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Issue with math in physics problem?

  1. Sep 9, 2014 #1
    Ok so for the problem i'm mainly having trouble with setting up one of the equations.
    The solutions manual jumped from:
    ωiz([(2/5mERE2)/(2/5mERE2) + (2/3mdebrisRE2)]-1)
    to:
    ωiz([mE/(mE + (5/3mdebris))]-1)

    I placed the brackets to clearly separate the fraction from the -1. Anyways i'm having trouble seeing how the math is done to get from the first equation to the second equation, how was it simplified? If anyone is confused on how i wrote the problem please just ask! Thanks!
     
  2. jcsd
  3. Sep 9, 2014 #2

    Mark44

    Staff: Mentor

    These aren't equations - they are expressions.

    Inside the parentheses you have (2/5mERE2)/(2/5mERE2), which is just 1.

    The fractions you wrote are ambiguous, which doesn't change what I wrote above.
    Is the numerator ##\frac{2}{5}m_ER_E^2##
    or is it ##\frac{2}{5m_ER_E^2}##?
     
  4. Sep 9, 2014 #3
    The numerator is ##\frac{2}{5}m_ER_E^2##. I get that ##\frac{2}{5}m_ER_E^2##/##\frac{2}{5}m_ER_E^2## is equal to 1, im mainly confused on how (2/3mdebrisRE2) became (5/3mdebris) or if the manual made a mistake.
     
  5. Sep 9, 2014 #4
    If you put an extra set of parentheses in the original expression, the ##R_E^2##s cancel and you can multiply everything by ##\frac{5}{2}## to get $$\frac{\frac{2}{5}m_ER_E^2}{\frac{2}{5}m_ER_E^2+\frac{2}{3}m_{\text{debris}} R_E^2}=\frac{m_E}{m_E+\frac{5}{3}m_{\text{debris}}}$$
     
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