two forces F1 and F2 of magnitudes PN an QN acting in the directions I-2j and 4i+3j respectively. Given that the resultant of F1 and F2 is F, show that P=16 and find Q where F=(48i+14j)N.
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two forces F1 and F2 of magnitudes PN an QN acting in the directions I-2j and 4i+3j respectively. Given that the resultant of F1 and F2 is F, show that P=16 and find Q where F=(48i+14j)N.
Make a sketch, this will greatly help you.
From the sketch, you know that:
Also that:
It's simultaneous equations :)
It doesn't work out to 16. It works out to.
To start with, you have
or
From that, you can just separate into two equations (since i and j are orthogonal to each other, they're linearly independent):
The i terms:
The j terms:
We can solve by elimination by doubling the first equation and adding the two together to get:
Plugging that back into the first equation, we get
Evejack, is there a typo in your question? If F1 points in the (i-2j) direction, there's no way both P and F can simultaneously have rational components.
As I read this question they have given you that P = 16 Newtons of force acting in the direction given by I-2j. Since this sets the direction of the force, P, you get that P is acting at an angle of -63.43 degrees. The angle is found by converting the unit direction vector of I-2j to its polar equalivent, [email protected] degrees. I am assuming no affect for the unit vector here except to give direction, so the P vector would be given as, [email protected] degrees. Then adding the Q vector to this we get a resultant force vector F of 48i+14j = [email protected] degrees. Now if you subtract the two vectors from each other you get:
F - P = Q; (48i+14j) - (7.16i-14.31j) = 40.84i+28.31j = [email protected] degrees = QN
Newton1Law, I agree with your math, but my interpretation of the question is different. To me the question pretty clearly says to show that P=16, not to find Q if P=16. Besides, it's crystal clear that Q is supposed to be in the 4i+3j direction (36.9 degrees if you want to convert to polar coordinates). Your answer for Q is not in that direction. My only conclusion is that the question must be invalid as written.
Yes it had a typo. Thanks the answers are correct. Thanks jcaron2's
yes it is a simultaneous equation. Thanks man.
You're welcome :)
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