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Project Number 1

Newton’s Law of Cooling

The topic for the project is Newton’s Law of Cooling, although you may select a different title. The purpose is to research how the temperature of a hot object is lost when it is kept in a cooler environment. You would needed to use your mathematical skills, like linear regression and knowledge of exponential functions. You would also be designing an experiment to determine how water cools down from its boiling temperature. The project is also a good introduction on how to prepare a professional report which you will be faced with in your career. You must take care to make sure that all spelling and punctuation is correct and that the overall look of the report is polished and clean.

The report must consist of the following components:

1. A cover page. Include the Student Name, Course Code, Title and Date. Your cover page is the first thing the reader sees so it may be a good idea to add graphics to the page to draw attention to your report.

2. Introduction to the topic. Research the topic of Newton’s Law of Cooling. prepare the mathematical form of the law and describe its physical meaning. Try to justify the law using common sense and exs from all around you. Does Newton’s Law of Cooling apply to convection, radiation, etc.? Briefly describe how, using Newton’s Law of cooling, you may prepare the temperature of a cooling body as an exponential function of time. Is Newton’s Law of Cooling still widely accepted? Are there any substitutes?

3. Description of the problem. Describe in detail how you will like to measure the rate of loss of temperature of water using an experimental set up. The experiment should be used to gather data for the temperature water versus time, as it cools down from its boiling point.  Your descriptions and diagrams should be clear enough that someone new to the subject would be able to read your paper. One good measure of completeness is to ask yourself if you would be able to understand the equation by reading your description and studying your diagram. In other words your description should be a clear, self-contained exposition of the topic, much like one that you could find in the textbook on a given topic.

4. Description of the steps involved in solving the problem. Give a detailed description of the experiment and collecting the data. Mention that at least 15 data points must be collected on almost equal time intervals before the water reaches the environment temperature.

5. A detailed solutions. Make a table of all of data you have gathered. Plot these data. What type of function do you expect to see? Describe how using linear regression you could find the rate of loss of temperature for water. Apply this method, using Excel or other software, to your data and evaluate the numerical value of the rate of loss of temperature. Once done with that, prepare down the equation for the temperature of water versus time. Plot this equation and all of the data points on the same graph, and comment on the discrepancies you observe.

6. Conclusion and analysis of the results. prepare a conclusion which highlights the key points of interest in your project and ties together some of the most interesting points you have covered.

7. Bibliography of all cited sources. The web site
http://www.library.mun.ca/guides/howto/apa.php

Outlines the format of a standard APA style bibliography, please follow this format.

Project Number 2

Heat loss in a Cylindrical Pipe

The topic for the project is Heat Loss in a Cylindrical Pipe, although you may select a different title. The purpose is to research a variety of pipes of different sizes made of different material, and a variety of insulators available in the market, and look at different combination which are economically feasible. The project is also a good introduction on how to prepare a professional report which you will be faced with in your career; you must take care to make sure that all spelling and punctuation is correct and that the overall look of the report is polished and clean.

The report must consist of the following components:

1. A cover page. Include the Student Name, Course Code, Title and Date. Your cover page is the first thing the reader sees so it may be a good idea to add graphics to the page to draw attention to your report.

2. Introduction to the topic. Research the topic of heat loss in a cylindrical pipe. Describe which laws of physics are used to discuss heat loss in a pipe, and briefly describe how the famous equation for the loss of heat in a cylindrical pipe is derived. Describe the different variables and parameters involved, together with their appropriate units.

3. Description of the problem. Describe that your intention is to investigate a variety of combinations of pipe material, insulation material and size which you can potentially consider when deciding on pipeline system for a house. What other factors must be considered? What are the typical combinations that people use in Brampton? Is this different from what you find for other countries? If so, what are the reasons behind this difference? Your descriptions and diagrams should be clear enough that someone new to the subject could be able to read your paper and understand it. One good measure of completeness is to ask yourself if you would be able to understand the paper by reading your descriptions. In other words your description should be a clear, self-contained exposition of the topic, much like one that you could find in the textbook on a given topic.

4. Description of the steps involved in solving the problem. Outline in clear terms how you would find the necessary information, and how you will analyze, categorize and display the information you have gathered.

5. A detailed solutions. List all the relevant types of pipes, insulators and sizes you have researched. Based on this information, find out the heat loss per meter for each of the combinations you can figure out. Summarize the result in a graphical way, like a table, such that they are easy to read and understand. Describe whether you’re finding for the best combination, which leads to the least loss of heat, matches what people use in your community. If not, elaborate on this. You might use a simple code to get the data and find all the heat losses for you.

6. Conclusion and analysis of the results. prepare a conclusion which highlights the key points of interest in your project and ties together some of the most interesting points you have covered.

7. Bibliography of all cited sources. The web site
http://www.library.mun.ca/guides/howto/apa.php

Outlines the format of a standard APA style bibliography, please follow this format.

