Kayla M.

asked • 11/10/15

Find the magnitude of the resulting force and the angle that it makes with the 70lb force.

Two forces, one of 80lbs and one of 70lbs, act on an object at 40 degree angles.  Find the magnitude of the resulting force and the angle that it makes with the 70lb force.
 
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Ben K.

40 degree angles compared to what?
 
Are both forces pointing in the same direction?
 
If they are both pointing in the same direction, then you should simply add them and the angle between the resultant force and the 70 lb force is 0 degrees.
 
I suspect that there is more to this problem, though.
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11/10/15

Kayla M.

That is all there is to this question.  Imagine 2 forces pulling 1 object at a 40 degree angle - that's what they're trying to say.  Both forces are pulling from the 1 object.  I've had sample problems and it's not as easy as just adding them.  Does this make anymore sense to you Ben?
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11/10/15

1 Expert Answer

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Bill K. answered • 11/10/15

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This a vector addition problem and you need to know the law of cosines and law of sines to solve this problem.
 
Two vector forces of 80lbs and 70 lbs act on an object at 40 degree angle between them.   
The magnitude of the resultant force can be found by applying the law of cosines:
c2 = a2 + b2 - 2abcos140°
where a = 80, b = 70 and c is the resultant force vector you are asked to find
 
Once you find the magnitude of the resultant force, then you can find the angle it makes wrt the 70lb force using the law of sines:
sinα/a = sin140°/c
where α is the angle opposite side a, or the angle between the resultant and the 70lb vector that you are asked to find.
 
 
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Kayla M.

So to be sure of my answer, what would the solution be?
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11/11/15

Bill K.

using
c2 = a2 + b2 - 2abcos140°
where a = 80, b = 70 and c is the resultant force vector you are asked to find
subsitituting the given values into this equation gives c = 140lbs.
using
sinα/a = sin140°/c
and substituting the given values
we get sinα = 0.36 or sin-1α = 21.39°
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11/12/15

Astrid M.

where did the 140 come from? Did you subtracts 180-40 and got 140? If yes,why?
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03/06/21

Bill K.

Adding vectors involve putting the vector head of one to the vector tail of the other. This means that the angle between them is really the supplement (180-40-140).
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03/06/21

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