Vectors - Resultant

ssb

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Apr 23, 2014
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Find the resultant of each pair of forces acting on an object

Q: forces of 6 N southwest and 8 N northwest

I got 10 for the resultant, but how do I find the angle?

The answer is apparently is 10 N, N82degW

Having a hard time visualizing this...
 
Find the resultant of each pair of forces acting on an object

Q: forces of 6 N southwest and 8 N northwest

I got 10 for the resultant, but how do I find the angle?

The answer is apparently is 10 N, N82degW

Having a hard time visualizing this...

Using Law of Sines (law cosines will do - but a bit convoluted).

Try it and show us your work if you are still having trouble.
 
Find the resultant of each pair of forces acting on an object

Q: forces of 6 N southwest and 8 N northwest

I got 10 for the resultant, but how do I find the angle?

The answer is apparently is 10 N, N82degW

Having a hard time visualizing this...
Using the usual x-y co-ordinate system, northwest is 135\(\displaystyle ^{\circ}\) and southwest is 225\(\displaystyle ^{\circ}\). So you have a vector of magnitude 8 at 135\(\displaystyle ^{\circ}\) and a vector of magnitude 6 at 225\(\displaystyle ^{\circ}\). Add them.
 
Find the resultant of each pair of forces acting on an object

Q: forces of 6 N southwest and 8 N northwest

I got 10 for the resultant, but how do I find the angle?

The answer is apparently is 10 N, N82degW

Having a hard time visualizing this...

Oh, and notice that N90\(\displaystyle ^{\circ}\)W is 180\(\displaystyle ^{\circ}\) in the usual x-y co-ordinate system.
 
Find the resultant of each pair of forces acting on an object

Q: forces of 6 N southwest and 8 N northwest

I got 10 for the resultant, but how do I find the angle?

The answer is apparently is 10 N, N82degW

Having a hard time visualizing this...
You really do not know the angle? What is your teacher teaching you?
I am hoping that you know what the the second and third quadrant are. Draw the x and y axes. The upper left side (quadrant) is the 2nd quadrant and the lower left side is the 3rd quadrant. North is up, south is down and west is to the left (I am sure that you know this). Northwest means that you draw a vector not going directly north (up) but a little to the west (left). If you are not given an angle then you know that the angle is 45 degree. So you draw a vector 45 degree angle to the left (west) of north (up).
You do a similar thing in quadrant 3. So what is the angle between the two vectors?

BTW, how did you get 10 without knowing the angle between the vector? Are the three values a Pythagorean triple? If yes, what does that tell you??
 
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