Project Number 3

Elliptical Paths of Celestial Bodies

The topic for the project is Elliptical Paths Of Celestial Bodies although you may choose a different title. The aim is to research ellipses in the context of eccentricities and to use the eccentricities and lengths of the semimajor axis of the planets and Halley’s Comet to graph the elliptical orbits of each of these celestial bodies.

Although Pluto is no longer officially considered a planet please consider this body as well. The project is also a good introduction on how to prepare a professional report which you will be faced with in your career, you should take care to ensure that all spelling and punctuation is correct and that the overall look of the report is polished and clean.

The report must consist of the following components:

1. A cover page. Include the Student Name, Course Code, Title and Date. Your cover page is the first thing the reader sees so it may be a good idea to add graphics to the page to draw attention to your report.

2. Introduction to the topic. Research the topic of eccentricities of conic sections focusing on describing ellipses using eccentricities. Outline how ellipses are related to the orbital paths of the planets and Halley’s comet (a search on Kepler may be very useful here). Briefly outline the key historical figures involved in modelling the paths of the planets and describe a time line of the discoveries. What are some interesting or surprising results discovered by these scientists that will peak the readers interest in your paper?

3. Description of the problem. Create a detailed diagram to describe the equation of an ellipse in terms of its eccentricity and indicate how the foci and major and minor semi-axes are involved. Your descriptions and diagrams should be clear enough that someone new to the subject will be able to read your paper and understand the equation. One good measure of completeness is to ask yourself if you will be able to understand the equation by reading your description and studying your diagram. In other words your description should be a clear, self-contained exposition of the topic, much like one that you could find in the textbook on a given topic.

4. Description of the steps involved in solving the problem. Outline in clear terms how the equation of an ellipse relates to the orbital paths of the planets and Halley’s comet. Detail the information you will need to find in order to create graphs of each of the orbits.

5. A detailed solution. Name all the significant figures needed for graphing each of the orbital paths in a table with the equation of each path. Create a high quality, scaled and labelled plot with each path on a single set of axes using either AutoCAD or if you do not have access to AutoCAD create the plot using another program such as the open source FreeCAD or Dessault’s free Draft Sight program which is an excellent AutoCAD clone.

6. Conclusion and analysis of the results. prepare a conclusion which highlights the key points of interest in your project and ties together some of the most interesting points you have covered.

7. Bibliography of all cited sources. The web site
http://www.library.mun.ca/guides/howto/apa.php

Outlines the format of a standard APA style bibliography, please follow this format.

Project Number 4

Complex Variables and RLC Circuits

The topic for the project is Complex Variables and RLC Circuits, although you may choose a different title. The purpose is to research how complex numbers facilitate some of the calculations in circuit theory. The analysis of several circuits could be summarized in a unified language, that is, the tool of complex variables. The aim of the project is to shed some light on that. The project is also a good introduction on how to prepare a professional report that you will be faced with in your career, you must take care to make sure that all spelling and punctuation is correct and that the overall look of the report is polished and clean.

The report must consist of the following components:

1. A cover page. Include the Student Name, Course Code, Title and Date. Your cover page is the first thing the reader sees so it may be a good idea to add graphics to the page to draw attention to your report.

2. Introduction to the topic. Research the topic of RLC circuits with AC sources. Describe what is given in a general problem involving a circuit and what is asked for. Describe the terms which comprise an RLC circuit, with appropriate diagrams and details of the functions of each component, such as resistor, etc. Briefly outline the key historical figures involved in modelling the RLC circuits with AC currents, and describe ho and how the use of complex variables in started circuit analysis for the first time.

3. Description of the problem. State clearly that the current in an RLC circuit with an AC source with and without the use of complex variables. And that the purpose of your project is comparing the advantages and disadvantages of these approaches. Your descriptions and diagrams should be clear enough that someone new to the subject would be able to read your paper and understand the equation. One good measure of completeness is to ask yourself if you would be able to understand the equation by reading your description and studying your diagram. In other words your description should be a clear, self-contained exposition of the topic, much like one that you could find in the textbook on a given topic.

4. Description of the steps involved in solving the problem. Outline in clear terms the steps you will take relate the solution of the problem of finding currents in an RLC circuit with and without using complex variables.

5. A detailed solutions. Using physical principles, describe how the current is obtained in an RLC circuit with an AC source. Describe how the phase difference between the current and voltage is obtained without use of complex variables. Support your theoretical statements with an ex. Describe how the same general problem could be solved using complex variables. Demonstrate that in both cases one obtains the same results.

6. Conclusion and analysis of the results. prepare the conclusion which highlights the key points of interest in your project and ties together some of the most interesting points you have covered.

7. Bibliography of all cited sources. The web site
http://www.library.mun.ca/guides/howto/apa.php

Outlines the format of a standard APA style bibliography, please follow this format.

