Adding Vectors with parallelogram/triangular rule.

[btbam91]

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

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

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

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




Thanks!

 

[Fightfish]

You could use a variety of geometrical identities relating to triangles, for instance the sin rule.

 

[btbam91]

I understand that, but I am having trouble figuring out how to apply that.

 

[btbam91]

I'm going to have to bump this! :p

 

[HallsofIvy]

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.