Need help understanding this

C

Comet

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Jun 30, 2022
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I have basically solved this entire problem, however, someone I know keeps telling me that I shouldn't have added the 180 to the angle that I found. In my mind it doesn't make sense, because in order to face the 3rd force force away from the others, I would need it to be in the range of 180.
Am I doing it wrong?
 

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Comet said:
I have basically solved this entire problem, however, someone I know keeps telling me that I shouldn't have added the 180 to the angle that I found. In my mind it doesn't make sense, because in order to face the 3rd force force away from the others, I would need it to be in the range of 180.
Am I doing it wrong?
Click to expand...
Are we to assume angles are measured in standard position, so that your answer is what I drew in red here?

1656624615328.png

Then you're clearly right to add 180 to the resultant of the two forces, which I drew in blue, to obtain the opposite vector.

What reason did this person give for his advice? (If there's no reason given, then there's no reason to believe him; but there are other ways to solve the problem that would not require that step -- and would give your answer.)

For confirmation, here is a scale drawing:

1656625114328.png
 
I asked a couple people I knew to check whether or not I was right in the way I was solving this problem, because I am quite new to calculus. He was the only one to say that I was wrong in adding the 180°, but he was very insistent that he was right.

I thank you for helping me with this, I feel a bit more confident in myself after seeing this.
 
It is clear that the resultant given force would be in quadrant 1. Dr Peterson showed this visually by completing the parallelogram.
The problem stated that the sum of the three forces equals 0. That is, F1 + F2 + F3 = 0 or F3 = -(F1 + F2). That is F3 is in the opposite direction of F1 + F2 and has the same magnitude of F1 + F2. That is in quadrant IV!

If all the (non zero) forces are in quadrant I, then ask your friend how the forces can possibly sum to zero.

I'm glad that you now have more confidence!
 
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