Conditions for Equilibrium Experiment Laboratory Report Tricia Desierto, Luis Diaz, Karhen Estella, Gabrielle Beatrix Francisco Department of Biological Science College of Science, University of Santo TomasEspanÃŒÆ’a, Manila, Philippines Abstract The object is said to be in a state of equilibrium, when the forces acting upon an object are balanced. There were four activities done in the experiment. In the first activity the equilibrant force was determined. The second activity, unknown forces was determined. For the third activity,center of gravity was located. The last activity, rotational equilibrium was demonstrated. I. Introduction Equilibrium is moving with constant velocity. It is a condition that the rotationalÂ motion of the body may also remain constant. A body is in equilibrium or at rest only when there is no movement or rotation done. When the resultant force acting on the object is zero the object is in equilibrium. The objectives of the experiment are: to determine the equilibrant force by using the component and table method;to determine the unknown forces using the first and second conditions for equilibrium; to locate the center of gravity of a composite body;and to demonstrate the rotational equilibrium. II. Theory A situation wherein the net force acting on a certain object is zero and an object that has no motion or undergoes no rotational and traditional accelerationis said to be in a state of equilibrium wherein net torque and net force on the object is zero in all directions. For an object to be in equilibrium, two conditions should be met. The first condition tells us that the net force acting on the object needs to be zero which only means that for a certain axis of motion, the forces acting along that particular axis should sum up to zero.The second condition needed to attain equilibrium, on the other hand, involves avoiding or neglecting accelerated rotation and it should maintain a constantÂ angular velocity. A rotating body can attain equilibrium if the rate of its rotation remains unchanged by the forces acting on that certain object. The center of gravity is a geometric property of any object. It is the average location of theÂ weightÂ of an object. TheÂ motionÂ of any object can be described through space in terms of the translation of the center of gravity of the object from one place to another and the rotation of the object about its center of gravity when it is free to rotate. Figure 1. Determination of the Center of Gravity using plumb line technique X= Center of Gravity m=Mass x= distance from a fixed point Equation 1.Center of Gravity Formula When an object is said to be in equilibrium, it is not moving or rotating. The pivotal axis can be any point outside or inside the object. The objects linear and angular accelerations are both zero and the sum of the torquesacting on a system should be equal to zero.The sum of the counter-clockwise torques should be equal to the sum of the clockwise torques. III. Methodology Activity 1: Equilibrant Force Three pans labelled as A, B and C was weighed. Pans A and B were hanged respectively at the 300 and 2000 marks on the force table. 100g was placed on pan A and 150g on pan B. The tension acting on the string, the weight of the pan plus the weight added to the pan was recorded as TA andTB respectively. The two tensions in the strings were balanced by placing weight on pan C or adjusting its position. The tensions are balanced if the pin is exactly at the center of the ring. The magnitude of the equilibrant, the weight of pan C plus the weight added to it, and its position was recorded. The theoretical equilibrant of the two tensions was determined by component method and the % error was computed. Activity 2: First Condition for Equilibrium A cylinder of unknown weight was suspended using the force board by means of two strings. A spring scale was attached to one of the strings and was pulled horizontally until the pin on the force board was exactly at the middle of the ring. The reading on the spring scale was recorded as T1. The angle that the other string made was recorded as Î¸. A free body diagram of the ring was drawn. The tension of T2 in the other string and the weight of the cylinder were solved. The cylinder was weighed for the accepted value and the % error was computed. Activity 3: Locating the Center of Gravity A circle with a diameter of 10cm and a square with a side of 10cm were cut out from a card board. The weights of WC and WS were determined. The center of gravity of the composite figure was determined by balancing method and plumb line method. The position of the center of gravity was specified using the leftmost side of the square as the y-axis and the bottom square as the x-axis. The results were checked by actual computation for the center of gravity. Activity 4: Second Condition for Equilibrium The center of gravity of an aluminium bar was located by balancing it on a pencil and the position