You want to design a solar collector that will concentrate the sun's rays at a point....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
You want to design a solar collector that will concentrate the sun's rays at a point. By symmetry this surface will have a shape that is a surface of revolution obtained by revolving a curve about an axis. Let's call this the x-axis and the rays parallel to this axis are focused at the origin. We will use differential equations to derive the equation for the curve. A cross section of the solar collector showing the curve is pictured: 1. The law of reflection says that the angles y and 8 are equal. Use this and geometry to show that 3 = 20. 2. The slope of the tangent line to the curve at point (r.y) is given by = tano. We can see from the diagram that y/z= tan 3. Show that 2dy/dz 1-(dy/dr) Useful trig identities are sin(28) = 2 sin cos 8 and cos(28) = cos 6-sin²8. 3. Solve for dy/dr to find a differential equation whose solution is the curve defining the cross section of the solar collector. 4. Show that the differential equation you found is a homogeneous equation (Section 2.6). Use an appropriate variable substitution to find a separable equation. 5. Use technology to find a general solution to the differential equation and graph a few curves from the one parameter family of solutions. Attach your work (with a staple and your name!) to this worksheet. 6. Extra Credit: Use technology (or great artistic skills) to draw a 3D representation of the solar collector surface. You want to design a solar collector that will concentrate the sun's rays at a point. By symmetry this surface will have a shape that is a surface of revolution obtained by revolving a curve about an axis. Let's call this the x-axis and the rays parallel to this axis are focused at the origin. We will use differential equations to derive the equation for the curve. A cross section of the solar collector showing the curve is pictured: 1. The law of reflection says that the angles y and 8 are equal. Use this and geometry to show that 3 = 20. 2. The slope of the tangent line to the curve at point (r.y) is given by = tano. We can see from the diagram that y/z= tan 3. Show that 2dy/dz 1-(dy/dr) Useful trig identities are sin(28) = 2 sin cos 8 and cos(28) = cos 6-sin²8. 3. Solve for dy/dr to find a differential equation whose solution is the curve defining the cross section of the solar collector. 4. Show that the differential equation you found is a homogeneous equation (Section 2.6). Use an appropriate variable substitution to find a separable equation. 5. Use technology to find a general solution to the differential equation and graph a few curves from the one parameter family of solutions. Attach your work (with a staple and your name!) to this worksheet. 6. Extra Credit: Use technology (or great artistic skills) to draw a 3D representation of the solar collector surface.
Expert Answer:
Answer rating: 100% (QA)
plz like the solution Solution Given xy unknown curve su... View the full answer
Related Book For
Essentials of Materials Science and Engineering
ISBN: 978-1111576851
3rd edition
Authors: Donald R. Askeland, Wendelin J. Wright
Posted Date:
Students also viewed these physics questions
-
You want to design a small remotely operated power tool and expects it to require 100 W and weigh not more than 1 kg. You plan to use it continuously for 1 hour. You have to decide whether to use a...
-
You want to design a large, permanent space station so that no artificial gravity is necessary. You decide to shape it like a large coffee can of radius 223 m and rotate it about its central axis....
-
You want to design a spy satellite to photograph license plate number. Assuming it is necessary to resolve points separated by 5 cm with 550-nm light, and that the satellite orbits at a height of 130...
-
Assume that a trader in HSBS has bought EUR 10,000,000 on Feb 03, 2020. Estimate one day VAR with a 95% confidence interval for the FX position with the Historical Simulation approach. Compose some...
-
The net income (after income tax) of McCants Inc. was $2 per common share in the latest year and $6 per common share for the preceding year. At the beginning of the latest year, the number of shares...
-
Devon is considering taking out a $7,000 loan. He went to two banks. Stevenson Trust Company offered him an 8-year loan with an interest rate of 8.6%. First National Bank offered him a 5-year loan...
-
What are the page limitations for memorandum of points and authorities?
-
Parker is a 100% shareholder of Johnson Corp. (an S corporation). At the beginning of 2010, Parkers basis in his Johnson Corp. stock was $14,000. During 2010, Parker loaned $20,000 to Johnson Corp....
-
Explain the procedure to test resistance and current flow of charging system circuits
-
The comparative financial statements of Marshall Inc. are as follows. The market price of Marshall common stock was $82.60 on December 31, 20Y2. Question not attempted. Determine the following...
-
Twenty sculptors were asked to produce molds of a model using a different medium for each one. The options are: having the model present at the session, using a photograph, and seeing the model, but...
-
Define the term statistics. What are the two basic types of statistics? Describe them and give examples.
-
Briefly explain why learning statistical inference is important for students of business and economics. Give two examples.
-
The most commonly reported indicator of stock market performance is the Dow Jones Industrial Average. Explain whether the firms whose share price are included in the DJIA represent a sample or a...
-
When a cosmetic manufacturer tests the market to determine how many women will buy eyeliner that has been tested for safety without subjecting animals to injury, is it involved in a descriptive...
-
Explain the difference between deductive and inductive statistics. Illustrate your answer with examples taken from everyday life.
-
The Blank______ view of stakeholder management views the management process as groups competing for the organization's resources. corporate governance symbiosis stakeholder claims zero sum
-
From 1970 to 1990, Sri Lanka's population grew by approximately 2.2 million persons every five years. The population in 1970 was 12.2 million people.What is the best formula for P, Sri Lanka's...
-
Cooling curves are obtained for a series of Cu-Ag alloys (Figure 11-33). Use this data to produce the Cu-Ag phase diagram. The maximum solubility of Ag in Cu is % and the maximum solubility of Cu in...
-
How many grams of aluminum, with a dislocation density of 1010 cm/cm3, are required to give a total dislocation length that would stretch from New York City to Los Angeles (3000 miles)?
-
What are the Miller indices of the slip planes in FCC unit cells that include the [101] slip direction?
-
What is the general reporting format on financial statements prepared in accordance with a comprehensive basis of accounting other than generally accepted accounting principles?
-
What is negative assurance within the context of an auditor's report? How does it differ from positive assurance?
-
What body establishes standards for a. All audits and for reviews of interim financial information and preparation of unaudited financial statements of public companies? b. Reviews and compilations...
Study smarter with the SolutionInn App