A Collection Of My Work Over The Course Of This Semester

Atwood Machine Lab Report

Abstract

The objective of this experiment was to use Atwood’s machine, an apparatus that consists of two composite masses connected by a flexible wire that runs over two ball-bearing pulleys, in order to calculate the acceleration due to gravity, g. The experiment involved varying the mass difference between the two masses in order to allow them to accelerate when set in motion. The following is a scatter plot representing the collected data, which consists of the measured acceleration of masses depending on the varying difference between the two masses. The graph displays the results with an error range for the measured acceleration, and the numerical values of error are displayed in the results section of this report. A line of best fit for this set of data is displayed, along with its equation. The slope of this line is 0.0028, which yields 9.8 m/s2 as the value for the acceleration due to gravity, g, as described by the given formula that the slope of the best-fit line is equal to the value g divided by the sum of the two used masses. This yields a percent error of 0.1% from the accepted value of g, 9.81 m/s2.

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Introduction

Atwood’s machine is an apparatus that consists of two composite masses connected by a flexible wire that runs over two ball-bearing pulleys, and it is shown in the figure at the right. The tensions of the wire on either end of the pulleys are different, and depend on the masses that are hanging on to them. According to Newton’s second law of motion, there is a relationship between force, mass, and acceleration and it is given by the formula Fnet = ma. When we apply this formula to the two masses of Atwood’s machine, two equations can be written to describe the net forces on either side of the pulley. The right side, with mass M1, can be represented by the equation T1-M1g = -M1a.

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The left side, with mass M2, can be described by the equation T2-M2g = M2a. The existence of the tension force in the apparatus causes the two masses to accelerate at a rate different from the acceleration due to gravity. However, the two masses move together, with the same acceleration. Acceleration can also be calculated by the formula s = ½ at2, if we are given the time, t, during which the mass moves through the distance, s. By carefully measuring the acceleration by varying the differences between the two masses, we can figure out what the acceleration due to gravity actually is. If we combine the two formulas and solve them for acceleration, a, we get the formula:

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When we plot the differences in masses against the resulting acceleration of the two masses, and we use a linear, best fit, trend line, the above formula matches with that of the formula of the trend line. The impact of this relationship is that the expression g/(M1+M2) is equal to the slope of the trend line, and we can solve for the acceleration due to gravity, g.

Procedure

I began the experiment with a total mass of 3,500 grams, with 1750 grams on either side of the pulleys. I measured the distance, s, between the top of one of the masses (if it were all the way at the bottom) and the bumper. From the left mass, I moved 10 grams to the right mass, creating a mass difference of 20 g. Then, I lowered the left mass all the way to the bottom of the machine, and timed its rise to the bumper at the top. Using the formula a = 2s/t2, I was able to calculate the acceleration of the two masses. I repeated this process five more times, increasing the difference between the two masses each time.

Results and Analysis

The distance, s, which was measured on my Atwood’s machine, was 1.758 meters. After I gathered all of the mass differences and resulting accelerations, I plotted the data, which resulted in the following graph.

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The following chart shows the numerical values for all of the points represented in the graph, as well as the error for the calculated acceleration, Δa, at each point. Luckily, the error was very small at all of the points.

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The impact of a small error is that when I used the formula given by the graph to calculate the acceleration due to gravity, the result:
g/(M1+M2) = 0.0028 g = 9.8 m/s2
This yields a percent error of 0.1% from the accepted value of g, 9.81 m/s2.

Conclusion

In conclusion, Atwood’s machine has aided in calculating the acceleration due to gravity on a system of masses hanging off a pulley. The results of my experiment were so close that the calculated g came out to 9.8 m/s2, which is very close to the accepted value for the acceleration due to gravity, which is 9.81 m/s2. There is an advantage to moving masses from one side to the other instead of just adding on new masses to one of the sides and this is because you are lightening one side while at the same time increasing the mass on the other side. If the original velocity was not zero, the results for the value of g would have been the same, but the values for acceleration and time would have been different, and thus the y-intercept would have been different, since the entire trend line would have been shifted upwards. If the acceleration of the descending mass were to be equal to the value of g, the tension in the rope would be zero, since the formula T1-M1g = -M1a would turn into T1-M1g = -M1g, and adding M1g to both sides of the equation would cancel it out completely. When I plotted my data the first time, I used a point where the mass difference is 10 grams, and the resulting acceleration is comes out to zero since the masses accelerate for a short distance and then stop completely, because the difference isn’t enough to overcome the friction in the pulley. Plotting this point changes the slope of the best-fit line in a way that causes it to stray from the theoretical value of g. If I had kept the point, the slop of the line would have been 0.0025, and the resulting g would have been 8.75 m/s2, which deviates from the accepted value for acceleration due to gravity by 10.7%.

First Ever Blog

Probably the most stark realization I've made upon entrance to an engineering school is the lack of English, or any recognizable form of communication, for that matter. The Steinmann Hall on the City College campus serves as the Grove School of Engineering headquarters and I've got this to say about it: it wasn't built by good engineers. In fact the building and everything within its vicinity is confusing as hell. Put aside the mislabeled room directions and the hallway entrances that look like janitor's closets, virtually everybody in the building is just plain bad at speaking English and communicating in a common language. While I mean not to discredit their genius, and undoubtedly, hard work, as a former English as a Second Language student I can't help but remember how crippling lacking the language commonly used in an environment is. Unfortunately, in America, as soon we can detect a poor adherence to grammatical convention in either speech or writing, we automatically write those speakers and writers off as disabled. This is something I witness daily as I watch my mother, a brilliant woman, struggle everywhere to express herself in a language that simply isn't one she knows well.

