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Math Help - Complicated Fractions

  1. #1
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    Complicated Fractions

    Hi there, I am new to the forums so I hope I am posting this in the right spot. I am studying Physics but seem to be hitting a roadblock when doing some more complicated fractions. I am sure that once I see it I will understand but would appreciate any help! I will list the two problems I am working on, thanks!

    Problem 1:

    Trying to solve for F_{f}!

    <br />
\frac {1}{P} = \frac {F_{f}}{P_{f}} + \frac {1 - F_{f}}{P_{L}}<br />

    Problem 2:

    Trying to reduce!

    mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0
    Last edited by Raezputin; May 15th 2009 at 09:23 AM. Reason: forgot angle symbol on problem 2
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  2. #2
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    Quote Originally Posted by Raezputin View Post
    Hi there, I am new to the forums so I hope I am posting this in the right spot. I am studying Physics but seem to be hitting a roadblock when doing some more complicated fractions. I am sure that once I see it I will understand but would appreciate any help! I will list the two problems I am working on, thanks!

    Problem 1:

    Trying to solve for F_{f}!

    <br />
\frac {1}{P} = \frac {F_{f}}{P_{f}} + \frac {1 - F_{f}}{P_{L}}<br />

    Problem 2:

    Trying to reduce!

    mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0
    <br />
\frac {1}{P} = \frac {F_{f}}{P_{f}} + \frac {1 - F_{f}}{P_{L}}<br />

    Note that \frac{1-F_f}{P_L} = \frac{1}{P_L} - \frac{F_f}{P_L}

    Subtract \frac{1}{P_L} to both sides and get the same denominator:

    \frac{1}{P} - \frac{1}{P_L} = \frac{P-P_L}{PP_L}

    On the rhs: \frac{F_f}{P_f} - \frac{F_f}{P_L} = \frac{F_fP_L - F_fP_f}{P_fP_L}

    Overall: \frac{P-P_L}{PP_L} = \frac{F_fP_L - F_fP_f}{P_fP_L}

    Factor F_f and solve relatively easily

    --------

    2. mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0

    Let \alpha = \frac {I_{c}}{MR^2} so that

    mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0 becomes mgsin\Theta - \frac {mgsin\Theta}{1 + \alpha} = 0

    Multiply through by 1+\alpha

    mgsin\Theta + \alpha mgsin\Theta - mgsin\Theta =0

    Cancelling: \alpha mgsin\Theta = 0  = \frac {I_{c}}{MR^2}mgsin\Theta=0
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  3. #3
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    Hey e^ thanks for the quick response, only had time to go through the first problem but had a question.

    You said:

    \frac{1}{P} - \frac{1}{P_L} = \frac{P-P_L}{PP_L}

    But with the cross multiplication on the left shouldnt it be

    \frac{1}{P} - \frac{1}{P_L} = \frac{P_L-P}{PP_L}

    The numbers came out correct but had a negative up top which made me look again. Also, after the switch I get the correct answer but the book gives me this as a solution:

    F_F = \frac{1-\frac{P_L}{P}}{1-\frac{P_L}{P_F}}

    Now it doesnt really matter, cause when I run the math I get the same answer, just wondering cause im curious =)

    Thanks for the help!
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  4. #4
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    Question 2:

    Hehe forgot to state that it was equal to a variable that was needed, instead of 0. But the tips you gave me still allowed me to solve on my own! Thanks again e^

    -Raez
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