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Mass Given Density Function and Area

  1. Mar 26, 2016 #1
    1. The problem statement, all variables and given/known data

    A quarter disc of radius 3 cm lies in the first quadrant. The areal density is (1.2 g/cm3)x + (0.7 g/cm3)y. Determine the mass of this object.

    2. Relevant equations

    1_1.png

    3. The attempt at a solution

    For my bounds:
    x: 0 to 3
    y: 0 to Sqrt[3 - x^2]

    2_1.png

    When I took this integral I got 2.07846 + 5.87878 I, which is obviously an imaginary number. Any idea how to get a real number? I'm not sure where I'm going wrong-- I thought this was simple calculus 2.
     
  2. jcsd
  3. Mar 26, 2016 #2
    UPDATE: I have converted to polar coordinates, giving density = 1.2 r Cos[theta]+ 0.7 r Sin[theta]. Then I solved the following integral:

    3_1.png

    This gave me 8.55 g which was incorrect. Where am I going wrong?
     
  4. Mar 26, 2016 #3
    Your bound for y is wrong, draw a diagram with your bounds (e.g. y as a function of x) and you'll see that's not the bounds of a circle quadrant. Hint: the relation is x^2 + y^2 = 3^2
     
  5. Mar 27, 2016 #4

    vela

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    If you check the units of your expression, you'll see that they don't work out. Your mistake is in the area element for polar coordinates.
     
  6. Mar 27, 2016 #5
    UPDATE NO. 2:

    I figured it out.

    they.png
     
  7. Mar 27, 2016 #6
    Thank you everyone for your help :)
     
  8. Mar 27, 2016 #7

    vela

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    You stumbled onto the correct answer, but your work isn't correct.
     
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