With all of that in consideration, I can only say that I know damn well how important proper communication is in this world, especially for engineers. I major in mechanical engineering. I want to be among the ladies and gentlemen who bring about significant changes in the way that our society uses technology in order to achieve a higher standard of living and a responsible use of our resources. While I was reading the first chapter of our required textbook, Technical Writing for CCNY, I kept reinforcing in my mind how applicable it is to the observations I've made. We often hear from our engineering professors how unimportant things like writing and speech are for engineers. We are told that as long as we know the math, science, and can convince our employers that we are geniuses, then we're set. However, I feel that I'm not particularly inclined to convince anybody that I'm a genius. I wold rather be able to communicate to my employer that I am both capable and competent and as I've mentioned, if I can't write or speak properly, it becomes quite hard to convince them of either.

As an engineer I expect to have to do a lot of technical writing. I expect to write many analytical reports, as I intend to work in the nanotechnology field, which is highly experimental. I expect to do a lot of specification reports, explaining to manufacturers how to build machines and tools that I will have designed. I can only imagine how terribly butchered my end product would be if I didn't give clear, comprehendible instructions of how to build it. In fact, I image a lot of money gets wasted this way, which, as I think of it now, is probably a high opportunity cost for employers who wind up spending their money on writing and speaking tutors instead of on messed up manufactured products.

As I recall the days when I spoke a language foreign to my peers, I am saddened by how difficult it was for me to express my thoughts to them in the classroom. Often becoming unmotivated because of the communication issue, I sat in dunce silence and felt like the stupidest person in the world. Today, I can put my thoughts into coherent words so as to express them to my peers and I intend to adopt the practice of technical writing to my best ability so that I can make both myself, the writer, and the reader feel confident as we go through the analyses, the specification reports, and the instructions.

"Life of Pi Movie" Review

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The engineering profession is often tied to a gray, dull life of mathematics and practicality. Engineers, it often seems, do little more than build structures and programs and have very little concern for anything other than efficiency. Such is not true, however, of the engineers behind blockbusters like the recent eleven Academy Award nominated film “Life of Pi”. The 2012 film is a modern visual masterpiece, made possible with computer generated imagery and the world’s largest self-generating wave tank in film industry history. The engineers behind “Life of Pie” used their skill to create a magnificent oceanic journey and to bring an “unfilmable” book to life.

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“Life of Pi” shares a plot with a New York Times bestseller and winner of Man Booker Prize novel by the same name, written by Yan Martel. It tells the story of an Indian boy who is washed away onto an incredibly journey of discovery and adventure after he becomes the sole human survivor of a shipwreck, on board a small life boat with a fearsome, Bengali tiger. Pi Patel is born and raised in French India and his family owns the animals of a government funded Zoo. When a land dispute with the government causes the family to shut down the Zoo, Pi’s parents must sell off the animals and move away to Canada. On the way there, their freighter succumbs to a powerful storm and sinks, leaving Pi alone on a lifeboat with four animals: a zebra, a chimpanzee, a hyena, and a tiger. The hungry hyena eventually brutally devours both the zebra and the chimpanzee and is, in turn, killed by the tiger, which was hiding in a secret compartment of the boat. Pi and the tiger, nicknamed Richard Parker, become companions on a journey of survival. Richard Parker becomes dependent on Pi for nourishment. Pi becomes dependent on Richard Parker’s companionship because tending to his needs provides him with purpose, and fearing that the tiger might rip him to shreds out of hunger keeps him alert.

Directors of such high caliber as M. Night Shyamalan and Jean-Pierre Jeunet originally deemed the film representation of the novel “unfilmable” and both abandoned the project pre-development. The most daunting aspect of filming “Life of Pie” is story’s prominent aquatic element. It is quite a difficult task to film out in the actual ocean. Mother nature often has her own plans, which can be quite inhibiting and costly. Ang Lee, the Taiwanese-American director who eventually went through with brining the life to “Life of Pi” chose to have a giant wave-generating tank constructed for use in filming the sea adventure.

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The tank took fourth months to develop and is the largest ever made for the film industry. It measured 70 meters long, 30 meters wide and 4 meters deep, with a capacity of 1.7 million gallons, and allowed the filmmakers to generate a range of water textures. The tank was carved into the middle of a Taiwanese airport runway. It even had a movable wall that helped take advantage of the natural sunlight.

Large tank aside, the computer-animated imagery played a crucial role in bringing to life the incredible animals used in the film. Nearly all of the animals used in major shots were created in a visual studio. The only on-set animal was the hyena. Ang Lee stated that he made the decision to have a live animal on set because he felt that the majesty of the real life thing set a standard for the visual animators and served as inspiration to create the surrounding animals to be as realistic and as majestic. Richard Parker was entirely computer-animated, although he did have four stunt doubles for pivotal scenes and reference. The visual effects specialists had to intercut between shots of a real tiger and the CGI tiger, which had never been done before, according to the film’s visual effects supervisor. A team of fifteen specialists worked on the hairs of the tiger, alone.
The film is a great inspiration and a great engineering feat. Perhaps more than any preceding movie, “Life of Pi” has shed an incredible amount of light on the production of a film and on the courage of the engineers and software technicians behind blockbusters. “Life of Pi” earned the 2013 Academy Awards for Best Achievement in Cinematography and Best Achievement in Visual Effects, quite the recognition for a team of engineers. The engineers behind “Life of Pi” are as imaginative and inspirational as the story itself.

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