Maximum vertical and horizontal forces.

[theBEAST]

Homework Statement

https://dl.dropbox.com/u/64325990/math.PNG

The Attempt at a Solution

So what I did was set up an system of equations such that the sum of the horizontal forces = 0 and the sum of the vertical forces = 0. I ended up solving for the tension in the rope BC and then found the vertical force which came out to be 490N which is not correct. I think I got this wrong because I am not finding the max force. How should I approach this question?

 

[TSny]

I think the question meant to say minimum rather than maximum.

Your method sounds good. You must have made some error in setting up the equations or in doing the algebra.

Another approach is to graphically add the three forces to make a triangle. Use trig on the triangle to find the tension in the rope BC.

 

[theBEAST]

I think the question meant to say minimum rather than maximum.

Your method sounds good. You must have made some error in setting up the equations or in doing the algebra.

Another approach is to graphically add the three forces to make a triangle. Use trig on the triangle to find the tension in the rope BC.

Thanks! I got the answer... but how can it be either the maximum or the minimum? There isn't anything in the diagram that you could optimize. I don't see how I can use derivatives to find the maximum or the minimum.

 

[TSny]

...how can it be either the maximum or the minimum? There isn't anything in the diagram that you could optimize.

In order for the ring at B to be able to support the system, it must be able to support a vertical force at least equal to the vertical component of the tension in the rope BC. To me, that's a way of saying that your answer represents the minimum vertical force that the ring must be able to support. But, I suppose the wording used in the statement of the problem is open to interpretation. I think it would have been best if the word "maximum" (or "minimum") had simply been deleted from the wording.