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Statics: two unknown angles and resultant force

by drnoisewater1
Tags: angles, force, resultant, statics, unknown
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Feb9-09, 11:28 PM
P: 2
1. The problem statement, all variables and given/known data

Two forces P and Q with respective magnitudes 100N and 200N are applied to the upper corner of a crate. The sum of the two forces is to the right (+x direction) with a magnitude of 250N. Find the angles that P and Q make with their sum - that is, with the horizontal line through +x axis.

2. Relevant equations

R = P + Q where R is the resultant vector and P and Q are vectors given in the problem

Rx = Px + Qx = 250

Ry = Py + Qy = 0

3. The attempt at a solution

All the information is given except the two angles. Plugging in the given values gives me the equation:

[tex]\Sigma[/tex]Rx = 100cos([tex]\theta[/tex]) + 200cos([tex]\phi[/tex]) = 250N

[tex]\Sigma[/tex]Ry = 100sin([tex]\theta[/tex]) - 200sin([tex]\phi[/tex]) = 0

where theta is the angle between P and R and phi is the angle between Q and R.

Basically this comes down to confusion on algebra for me. I attempted substitution and that got me nowhere. I know there is some kind of trick to solving this, but I cannot figure it out. There are two equations and two unknowns so there must be a way to do it. I have worked a similar problem where one of the angles is known and the other was supposed to be at a maximum and calculus could be used there. Is that a possibility in this problem or is there just a little trick that I am missing?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
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Feb10-09, 12:07 AM
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djeitnstine's Avatar
P: 619
How about [tex]tan(\theta)[/tex] does that equal anything?
Feb10-09, 12:20 AM
P: 2
I tried that, but still had phi in the expression.

Rx: sin([tex]\theta[/tex]) = 2sin([tex]\phi[/tex])

Ry: 2.5 - 2cos([tex]\phi[/tex])

I thought that since magnitude of R is sqrt[Rx^2 + Ry^2] = 250 things might cancel out. Well all the angles canceled out so i just got an incorrect expression.

I tried Ry/Rx just for fun, to get a tan expression and that was not beneficial because nothing canceled out there either. I just thought about this though: if you take tan inverse of Ry/Rx the resultant angle will be 0 since the resultant is about the x-axis. However, that means little as I don't know if you can evaluate arctan[0.8sin[tex]\phi[/tex]) - tan([tex]\phi[/tex])]

Feb10-09, 01:12 AM
P: 154
Statics: two unknown angles and resultant force

Since vectors add head-to-tail, could you maybe draw a force triangle with P, Q, and R and find the angles that way?

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