Experimenting with compound pendulums and moment of inertia Essay Example

Experimenting with compound pendulums and moment of inertia Paper Two compound pendulums with different weight distributions were used to experimentally determine if the laws of simple harmonic motion would apply to them as well. The moments of inertia were determined experimentally, based on the periods of the pendulums, and compared to theoretical calculations. The average percent error for the pendulum with the shorter R (distance from pivot point to cm of the weights) was 2. 67%, and for the longer R was 6. 15%. Introduction The laws of simple harmonic motion are based on the periodic displacement, acceleration, and velocity of an object. A period is the time taken between peaks of maximum amplitude. When this type of motion is free of nonconservative forces, and the force needed to displace the object is proportional to the displacement, it is called simple harmonic motion. A simple pendulum is one in which a point mass is suspended from a string of negligible mass. It swings with a period of: T = 2 (L/g) where L is equal to the length of the pendulum. In a compound pendulum, the mass of the pendulum arm provides torque and must be described using Newtons second law for rotation: ? = Iarm? , and the torque is ? = -mgLcmsin ?. This leads to the equation for the period of a compound pendulum: T = 2 (Iarm/mgLcm) We will write a custom essay sample on Experimenting with compound pendulums and moment of inertia specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Experimenting with compound pendulums and moment of inertia specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Experimenting with compound pendulums and moment of inertia specifically for you FOR ONLY $16.38 $13.9/page Hire Writer which is similar in form to the simple pendulum equation, adding the compensation for the moment of inertia inherent in the arm of the pendulum. A pendulum is suitable for experiments in simple harmonic motion, because it provides a motion similar to a vertical spring oscillating up and down (or back and forth for a horizontal spring). This is because gravity provides the force to move the pendulum initially from its point of all potential energy to its point of all kinetic energy. In the absence of friction and air resistance, a pendulum would oscillate forever in simple harmonic motion, much the way an ideal spring would. In this experiment, a compound pendulum was constructed out of two weights that could be screwed together through a series of holes in a flat steel bar. The weights were attached near one end, and the center of mass of the system was determined by balancing. A hole toward the other end of the bar was chosen as the pivot point, and measurements were taken for the length of the bar, the width of the bar, the center of mass of the bar to the pivot point, the center of mass of the pendulum to the pivot point, the center of mass of the weight to the pivot point, and the radius of the weight. A scale was used to measure the weights of the bar and the weight. The pivot hole was placed over a knife-edge support, and the pendulum was pulled to the side and released to start it oscillating. One oscillation is the motion for one complete trip to and fro. The swing needed to be less than ten degrees from vertical, so that sin? ? ?. A stopwatch was used to measure the time for ten complete oscillations. Five trials were performed, and the experimental moment of inertia was calculated from the resulting period. The weight was moved on the bar, and a different pivot point was chosen for a second set of trials. The resulting moments of inertia were then compared to theoretical calculations for the moment of inertia. Purpose To demonstrate that the laws of simple harmonic motion apply to a compound pendulum. Procedures 1. Take measurements of the mass of the bar, the mass of the weights, the length and width of the bar, the radius of the weight, and distances from the pivot point to the centers of mass of the bar, the weight, and the bar and weight combined. 2. Select a pivot hole. Hang the bar from the knife edge support through the pivot hole and swing the pendulum with an angle of less than ten degrees. 3. Start timer at the beginning of an oscillation and stop it after ten complete oscillations. 4. Record the time. 5. Repeat for five trials. 6. Change conditions, i. e. the location of the weight on the bar and the pivot hole used, and repeat the above. Sources Wozniewski, L. (2000). Physics Laboratory Manual: Coefficient of Static and Kinetic Friction. Retrieved October 19, 2003, from Indiana University Northwest, Department of Chemistry, Physics, and Astronomy Web site: http://www. iun. edu/~cpalw/pweb/pendulum/pendulum. htm Cutnell, John and Johnson, Kenneth. Physics Sixth Edition. Hoboken, NJ: Wiley and Sons, 2004. Tables of Experimental Data set/triaConclusion The motion of a compound pendulum was similar to the motion of simple harmonic motion. The oscillations of the pendulum were similar in velocity, acceleration, and period to that of an ideal spring oscillating back and forth in harmonic motion. Therefore, the laws of simple harmonic motion could be applied to a compound pendulum also, because the experimental moment of inertia was comparable to the theoretical moment of inertia. It should be noted that moving the center of mass of the weights further from the pivot point increased the moment of inertia, and thus slowed down the rotation of the pendulum about the pivot point. Bringing the weight in closer to the pivot point provided less torque, which allowed faster times for the period. The average percent error for the shorter R was 2. 67%, and for the longer R was 6. 15%. This may be due to the greater time involved in the swing, which allowed friction and air resistance more time to act on the pendulum, as well as the larger swing area that front to back movement of the pendulum could have been introduced. Also, the theoretical calculation was based on ideal conditions, without friction or air resistance, which could not be obtained in the lab setting. Human error could have played a role in the error of the experiment, also. Measurements were taken by yardsticks, and the angle that the pendulum was started at may have been greater than ten percent, which could have skewed the results on one or both of the pendulums.

