’s motion, which is equal to half of the swing’s period. Cam leaves the swing at time t=1.235 seconds, so this provides that the swing’s total period is 2.47 seconds long. Since frequency is the inverse of the swing’s period, this leads us to obtain a frequency for the system of 0.405 Hz. Similarly, if angular frequency is multiplied by 2  the value for frequency is .337 Hz and the period found by the inverse of frequency is 2.972. Since the theoretical and the observed values for frequency and period are very close it shows the accuracy of our lab. With percent errors of 20.2% and 16.8% it is easy to see that the data was quite accurate.

List of Resources/Links

For further help obtaining the information of the pendulum in this system, we utilized the following websites:

·         http://www.physicsclassroom.com/Class/waves/u10l0c.cfm

·         http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html

Sample Calculations

For a lot of our calculations we used excel to produce graphs and lines of best fit to represent the data that we had collected. For example for the y-acceleration we found the linear line of best fit and compared our slope to the value of the accleration due to gravity. Addtionally other mass we calculated we found the kinetic and potential energy we used the equations K= 1/2mv^2 and U=mgh. We took half of Cam's mass, after converting it from pounds, and multiplied by the velocity vector squared to find the kinetic energy of the motion. And then we took Cam's mass and multiplied it by the acceleration due to gravity and Cam's y-position to find the potential energy of the system. Then to find the total energy we found the sum of these two values, and to get one value for the total energy we averaged all of our total mechanical energies. For the simple harmonic motion of the pendulum we had to calculate the amplitude, period, angular frequecy, and frequency of the motion. We found amplitude by using our y position vs. time graph to find the distance from the line of equilibrium. To find the period we used our x position vs. time graph to figure out the time at which Cam's body leaves the swing. This value is equal to half of the period which made it easy to find. For the angular frequency we plugged our data into the equation ω = √(g/l). And we found frequency by taking the inverse of period (1/T).

Total Mechanical Energy

For the total mechanical energy of our systen we found the average sum of the kinetic energy and the potential energy. We found that the mechanical energy hovered around 864.0717 Joules. Our calculated energy does not stay perfectly constant probably due to friction in the swing and air resistance.

Kinetic Energy

Here is our graph of Kinetic Energy versus time here using our values of velocity in the x and y direction I used vector addition to find the resulting velocity which I then squared. After obtaining v² I multiplied it by Cam’s mass and then divided it by two. These steps gave me the kinetic energy using 1/2mv² at each time. You can see that the kinetic energy peaks between .5 and 1 seconds and between 1.5 and 2 seconds. Which means these are points where the velocity is the highest.

Potential Energy

Here is the graph of Cam’s potential energy versus time. As you can see the potential energy graph shows peaks and dips over time. At the beginning of Cam’s motion where he is at the top of the swing’s period the potential energy is at its highest. Also the potential energy peaks again when Cam leaves the swing at the other end of the swing’s period. Another interesting note to keep in mind is that energy is conserved. When comparing the two energy graphs you can see that the peaks of the kinetic energy graph are also the dips of the potential energy graph.