for the center of gravity was marked. The cylinder used in the previous activity was hanged 5.0cm from one end of the bar. Using the force board, the aluminium bar was supported by means of a spring scale on one end and a string on the other end until the bar assumed a horizontal position. A free body diagram of the bar was drawn. The second condition for equilibrium was used to determine the weight of the bar and the tension in the string. The theoretical weight of the cylinder was used in the computation. The bar was weighed for the accepted value and the % error was computed IV. Results and Discussion V. Conclusion The equilibriant force was successfully determined using the component and table method, with an acceptable value for the % error â€“ 8.70% and 4.47%. The unknown forces were also determined using the first condition of equilibrium with a % error of only 4.57% The center of gravity was defined more accurately with the Plumb Line Method as opposed to the Balancing Method. The unknown forces were unsuccessfully defined using the second condition of equilibrium, as the % error exceeds the acceptable range at 51.76%. VI. Applications VII. References Lesson24:Equilibrium. (n.d.). Retrieved December 8, 2013, from studyphysics: http://www.studyphysics.ca/newnotes/20/unit01_kinematicsdynamics/chp06_vectors/lesson24.htm First Condition. (n.d.). Retrieved December 8, 2013, from boundless: https://www.boundless.com/physics/static-equilibrium-elasticity-and-torque/conditions-for-equilibrium/first-condition/ Second Condition. (n.d.). Retrieved December 8, 2013, from Boundless: https://www.boundless.com/physics/static-equilibrium-elasticity-and-torque/conditions-for-equilibrium/second-condition/ Rotational Equilibrium. (n.d.). Retrieved December 8, 2013, from faculty: http://faculty.wwu.edu/vawter/PhysicsNet/Topics/RotationalDynamics/RotEquilibrium.html Benson, T. (2008, July 18). Center of gravity. Retrieved December 8, 2013, from grc: http://www.grc.nasa.gov/WWW/k-12/airplane/cg.html
The Importance of Clothing in Macbeth In Shakespeare's Macbeth, clothing imagery represents the titles that Macbeth wears. Macbeth receives two new titles throughout the play; one is earned and the other stolen. The first, Thane of Cawdor, is rightfully his because he earned it. The second, King of Scotland, is a stolen title that does not fit him honestly. Macbeth's clothing in the play symbolizes both of the titles that he acquires. In the beginning of the play, Macbeth already bears the title Thane of Glamis. After a Norwegian invasion and local rebellion in which Macbeth captures the Thane of Cawdor, Macbeth receives his title. When Macbeth is first hailed Thane of Cawdor by Ross he responds with, "Why do you dress me in borrowed robes?" (Act I, Scene III, Line 116). The "borrowed robes" are that of the previous Thane of Cawdor. Macbeth says this not knowing that Duncan, the King of Scotland, has sentenced the treacherous Thane of Cawdor to death and named Macbeth with his title. Banquo, Macbeth's friend at the time compliments Macbeth on his new title, but at the same time says they do not quite fit him yet. New honors come upon him, Like our strange garments, cleave not to their mold But with the aid of use (Act I, Scene III, Line 161). He is saying that Macbeth is not used to wearing the Thane of Cawdor title because it is such a new feeling. Macbeth does not feel comfortable with the title although he earned it by catching a traitor to the king and to Scotland. &n... ...someone else. This is because they do belong to someone else. They were stolen from Duncan, the "giant" (V, II, 24), by "a dwarfish thief" (V, II, 25), Macbeth. The previous quote gives an image of a small, wicked man taking the rightful position of a large, strong man through treachery and betrayal. Macbeth's robes "hang loose" (V, II, 24) because he is not big enough to fill them up. Throughout the play, Macbeth is seen as a small dishonorable man always wearing clothing that does not belong to him. Whether the clothes are too small or too big, the main point is that they do not fit Macbeth because they do not rightfully belong to him. Shakespeare fills his play with clothing imagery in order to easily show Macbeth's different titles.
Developing countries face severe environmental issues as the rapid economic and population growth had created serious social and environmental problems which if left unattended can bring about very serious consequences. Some of these burning environmental issues faced by these Asian regions are the deforestation, global warming, air and water pollution, limited safe drinking water etc. apart from this manipulation of the natural resources and using unhealthy ways and means for developmental purposes is slowly destroying the resources of these nations which are of serious concern and needs immediate steps by the government and non governmental organizations to protect and rescue them from extinction.
