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.

History of Ice Cream

History of Ice Cream The origins of ice cream can be traced back to at least the 4th century BCE. Early references include the Roman emperor Nero (37-68 CE) who ordered ice to be brought from the mountains and combined with fruit toppings, and King Tang (618-97 CE) of Shang, China who had a method of creating ice and milk concoctions. Ice cream was likely brought from China back to Europe. Over time, recipes for ices, sherbets, and milk ices evolved and served in the fashionable Italian and French royal courts. After the dessert was imported to the United States, it was served by several famous Americans. George Washington and Thomas Jefferson served it to their guests. In 1700, Governor Bladen of Maryland was recorded as having served it to his guests. In 1774, a London caterer named Philip Lenzi announced in a New York newspaper that he would be offering for sale various confections, including ice cream. Dolly Madison served it in 1812. First Ice Cream Parlor in America - Origins of Name The first ice cream parlor in America opened in New York City in 1776. American colonists were the first to use the term ice cream. The name came from the phrase iced cream that was similar to iced tea. The name was later abbreviated to ice cream the name we know today. Methods and Technology Whoever invented the method of using ice mixed with salt to lower and control the temperature of ice cream ingredients during its making provided a major breakthrough in ice cream technology. Also important was the invention of the wooden bucket freezer with rotary paddles, which improved the manufacture of ice cream. Augustus Jackson, a confectioner from Philadelphia, created new recipes for making ice cream in 1832. Nancy Johnson and William Young - Hand-Cranked Freezers In 1846, Nancy Johnson patented a hand-cranked freezer that established the basic method of making ice cream still used today. William Young patented the similar Johnson Patent Ice-Cream Freezer in 1848. Jacob Fussell - Commercial Production In 1851, Jacob Fussell in Baltimore established the first large-scale commercial ice cream plant. Alfred Cralle patented an ice cream mold and scooper used to serve on February 2 1897. Mechanical Refrigeration The treat became both distributable and profitable with the introduction of mechanical refrigeration. The ice cream shop or soda fountain has since become an icon of American culture. Continuous Process Freezer Around 1926, the first commercially successful continuous process freezer for ice cream was invented by Clarence Vogt. The Ice Cream Sundae Historians argue over the originator of the ice cream sundae but three historical probabilities are the most popular Ice Cream Cones The walk-away edible cone made its American debut at the 1904 St. Louis Worlds Fair. Soft Ice Cream British chemists discovered a method of doubling the amount of air in ice cream creating soft ice cream. Eskimo Pie The idea for the Eskimo Pie bar was created by Chris Nelson, an ice cream shop owner from Onawa, Iowa. He thought up the idea in the spring of 1920 after he saw a young customer called Douglas Ressenden having difficulty choosing between ordering an ice cream sandwich and a chocolate bar. Nelson created the solution, a chocolate covered ice cream bar. The first Eskimo Pie chocolate covered ice cream bar on a stick was created in 1934.​ Originally Eskimo Pie was called the I-Scream-Bar. Between 1988 and 1991, Eskimo Pie introduced an aspartame-sweetened, chocolate-covered, frozen dairy dessert bar called the Eskimo Pie No Sugar Added Reduced Fat Ice Cream Bar. Haagen-Dazs Reuben Mattus invented Haagen-Dazs in 1960, He chose the name because it sounded Danish. DoveBar The DoveBar was invented by Leo Stefanos. Good Humor Ice Cream Bar In 1920, Harry Burt invented the Good Humor Ice Cream Bar and patented it in 1923. Burt sold his Good Humor bars from a fleet of white trucks equipped with bells and uniformed drivers.

Is a justified war ethical Essay Example | Topics and Well Written Essays - 1250 words

Is a justified war ethical - Essay Example historians and theologians depict them as holy wars fought to oust Muslim domination and regain control of Christian Holy Lands, while others portray the wars as a series of ruthless and intentional attacks by religious extremists (Guibert). The stance of the Church is that the Crusades were ethically justified. They heavily base their arguments on the ‘Just War Theory’ that was proclaimed by two of the Church’s most celebrated theologians – St. Augustine and St. Thomas Aquinas. The former was a renowned Catholic Bishop and theologian who lived in the 5th Century, author of many books of which ‘City of God’ and ‘Confessions’ are the most famous. He is looked upon as the creator of the Just War Theory. His effect on Christian theology is so immense that his influence persisted from the time of the middle ages up to the current period (Crusade-Encyclopedia). St. Thomas Aquinas was a renowned Catholic priest, philosopher and theologian who lived in the 13th Century. He totally agreed with his 5th Century counterpart’s Just War Theory principles, adding that religious and philosophical truths do not oppose each other, but in fact each one complements the other, as they are nothing but two different sides of the same truth. St. Aquinas went on to add that perception power and thought were required to comprehend the many facets and workings of the Universe (Bbc.co.uk). St. Augustine’s Just War Theory states that in case of defending oneself solely and personally in matters related to life or material possessions, one does not have the right to take the life of another human being. This train of thought follows the abstract idea of Christian charity which proclaims that if struck on the cheek, one should not retaliate likewise but instead exercise restraint and meekly ‘turn the other cheek’ to receive additional punishment. However, when it involved the good and safety of others the above principle ceases to hold relevance and one faces the moral