# Two forces; 2d rigid body, only one resultant known

1. Oct 15, 2011

### togo

1. The problem statement, all variables and given/known data

Two forces P and Q are applied as shown to the corners A and B of a square plate. Determine their magnitudes P and Q and the angle (weird B) knowing that their resultant R has a magnitude R = 120 N and a line of action passing through O and forming an angle of 30 degeres with the x axis.

2. Relevant equations
3. The attempt at a solution

(R = 120 N @ 30 degrees) = sqrt ( (Px+Qx)^2 + (Py+Qy)^2) )

I could go further on that but know that somehow a moment is involved here and don't know how to place it. Thanks.

2. Oct 15, 2011

### togo

dunno what else to say

Last edited: Oct 15, 2011
3. Oct 15, 2011

### phinds

I must be missing something 'cause it seems to me that you don't have enough information to get an answer. I'm ASSUMING here that the goal is to get NUMERIC answers, yes?

The alternative would be a pair of equations as a function of length a --- do you reckon that's what's wanted? I don't even see how you could do that. It seems to me that "a" is irrelevant, but again, I may be missing something.

EDIT: OOPS --- I think what I'm missing is that, as you said, there's a moment involved (2 of them of course) and I don't know how to handle it either. I STILL think you don't have enough info to get a numeric answer.

Last edited: Oct 15, 2011
4. Oct 15, 2011

### togo

It should be possible, you shouldn't need to know 'a', you can assume 'a' is one.

whether it needs moments or not I assume it does since its in a moment chapter, but once of those forces is perpendicular to the line of action and the other at an angle and this must be possible to do somehow.

You could have one force pulling on the top and nothing at the bottom, the resultant and angle would be below the horizontal.

You could have one force pulling at slight angle on the right and almost none on the top, with a similar result.

a specific combination of forces on top and on the side would produce the given result and I am positive that an equation would solve it. Also the amount of pounds should be available too. You can't come up with arbitrary answers for this one.

5. Oct 16, 2011

### togo

please help. I had a meeting with the man in charge of our department at college and he doesn't think I can get through this but I fought tooth and nail to get in.

I am desperate to pass this course and in fact do well in it

desperate and determined, I'm paying someone in 3rd year for all his tests for whatever advantage comes out of it.

6. Oct 16, 2011

### phinds

Well my first approach was to simply take the two given vectors, put them at the origin, and put the resultant at the origin as the diagonal of the parallelagram created by the other two and then try to solve for the other two.

I can't get very far w/ that approach, so I assume I'm missing something, and how the moment works seems to be the only thing I can think of.

I just can't see any way you can get numeric answers out of this. IS that what's being called for? You didn't answer me when I asked that the first time.

7. Oct 16, 2011

### togo

P = 60 N, Q = 74.4 N, B = 53.8 degrees

8. Oct 16, 2011

### phinds

Did you get that or is that the answer from the back of the book?

EDIT: I checked and that definitely rules out a simple vector solution since those answers are not consistent with one, so there HAS to be something else (like a moment) involved.

9. Oct 16, 2011

### togo

from the back of the book. the book was in my car and i didnt have the answer till this morning.

10. Oct 16, 2011

### phinds

Well, as I said, it's not a simple vector solution, so I'm at a loss. Don't know why some knowledgeable ME hasn't jumped in here. It's probably not hard once you know WHAT to do.