Two main problems that I wish to discuss in this research paper is air pollution and the increasing deficit in drinking water supply which is a great threat to the nations overall economic development. India is a fast developing country and its growth in the IT and industrial sector over the years is abundant. With the per capita income increasing with the sudden boom in industrial and technological sectors purchasing power has increased. Easy EMI and retail option enable almost anyone to get a vehicle and as the result traffic congestion, air pollution and noise pollution etc have increased thereby endangering the whole atmosphere and paving way to global warming.
Water is the elixir of life we all know but although the world is third filled with water drinking water is available in limited quantity. India largely depends on monsoon rains for it agriculture and underground drinking water resources. Due to environmental issues like global warming, air pollution, industrial wastes, use of fertilizers etc result in less rainfall. Moreover the little rainfall received is wasted as it reaches the ocean without any proper preservation methods. The existing dams and water reservoirs are maintained poorly and hence little water collected due to seasonal rains are wasted. Hence an emergency plan to preserve this resource is necessary and steps to minimize air pollution should also be undertaken.
Land usage in India:
Area of the country: 3287260sq.kms
Cultivable area: 1839560sq.kms
Cultivated land area: 1697000sq.kms
Total population 1038056000
Rural: 71%Â Â Â urban â€“ 29%
Internal renewable water: 1260540 million cubic meters
Total renewable water 1907760 million cubic meters
Total withdrawal: 500000 million cubic meters
Irrigation potential: 1135120 sq. kms
Land under irrigation: 501010 sq. kms
Surface irrigation: 493300 sq. kms
Area irrigated with surface water 40.5%
Area irrigated with ground water 53%
( research paper on survey of Indian resources â€“ 2005)
The above facts clearly state the environmental condition of this great nation. The need for ground water for irrigation alone is almost 53% and this ground water level is diminishing today due to lack of rains and improper irrigation methods. The surface water again is becoming polluted because of unhygienic and improper maintenance and preservation methods. Further use of chemicals and pesticides for industry and agriculture has highly polluted both surface and ground water. When agriculture uses highly toxic pesticides it destroys not only the soil but also the water underneath.
Some of the reasons for water scarcity in India are
rising demand for water as population increases over extraction of surface and ground level water delay in completion of developmental projects due to lack of funds and political pressure or instable governments contamination of water resources due to the increased human impact globalization and industrial development polluting air ad water thereby altering urban climate Etc.
There is a huge demand for water in the years to come especially keeping in mind the population the demand seems to be a nightmare.
In almost all parts of India water deficiencies show an increasing trend and the surplus show a decreasing trend Four states and one union territoryÂ have no surplus water The availability of water will reduce one fifth in three decades Government role to curb further water shortage:
From time to time government plays a major part in implementing measures to check this water scarcity. Development projects like building dams, reservoirs, cleaning tanks and increasing awareness to store and use drinking water sensibly is being undertaken. State and central governments join together and use the allotted funds to implement such projects. But political pressure, unstable government and lack of funds create a void in these projects which is either dropped or not put into practice wholly. Moreover bribery in all fields curbs the growth and development of these projects.
Although many NGOâ€™S and non governmental organizations and business establishments try to fund these projects the funds are highly misused or mishandled by faulty politicians. Balanced growth in both agriculture and industry is needed for a countries overall performance and development. But industry is developing in India in a faster pace and it looks like agriculture is neglected. Plans to curb air pollution are needed desperately as it affects the rain and overall climatic condition of the nation. More plants should be planted and forests should be conserved and all measures to save rain water undertaken. Rain water harvesting was seriously implemented in some states and the result is yet to be seen. The roads and the infrastructure is very poor and even the slightest rain causes flash floods. Proper drainage and town planning is missing in cities like Mumbai and Chennai.
Great awareness of the results of such negligence should be spread around and people should be educated as to the affects of global warming and air pollution. Individuals should take this mission in their hands to ensure safety for future generation. Every successful business concern should adopt one area or town to implement development projects like planting trees, cleaning drinking water reservoirs and damâ€™s etc. individuals for their part should maintain hygiene and prevent wastage of water.
Governments should curb the vehicles promotion by making strict laws against easy availability of driving license and fine or punishment if driving unchecked vehicles against air and noise pollution. Industries should be made to dispose their chemicals and smoke safely so as not to pollute the air and water. Strict laws and cancellation of their industrial license should be enacted. If everyone could use water sensibly and avoid polluting substances India would become a super power rich in natural resources and hygiene.