Project Number 5

Automotive Cruise Control System

The topic for the project is to design an Automotive Cruise Control System although you may choose a different title for your report. The aim is to research cruise control systems and the practical considerations involved in implementing a cruise control system in a vehicle. Essentially you will be designing a cruise control system of your own and facing some of the challenges that an automotive designer would encounter. The project is also a good introduction on how to prepare a professional report which you will be faced with in your career, you must take care to make sure that all spelling and punctuation is correct and that the overall look of the report is polished and clean.
The report must consist of the following components:

1. A cover page. Include the Student Name, Course Code, Title and Date. Your cover page is the first thing the reader sees so it may be a good idea to add graphics to the page to draw attention to your report.

2. Introduction to the topic. Research the topic of cruise control systems in a historical context and identify the complex mechanical and electrical hardware involved in implementing such a system. What are some of the difficulties that terrain, weather, safety and congested driving conditions introduce? What are some of the interesting modern developments in cruise control systems that contrast with comparatively basic old systems that may grab your reader’s interest?

3. Description of the problem. describe the cruise control system which you intend to implement along with the features you will like to include. What would set your system apart from other systems on the market and why will your system be preferred? Would your system be designed for high end vehicles or will it focus on economic applications?

4. Description of the steps involved in solving the problem. Recognize the physical hardware and electronic or mechanical control devices that your system would include such as cameras and electronic throttle controls. What steps will required to be taken to take your proposition to production. What would be the most cost and time intensive components to design and manufacture, will any of the components be available as off-the-shelf products or will they need to be designed from the ground up?

5. A detailed solutions. Create a detailed table of all the inputs and outputs your system would include along with the physical devices which will be needed by each input and output, feel free to add other fields like cost, supplier, and quantity. Make a complete and aesthetically appealing flowchart which details your systems operation, include graphics which will convince your boss, investor, or client that your system is the best choice.
How would your system handle the logic involved in combining all of the inputs to produce a safe and predictable way of controlling the vehicle? Would you be able to make use of any mathematical functions or methods when you are processing the logic?

6. Conclusion and analysis of the results. prepare the conclusion which highlights the key points of interest in the project and ties together some of the most interesting features you intend to include.

7. Bibliography of all cited sources. The web site
http://www.library.mun.ca/guides/howto/apa.php

Outlines the format of a standard APA style bibliography, please follow this format.

Project Number 6

Rotating Biological Contactor (RBC) Model

The topic for the project is to study and carry out calculation in Rotating Biological Contactor although you might select a different title for your report. The purpose is to research how the RBC could be used in wastewater treatment In wastewater treatment, rotating biological contactors (RBCs) are used in small scale industrial and municipal treatment facilities to remove pollutants. The RBCs are made up of a series of round discs that are covered (on both sides) with microbes which consume the pollutants as food. Discs are mounted on a shaft that rotates so that the microbes are submerged in the wastewater and then are exposed to oxygen in the atmosphere above. The shaft is 0.4m in diameter and goes through the center of all the discs and is powered by a motor. As per the drawings below, 40% of the discs Area is submerged in the wastewater. Suppose you are designing an RBC and based on the space you have available, each disc will be 3 m in diameter and 5 cm thick. There will be 20 discs in each module (shown in Side View below) and you will have 5 modules in parallel, sitting inside a rectangular tank. This project is also a good introduction on how to prepare a professional report which you will be faced with in your career; you should take care to ensure that all spelling and punctuation is correct and that the overall look of the report is polished and clean.

The report must consist of the following components:

1. A cover page. Include the Student Name, Course Code, Title and Date. Your cover page is the first thing the reader sees so it may be a good idea to add graphics to the page to draw attention to the report.

2. Introduction to the topic. Research the topic of RBC model and role of bacteria in degradation and producing useful products from waste. describe how this can be environmentally important

3. Description of the problem. describe all mechanism and steps involving in RBC model also suppose the 40% of area submerged in the waste water at any time what percentage of radius is submerged in the pollutant? What is the total surface area (in m2) that your microbes would cover? If disc revolve with speed of 2 rev /minute determine the contaminated area after 15 sec Let suppose the bacteria will growth exponentially on the surface of disc with 2 CFU “Colony forming unit” per day if in each rotation we have CFU per area unit attachment, find the total bacteria per unit area after 2 days

4. Description of the steps involved in solving problem. Recognize that how you dealing with solving problems in each part especially a nonlinear equation arising in part 1. describe output of system and measure the amount of produces substance, how you can define efficiency in this model ?

5. A detailed solutions. Create a detailed solution of all described problems at 3.

6. Conclusion and analysis of the results. prepare the conclusion which highlights the major points of interest in the project and ties together some of the most interesting features you intend to include.

7. Bibliography of all cited sources. The web site
http://www.library.mun.ca/guides/howto/apa.php

Outlines the format of a standard APA style bibliography, please follow this format.

• Category:- Math
• Reference No.:- M91417

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