# Resolving forces

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• May 13th 2011, 11:22 PM
elieh
Resolving forces
Hey guys,
Question: A mass of 2.6 kg is maintained in equilibrium in a vertical plane by forces of 5P N and 12P N (where P is an unknown constant) which are perpendicular.
5P is at an angle $\displaystyle \alpha$ from the vertical.
Find the value of $\displaystyle \alpha$ and the value of the constant P.

So 12p is at an angle of $\displaystyle 90-\alpha$ from the vertical. (My reasoning)

Resolving vertically I get: $\displaystyle 5p\cos \alpha + 12p\sin \alpha =26$
And horizontally: $\displaystyle 12p\cos \alpha = 5p\sin \alpha$

After that I'm stuck, simultaneous equations I presume.
• May 13th 2011, 11:34 PM
abhishekkgp
Quote:

Originally Posted by elieh
Hey guys,
Question: A mass of 2.6 kg is maintained in equilibrium in a vertical plane by forces of 5P N and 12P N (where P is an unknown constant) which are perpendicular.
5P is at an angle $\displaystyle \alpha$ from the vertical.
Find the value of $\displaystyle \alpha$ and the value of the constant P.

So 12p is at an angle of $\displaystyle 90-\alpha$ from the vertical. (My reasoning)

Resolving vertically I get: $\displaystyle 5p\cos \alpha + 12p\sin \alpha =26$
And horizontally: $\displaystyle 12p\cos \alpha = 5p\sin \alpha$

After that I'm stuck, simultaneous equations I presume.

from the second equation you get the value of $\displaystyle \tan \alpha =12/5$. hence $\displaystyle \sin \alpha=12/13$ and $\displaystyle \cos \alpha = 5/13$ (why?).
substitute in above.
• May 13th 2011, 11:51 PM
elieh
didn't see that!
Thank you!