Short term practical solutions:
Keeping the surroundings clean and maintaining a social responsibility to preserve and conserve our natural resources is every individualâ€™s imminent responsibility Creating social awareness of this burning issue among the general public by conducting seminars, student programs and through entertainment to educate even the uneducated and down trodden To keep water bodies clean and check for pollution from nearby factories and industries Proper recycle of industrial wastes Undeterred implementation of government development schemes Strict implementation of anti pollution laws Increasing facilities in public transport and curtailing the use of private transport facilities Planting more trees Long term practical solutions:
general infrastructure of the cities and towns should be properly planned and implemented keeping the long term benefit in mind strict adherence to herbal petrol and enabling gas or pollution free fuel regular pollution control checks in vehicles and factories strict laws against faulty companies which release industrial waste into water bodies building tanks, dams and reservoirs to save the excess rain water from reaching the sea soil promotion and banning chemical pesticides in agriculture organic farming should be encouraged and promoted funds must be set aside for developmental projects awareness for the need for funds should be created among NRI and all steps to utilize these funds properly should be undertaken social organizations, business establishments and individuals should be encouraged to undertake or adopt certain social duties to minimize government pressure Singapore is the worldâ€™s second free economy and second most competitive Asian economy. It is the best connected countries with a robust infrastructure to suit another century or so. Globally connected, top ranking business environment, with stable infrastructure and diverse world class business solutions has made Singapore the top ranked and most preferred business ground. Free trade will definitely enable people from all over the world to throng Singapore but how does it maintain its resources against the growing demand, how is it possible for this small nation to keep its streets and water bodies clean and vehicles free from polluting the atmosphere.
With a total land area of only 699.0 sq. km together with the mainland and other small islands surrounding it has a annual rainfall of about 2,136 mm. the resident population is 4,483,900 and mainly consist of immigrants from neighboring Asian countries like china and India. The literacy rate above 15 years is 95% and the per capita GDP is S$ 44,666. Labor force in this country is 2,367,300 and the unemployment rate is just 3.4%.
( http://www.sedb.com/edb/sg/en_uk/index/why_singapore/singapore_rankings.html )
The country synthesis report on urban air quality management conducted in 2006 clearly states the measures taken by Singapore to prevent or restrict air pollution. The ambient AQ is regularly monitored with the help of 14 air monitoring machines placed across the island of Singapore. This monitoring has aided in the review of pollution control measures and this has given a positive result in controlling air pollution in the country. AQ monitoring methods used are based on the United States Environmental Protection Agency. The offenders were prosecuted and were required to take remedial action.
Since 1971 many laws are set up to maintain clean air focusing much on vehicular pollution and industrialization. The EPCA combines laws for air, water and noise pollution and gives a legislative framework to control pollution of the environment. Lead petrol was stopped and slowly the level of sulfur from diesel was also reduced considerably to control and reduce emission from vehicles.
Ultra low sulfur diesel was introduced to implement euro 4 emission standard and it took effect from October 2006. Air quality in Singapore is the best in the world and it was possible only through strict measures taken by the government to control emission and resolve different forms of pollution. Green plan 2012 is another great step undertaken to further improve the quality of the environment for the years to come.
Highly compatible and well maintained reservoirs catch every drop of rain water and this is utilized by almost half of Singapore uses this water. New projects to build new dams and reservoirs desalination plants, etc are also are being developed. To aid in this mission MEWater is set up which is high quality water received from water reclamation from 2003. Sustainability and cleanliness of water supply and environment is maintained well as Singapore stands tall as a very good example of how we should conserve and preserve our natural resources for a better tomorrow.
It is clearly evident that Singapore has successfully implemented anti pollutant measures and even though its economy is growing fast the infrastructure and the low pollution levels are unchanged. There is enough water to meet all the growing needs and the greenery and the cleanliness stands proof of the people commitment to make their country a higher power standing out and setting an example to all other nations. Asian countries like India and china can take this as an example and with proper coordination with this country try to implement such strict rules in their country too. Finally it is a joint responsibility of both the government and the individuals and they should both commit themselves to make a better, cleaner and pollution free nation not only for us but also to our future generations.
Survey of Indian resources â€“ research paper submitted to the Annamalai Open University. India
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