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
Bees able to spot which flowers offer best rewards before landing
Classic Lewis Carroll character inspires new ecological model
When cooperation counts: Researchers find sperm benefit from grouping together in mice
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