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.

 

[Nickie]

As a scientist, it is important to approach problems like this with a systematic and analytical mindset. In this case, it seems like you have correctly set up the equations for the sum of the horizontal and vertical forces, but may have made a mistake in solving for the tension in the rope BC. It is important to carefully check your calculations and make sure you are using the correct values for the given forces.

Additionally, in order to find the maximum vertical and horizontal forces, you may need to consider the concept of equilibrium. This means that the sum of all forces acting on an object must equal zero in order for it to remain in a state of rest or constant motion. In this problem, you may need to consider the maximum values for the forces acting on the object in order to determine the maximum vertical and horizontal forces.

Furthermore, it is important to consider the physical limitations and properties of the object in question. For example, the maximum vertical force may be limited by the weight of the object itself, or the maximum horizontal force may be limited by the strength of the ropes or other materials used in the setup.

Overall, it is important to approach this problem with a thorough understanding of the principles of forces and equilibrium, and to carefully analyze the given information in order to determine the correct maximum values for the vertical and horizontal forces. If you are still having trouble, it may be helpful to consult with a colleague or professor for additional guidance and support.