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Homework Help: Can't use a simple integral properly-must be retarded

  1. Aug 30, 2012 #1
    I will show you my (obviously wrong) way of thinking when i have to apply an integral.
    Please correct me where i'm wrong.

    (imaginary question)
    Suppose you have a mass distribution across a line, where the mass of each point is given by the equation f(x)=a*x (assume a is a constant)
    find the total mass, if the line is c meters long (beggining @ x=0)

    (My stupid train of thought)
    We have to add up all the individual masses on the line.
    so devide the line into n segments, calculate the mass for each one and add them up
    f(x1)+f(x2)+...+f(xn)=
    a*x1+a*x2+...+a*xn=
    a(x1+x2+...+xn)=
    a*c

    What am i doing wrong?
    (Besides the language use, i'm not a native and have little experience in such teminology)
     
  2. jcsd
  3. Aug 30, 2012 #2

    ehild

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    Mass at each point does not have much sense. Is not f(x) the density at point x? Then the mass dm of a line element around x is dm=f(x) dx and you have to integrate from 0 to c.

    If f(x) means the mass from 0 to x, then the total mass at x=c is just f(c) :smile:

    ehild
     
  4. Aug 30, 2012 #3
    Thank you. But how can you define density in segments while you cannot define mass?
     
  5. Aug 30, 2012 #4
    a(x1+x2+...+xn)=
    a*c
    ..........................
    (x1+x2+...+xn)≠c

    x1=0
    xcenter=c/2
    xn=c
     
    Last edited: Aug 30, 2012
  6. Aug 30, 2012 #5

    ehild

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    Homework Helper


    If you have a continuous line the mass of a point of it is zero.
    But you can cut out a small length at position x, and measure the mass: it is Δm, and the length is Δx. The average linear density is Δm/Δx. If you cut out shorter and shorter pieces that ratio tends to the density at point x, to dm/dx = f(x). The total mass is the integral of f(x).

    ehild
     
    Last edited: Aug 30, 2012
  7. Aug 30, 2012 #6
    The linear density at point x, f(x), is the mass per unit length. Think of it as a chain.
     
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