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Rearranging an equation and drawing a blank

  1. Feb 28, 2016 #1
    I need to rearrange this equation to solve for b but I can not get it worked out to where my units end up being correct.

    (a-b)=(F*b)/(A*E)
     
  2. jcsd
  3. Feb 28, 2016 #2

    fresh_42

    Staff: Mentor

    Can you retype it with units? Where's your difficulty?
     
  4. Feb 28, 2016 #3
    I end up with b=(AEa)/(F+AE) but A=mm^2 E=N/mm^2 a=mm F=N and b needs to be mm but I am left with the N from F with nothing to cancel it out.
     
  5. Feb 28, 2016 #4

    fresh_42

    Staff: Mentor

    ##unit(b) = \frac{unit(AEa)}{unit(F+AE)}= \frac{unit(A)unit(E)unit(a)}{unit(F)+unit(A)unit(E)}= \frac{mm^2 \cdot \frac{N}{mm^2} \cdot mm}{N + mm^2 \cdot \frac{N}{mm^2}} = \frac{N \cdot mm}{N} = mm##
     
  6. Feb 29, 2016 #5
    I don't understand why the N is still on top. Doesn't A and E both cancel each other out so that all that remains is F and a?
     
  7. Feb 29, 2016 #6

    fresh_42

    Staff: Mentor

    What do you mean by "cancel each other out"? ##unit (A\cdot E) = unit(A) \cdot unit (E) = mm^2 \cdot \frac{N}{mm^2} = N##.

    If you divide by ##AE## first then you'll have ##b = \frac{a}{\frac{F}{AE} + 1}## and therefore $$unit(b) = \frac{unit(a)}{\frac{unit(F)}{unit(AE)}+unit(1)} = \frac{mm}{\frac{N}{mm^2 \cdot \frac{N}{mm^2}}+0} = \frac{mm}{\frac{N}{N}} = \frac{mm}{1} = mm$$.
     
  8. Feb 29, 2016 #7
    Alright thank you that just finally made it sink in. I was looking at it if there is an AE on the top and bottom they would just cancel each other out but the way you laid it out here makes a lot of sense.
     
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