UCLA Graduate School Admission Essay Example

UCLA Graduate School Admission Essay Example Free Online Research Papers UCLA Graduate School Admission Essay Example 1. Please provide us with a summary of your personal and family background. Include information about where you grew up, your parents, your siblings, and perhaps a highlight or special memory of your youth. One of the special memories of my youth dates back to 17 years ago. Four siblings of us were living relatively affluent lives thanks to our parents who had very respectful and well-paid jobs: my father was a judge and my mother, a pharmacist. However, as my maternal grandfather’s business, which my mother stood guarantee for, went bankrupt, we faced a crucial crisis. The creditors created a series of commotion at our house for almost everyday. We had to square the debts by disposing the whole of our fortune and subsequently had to move to a small and shabby place. My father heartily consoled my mother who reproached herself for all the mishaps. And he also told his children, who were having difficulties adapting themselves to the circumstances totally different from the ones they had in the past, that the crisis we were undergoing was only one of the many challenges we would have to face in the course of our lives. This financial crisis eventually forced my father to quit working as a judge and he had no choice but to practice law in order to stabilize our family’s finance. Despite his financial difficulties, my father never gave up living up to his own motto, â€Å"A life with justice and volunteering†. He not only provided free legal services to the poor and the powerless but also continued to offer donations to xxx (an institution for the disabled) which was a shock to me when I first visited. Having compared myself with those disabled people, I came to realize that my life was so blessed that I should be living with more passion and effort. From that day on, I volunteered with my father to take care of the disabled children every weekend. My father’s confident way of life gave our siblings great courage. We began to work part time in order to help our parents. My sisters, who had extraordinary talents in music, tutored young children in piano and violin. My brother and I worked at carwash and delivered newspapers. We kept saving money in a siblings’ savings account. After a few years of united family efforts, we were able to move into a new and better place. I would never forget the emotional sensations and delights we felt and shared at that moment. My siblings and I spent a part of money we saved on decorating the front yard of the new house and donated the rest of the money to xxx. After a long time, my brother became a lawyer. He serves as a key member of the Association of the Lawyers who care for the Human rights, a non-governmental organization composed of lawyers that actively seek to enhance social welfare and justice amongst the underprivileged. His continuous and active participation in these social activities despite his hectic life schedule as a practicing lawyer demonstrates to me his enthusiasm for acting on his own convictions. His enthusiasm has inspired me to act on my own beliefs. One of my sisters became a physician and the other, a broadcasting writer. Both of them are leading passionate lives at present. My family has shaped my beliefs and actions in profound ways. From my family’s never-ending practice, I have learned the courage to fight against the hardship as well as the generosity to help the underprivileged people. I truly love and respect all members of my family. Given the chance, I hope to show to my future classmates of Ander son, the perseverance and the sense of sacrifice for others that I have learned from my family. 2. Discuss a situation, preferably work related, where you have taken a significant leadership role. How do this event demonstrate your managerial potential? I believe the primary element of a leadership is to build confidence from the associates. In addition, I believe that this confidence is possible when there is professionalism, passion and a clear vision of the future about the assigned duty. My confidence in the leadership was achieved through a project on the merger of xxx and our company xxx in which I participated for 3 months in 19xx. As a leader of one of the 5 loan-evaluation teams to inspect the bad loan section of xxx, I conducted a research on the actual status of the loan of xxx. As a result of a meeting for the conclusion after the research, 4 leaders, except me, turned out to be against the merger. That’s because there was too much risk involved in the poor loan of xxx. For the 3 months, I worked on average over 100 hours a week, researching every inch the loan companies of xxx. Because I had confidence on the successful outcome of the merger based on my research, I proposed an additional meeting. In this meeting, I emphasized two factors. First, there is huge possibility for the poor loan of xxx to be transferred into a high grade loan assets within 2~3 years because the Korean economy is getting back on the right track with rapidity out of the IMF regime. Secondly, xxx is relatively vulnerable where xxx is strong in terms of market share. Therefore, xxx has a good chance to revive through the maximization of the synergy effect. The research leaders and executives encouraged by my argument based on comprehensive research decided to take over xxx in the long run. After a year of restructuring, the poor loan has recovered to great extent as I expected. In this context, the merger was considered successful. Throughout the experience, I was able to refine and prove my leadership skills, particularly in leading the participation of my colleagues by suggesting a clear vision for the future based on in-depth research and analysis. I believe that my leadership skills will continue to improve and will in the end enable me to serve as an effective manager in the future. 