Graduated from York College of Pennsylvania with a Bachelor of Science in Mechanical Engineering. While there, grew to love design, prototype, and develop solutions for tough engineering challenges. Skilled in working in team-oriented and multi-disciplinary settings. Proficient with a wide variety of engineering software tools such as SOLIDWORKS and ANSYS packages. Proven track record of success in project completion. Always seeking to expand knowledge of engineering knowledge by joining organizations such as ASME and IEEE.
Student Competition using Differential Equation Modeling (October 2018)
I decided to participate again in SCUDEM. This time I had a new team whom consisted of Jack Anderson, Matthew Morrow, Devon Matt. We again had a selection of three problems but we narrowed it down to one problem.
Once again we only had a week to develop a differential equations. As always this problem was again very challenging since most of my teammates were not exposed to rotational systems. In addition, attempting to model a moving pendulum around a central pole is still challenging without having taken Dynamics but we all pulled together and researched possible ways of modeling it. We even decided to purchase equipment and material to build a physical model to aid us in developing our differential equations. We poured in over 20 hours in a week span while still taking a full course load (It was Brutal!) but we were able to develop a solution. In addition, we also developed a PowerPoint to present it at Towson University.
Executive Summary Problem B
Statement of Problem: Our team has been asked to design a swinging pendulum system to be displayed at museum. In addition, a metal ball whose mass is 600 grams will roll down a ramp in order to strike the stationary ball which will set the system in motion. We are required to determine at what distance we want the domino to be located at. We have determined the distance we want the domino to be at when we strike which is m. Since the system will have a constant velocity and angular velocity, we have determined that we will have some constant angle, θ, a velocity, v, an angular velocity, ω, and a height of the ramp, h. The metal ball (600 grams) will roll down from the ramp at some velocity, v, generated by some height, h which will strike the stationary ball. This collusion will cause some constant velocity, v, which will then lead to some constant angular velocity, ω. This will lead to some theta, θ, that will cause the ball to strike the domino.
Theory:
FBD of ramp and swinging pendulum
The equation of the pendulum rotating around the central pole can be derived using the Lagrange equation. From the Lagrange equation of motion, we have L = T – V which is the total rotational kinetic energy minus the total potential energy of the ball [1].
Where T is defined as;
Results: Since we know the theta that we want to hit the ball, we can work backward in the problem and calculate the necessary velocity the ball would have to move at in order to hit the domino. Since the theta must be 29 degrees, and we know that if we assume constant angular velocity and constant velocity then the system is in static equilibrium for the hanging rod and ball. We can develop a free body diagram from the weight and the tension and solve for the tension since we know the weight. We know tension is equal to and as such we obtain 2.95 m/s. From this velocity, we can use the gravitational potential energy and kinetic energy to calculate the height. The calculated height is 0.887 m. In addition, we used a physical model in order to try to validate our assumptions. During our experiments, the friction from the model was great enough that it was difficult to obtain an ideal result. When impacted it was observed that the ball would not go into uniform circular motion but instead the motion was chaotic. It would not even complete a full rotation around the central pole.
Conclusion: The differential equation developed describes the motion of a pendulum with a constant angular velocity via energy equations. Using the Lagrange equation, we can attempt to at least model the motion of the ball in order to develop a differential equation. Due to the physical restraints of the materials we could buy and time, the physical model developed didn’t confirm the differential equation we developed.
References:
[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. Hoboken, NJ: Wiley.
[2] K., Alam, N., Alam, N., R., & F. (2013, September 22). Dynamic Analysis of Rotating Pendulum by Hamiltonian Approach. Retrieved from https://www.hindawi.com/journals/cjm/2013/237370/
Presentation:
This is a small demonstration video since due to time constricts we weren't able to fully complete the physical model, but that didn't stop us from experimenting with what we had. We ended up scoring 4.2 out of 5 this year which was a great improvement from last year. We still lost to an amazing group of cadets from the Naval Academy, but we had lots of fun and learned a great deal.