Register to reply

Statics: two unknown angles and resultant force

by drnoisewater1
Tags: angles, force, resultant, statics, unknown
Share this thread:
drnoisewater1
#1
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
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
djeitnstine
#2
Feb10-09, 12:07 AM
PF Gold
djeitnstine's Avatar
P: 619
How about [tex]tan(\theta)[/tex] does that equal anything?
drnoisewater1
#3
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])]

mplayer
#4
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?


Register to reply

Related Discussions
Statics - Resultant Force Engineering, Comp Sci, & Technology Homework 2
Resultant Vectors with angles and magnitude Introductory Physics Homework 3
How would I find the 2 unknown angles ? :P Introductory Physics Homework 1
HELP This has to do with magnitude, resultant, and angles Please answer Introductory Physics Homework 1
How to get mag. & angles of resultant couple moment Introductory Physics Homework 1