3. Discuss your career goals and why you want an MBA, particularly at this point in your career. Why, specifically, are you applying to the Anderson School? My long-term career goal is to establish a consulting firm offering integrated services for small to mid-sized companies in Asian countries such as Korea and China. In Korea, they currently accounted for over 60% of national GDP. However, their management skills and business approach are rather unsophisticated. I want to offer them integrated services that would cover major aspects of their needs especially in strategy development and financial infrastructure. I will contribute not only to their growth, but help them attain management expertise to compete with bigger and richer companies. In 19xx, I chose the xxx Company, a high-performing affiliate of the $xx billion of the Korean conglomerate, as my first career step out of college in order to broaden my professional capabilities in corporate finance and to obtain a more comprehensive understanding on the actual business organization. I majored in the field of philosophy in college and volunteered for the ‘Intensive Course on Financial Management’ from xxx after entering the firm in order to develop my inadequate knowledge related to the field of financial affairs. In effect, I completed 6 basic subjects such as Financial Reporting, Financial Statement Analysis and Capital Budgeting in full-time during 4 months. My experiences at the Loan Team and the Credit Analysis Team during the first 3 years provided me with skills in corporate analysis and evaluation, an understanding of corporate financial structure, and a professional knowledge of Korea’s financial industry. During the next one year, I have also gained knowledge on various functions, ranging from corporate vision development to management system control at the Business Administration Team. However, while I have had the hands-on experiences in the real business world, I believe a more structured training to complement my real-world exper iences at this point in my career will enable me to advance into a more sophisticated level of thinking. I am convinced that I will be able to cultivate my consulting foundation through an MBA program. By selecting courses for my major such as management strategy, finance, and entrepreneurship, I intend to establish a solid and fundamental framework of business management knowledge that is essential to a consultant. Aside from gaining theoretical business knowledge from an MBA, I would like to form a long-lasting relationship with my future classmates with whom I can provide help as well as receive support. When I establish my consulting firm, the international networks that would have formed during the MBA courses will help me reach potential clients, share knowledge, join partnerships and exchange our resources. Im very attracted to Anderson School for its well-deserved reputation in entrepreneurship. I learned that Anderson School offers many extracurricular activities for entrepreneurial students through the Harold Price Center of Entrepreneurial Studies. I would like to have chances to advance the theory and practice of entrepreneurship to make my future clients successful. An other reason I apply for Anderson is a wide range of opportunities with reference to geographic advantages of Los Angeles, one of the biggest international cities. I will make vigorous efforts to become a substantial leader in international arena in the upcoming 21st century by developing global business perspectives at Anderson. Upon graduation from the Anderson School, I would like to work for an international consulting company such as McKinsey, BCG or A.T.Kearney as a management consultant in order to develop more diverse experiences before I venture out to set up a consulting company. Based on my current experiences and the potential knowledge obtained at Anderson as well as the professional consulting firms, I will be able to achieve my long-term goal of establishing a consulting company for the small to mid-sized enterprises of Korea and other Asian countries within 10 years to come. 4. Describe your most significant personal accomplishments to date, explaining why you view it as such. My most significant personal achievement was the contribution to the successful establishment of a night school when I was a college student. Because I was interested in minority rights, social injustice and other social issues, I joined the ideology-focused student movements after entering the xxx University. After a while, however, I realized that these movements could not grant real support to those who were suffering from the pain. I changed my personal interest into the solution of the practical social problems. My congenial friends and I tried every effort to find out something we could do in an underprivileged region of Seoul. We soon realized that most of the students in the region, aged 13 to 17, could not attend school at all because they had to earn money to support their families or because of their parent’s objections and disinterest in their children’s education. We decided to offer a more comprehensive educational program in place of regular schooling to provide the essential education in a more personal setting. I was responsible for recruiting more teachers and soliciting donations, while others recruited students and developed various contents of the programs. Owing to two years of our personal sacrifice, this institute named xxx built strong reputation as a secondary educational institution within the community. This night school in which I am participating as a counselor has developed into one of the biggest institutes among the night schools run by college students. I was able to learn leadership and the way to manage an organization by solving a lot of problems originated during the process of establishment and management of the school. I was also able to mature myself in terms of humanity by working together with teen-agers from underprivileged environments. Above all, I am most proud that I was able to serve as an inspiration to the underprivileged people in terms of hope and courage. Student Name Applying for MBA Berkeley -Haas Research Papers on UCLA Graduate School Admission Essay ExamplePersonal Experience with Teen PregnancyBook Review on The Autobiography of Malcolm XThe Relationship Between Delinquency and Drug UseTwilight of the UAWHip-Hop is Art19 Century Society: A Deeply Divided EraThe Effects of Illegal ImmigrationRelationship between Media Coverage and Social andComparison: Letter from Birmingham and CritoPETSTEL analysis of India