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Math Help - Rearranging in terms of

  1. #1
    Newbie hymnseeker's Avatar
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    Rearranging in terms of

    A mechanics problem has led me to the following but I have to rearrange in order to find a solution in terms of P.

    Pcos20=(30g-Psin20)

    Where =0.4 and g=9.8

    How do I go about rearranging this? I have been trying for hours and many screwed up pages later I am no closer to making the connection. It is probably really simple.

    Thanks guys.
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  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
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    Hello,

    Quote Originally Posted by hymnseeker View Post
    A mechanics problem has led me to the following but I have to rearrange in order to find a solution in terms of P.

    Pcos20=(30g-Psin20)

    Where =0.4 and g=9.8

    How do I go about rearranging this? I have been trying for hours and many screwed up pages later I am no closer to making the connection. It is probably really simple.

    Thanks guys.
    P \cos 20=\mu (30g-P \sin 20)

    Expanding :

    P \cos 20=30 \mu g-P\cdot(\mu \sin 20)

    Adding both sides by P\cdot(\mu \sin 20) :

    P \cos 20+P\cdot (\mu \sin 20)=30 \mu g

    Factoring :

    P(\cos 20+\mu \sin 20)=30 \mu g


    \implies \boxed{P=\frac{30 \mu g}{\cos 20+\mu \sin 20}}
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  3. #3
    Newbie hymnseeker's Avatar
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    Thank you Moo

    The common factor of P slipped my mind.

    Peace out.
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