Adding Vectors with parallelogram/triangular rule.

  • Thread starter btbam91
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In summary, the conversation discusses a problem involving two structural members in compression and determining the resultant force using graphical methods. The individual is having difficulty with the diagram and is seeking assistance in solving for the resultant force. The expert provides guidance on how to correctly draw the diagram and suggests using geometric identities to find the magnitude and direction of the resultant force.
  • #1
btbam91
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Hello,

I am have slight problems with this problem. If I were able to use rectangular components, I'd be able to do it easily, but my professor was specific in that he wanted us to reach the solution using graphical methods.

The problem is:


"Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in compression and that the force is 10 kN in member A and 15 kN in member B, determine the magnitude and direction of the resultant of the forces applied to the bracket by members A and B.

A rough sketch of the original diagram:

[PLAIN]http://a.imageshack.us/img210/4468/vector1f.png [Broken]

And my attempt at making the diagram using the triangle rule.

[PLAIN]http://a.imageshack.us/img706/8850/vector2b.png [Broken]

If my 2nd diagram is correct, how would I go about solving for the resultant force?




Thanks!
 
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  • #2
You could use a variety of geometrical identities relating to triangles, for instance the sin rule.
 
  • #3
I understand that, but I am having trouble figuring out how to apply that.
 
  • #4
I'm going to have to bump this! :p
 
  • #5
No, you don't have to bump anything! And doing that too often just might get you banned.

Your basic problem is that your picture is wrong. You want to add the two vectors and what you show is their difference. You should have your vector "B" with its tail at "A"s tip. That will give you three angles made with the vertical, the top angle being 40 degrees and the lowest angle being 20 degrees. Since those add to 60 degrees and the three must add to 180 degrees, the middle angle, which is an angle in the triangle formed after you draw in the resultant, is 180- 60= 120 degrees. You now have a triangle in which you know the "lengths" of two sides and the angle between them. You can use the cosine law to find the "length" of the third side, the magnitude of the resultant vector. Then you can use the sine law to find the other two angles, giving you the angle the resultant vector makes with the vertical.
 

1. How do I determine the direction of the resultant vector using the parallelogram rule?

To determine the direction of the resultant vector, draw a diagonal line connecting the two initial vectors in the parallelogram. The direction of the resultant vector is the same as the direction of this diagonal line.

2. Can the parallelogram rule be used for more than two vectors?

Yes, the parallelogram rule can be used for any number of vectors. Simply draw all the initial vectors using the head-to-tail method, and then complete the parallelogram by drawing the remaining sides. The resultant vector is still determined by the diagonal line connecting the initial vectors.

3. How does the triangular rule differ from the parallelogram rule?

The triangular rule is a simplified version of the parallelogram rule, and can only be used for adding two vectors. Instead of drawing a parallelogram, the triangular rule involves drawing the second vector starting at the tip of the first vector, and then drawing the resultant vector from the tail of the first vector to the tip of the second vector.

4. What happens if the vectors being added are not at right angles to each other?

If the vectors being added are not at right angles, the parallelogram or triangular rule can still be used. The only difference is that the diagonal line or resultant vector will not be at a right angle to the initial vectors.

5. Can the parallelogram or triangular rule be used for subtracting vectors?

No, the parallelogram and triangular rules can only be used for adding vectors. To subtract vectors, you must first convert the vector to be subtracted into its opposite direction, and then add it to the other vector using the parallelogram or triangular rule.

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