Centroid of a Thin Prismatic Plate (3% of final grade) Due: June 8 ...

Centroid of a Thin Prismatic Plate(3% of final grade)Due: June 8, 2011 at 11AM in classItems needed1. Get a foam poster board with from an arts supply store or a superstore. There isan arts supply store on 56 th street between Fowler and Fletcher.2. Get the cheapest plumb bob from a hardware store. There is an ACE Hardwarestore on 56 th street between Fowler and Fletcher. You can share this item withyour classmates.3. Get a couple of feet of a fishing line or some other thin, light, and strong string.You can share this item with your classmates.4. Engineering Graph Paper – Staples or Office Depot. Costs about $12 for a packfor 100-sheet pad.5. Pencil – Anywhere – My favorite store is the 24-hour Wal-Mart Superstore. $1for a dozen.6. Ruler – Anywhere – My favorite store is the 24-hour Wal-Mart Superstore. $1per unit.Experiment:1. Make a plate of your own that is close in shape to what you see in Figure 1. Justbe sure that you do not have more than one value of y for same value of x. Thesize of the plate is up to you.yxFigure 1: Approximate shape of plate

Figure 2 Finding the centroid of an arbitrary prismatic shape.2. See Figure 2 now. Suspend the plate from a location near an edge by making asmall hole near the edge and putting a straight-wire piece from a wire-hangerthrough it, and suspend the plumb line from the wire piece while holding on to thewire piece. The straight-wire should be a little loose in the hole. Drop a plumbline. Mark along the plumb line with a marker.3. Repeat the above step at another location (but not too close to the first).4. The intersection of the two lines is the experimental center of mass of the plate(we consider this to be centroid of the area as well). Record the x-y location of thecentroid.5. Take a picture of the plate with the marked lines and print it out (B&W output isfine).

Exercises to do (counts as 100 points):Follow the sample project guidelines as given athttp://numericalmethods.eng.usf.edu/EML3041/homework/sample_experimental.htmlUse MATLAB to solve Problems (3) through (5). Use comments, display commands andfprintf statements, sensible variable names and units to explain your work. The hardcopy needs to be in published MATLAB format. Staple all the work in the followingsequence. Use the USCS system of units throughout the project.1. Signed, typed affidavit sheet.2. On engineering paper, write down the equations you used to calculate the centroidof the plate area. Write the original data you collected - the y vs. x data forcalculation of the centroid. Attach the hard copy of the picture of the markedplate.3. Put all the recorded input data as MATLAB statements in the beginning of themfile as a separate block. Any changes in the input data should not require one tochange any part of the rest of the program.4. Use MATLAB to calculate the theoretical centroid. Hint: The MATLABcommand trapz does numerical integration of discrete functions.5. Compare the results from #4 via definition of absolute relative true error withwhat you measured.Note: Until you get the grade back, hold on to the foam shape and the MATLABprogram. You may be asked to submit the two items.