Angular Contact

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Frequently Asked Questions...

Engineering Mechanics Statics?

I have here a figure given by my professor:
link:

http://s737.photobucket.com/albums/xx20/facesale01/?action=view&current=ascrg.jpg&newest=1

Find the sag value.

The check means that the value for that specific variable is given. He said that this is a combination of cables and belt friction. please give me a solution even if you give sample values to the variables. tnx for your help ^_^.
R= radius if the circle
S-length of the cable
f=coefficient of friction


Best Answer...

Answer:

Well, I have trouble understanding your drawing. It is really blurry. And it isn't really clear what you are given, and what you are to find.

All I can tell you is the following:
1. Use the hyperbolic cosine curve (as far as you are concerned, this has nothing to do with hyperbolas or trigonometry cosine) as a model for the shape of the sagging cable.
2. Find the derivative at the contact with the circular peg.
3. Convert this derivative into an angle (theta), using arctangent.
4. Repeat steps 2 and 3 for the left end of the cable
5. Perform equilibrium calculations on the sagging cable, balancing its weight against the two tensions.
6. Use this angle with some visualization to figure how this angle relates to the amount of angular contact (beta) with the peg
7. Use the formula T2 = T1*exp(beta*mu_s), to relate the tension in the right portion of the cable to the tension in the left portion of the cable. Which tension is which? Let's find out.
8. Compare the right side tension found in part 5 to the weight of the free end of the cable. Which ever is larger is T2 in the formula in part 7.