# Rearranging in terms of

• May 20th 2008, 01:54 PM
hymnseeker
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=µ(30g-Psin20)

Where µ=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.
• May 20th 2008, 01:58 PM
Moo
Hello,

Quote:

Originally Posted by hymnseeker
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=µ(30g-Psin20)

Where µ=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.

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

Expanding :

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

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

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

Factoring :

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

$\displaystyle \implies \boxed{P=\frac{30 \mu g}{\cos 20+\mu \sin 20}}$
• May 20th 2008, 02:03 PM
hymnseeker
Thank you Moo :)

The common factor of P slipped my mind.

Peace out.