Two Angle, Leaning Stick Static Friction Problem

[lizzyb]

State the Problem

End A of a slender, uniform rod of weight w and length L bears on a horizontal surface ash shown, while end B is supported by a cord BC of length L. Knowing that the coefficient of static friction is 0.40, determine (a) the value of theta for which motion is impending, (b) the corresponding value of the tension in the cord.

http://img198.imageshack.us/img198/4025/0823bookdiagram1.jpg

Related Equations
F = mu * n

Work Done So Far
http://img243.imageshack.us/img243/4356/082310001.jpg
http://img198.imageshack.us/img198/1922/082310002.jpg
http://img42.imageshack.us/img42/558/082310003.jpg
http://img20.imageshack.us/img20/2554/082310004.jpg
http://img86.imageshack.us/img86/9180/082310005.jpg

I put these into the computer but it couldn't give me an answer; does this look set up okay to you?

 

[nvn]

lizzyb: I can't read the illegible writing, so let me take a guess. What is that stuff under the square root sign for? What's that all about? Eliminate it, then try solving again. The solver needs to be a good one for this problem. Bad solvers, or good solvers on bad machines, can have trouble with this problem.

 

[Mene]

The problem at hand is to determine the value of theta and the corresponding tension in the cord BC in a static friction situation involving a leaning stick. The setup consists of a slender, uniform rod with a weight of w and length of L, where one end A is in contact with a horizontal surface and the other end B is supported by a cord BC of length L. The coefficient of static friction between the rod and the surface is given as 0.40.

To solve this problem, we can use the equation F = mu * n, where F is the force of friction, mu is the coefficient of friction, and n is the normal force. In this case, the normal force is equal to the weight of the rod, w. Therefore, the equation can be rewritten as F = 0.40 * w.

To determine the value of theta for which motion is impending, we need to find the maximum angle at which the force of friction is equal to the weight of the rod. This can be found by setting F = w and solving for theta. Using the equations shown in the work done so far, we can set up an equation with theta as the variable and solve for it. However, the computer was unable to give us an answer, indicating that the setup may not be correct.

To determine the corresponding tension in the cord BC, we can use the fact that the sum of the forces in the vertical direction must equal zero. This means that the tension in the cord, T, must be equal to the weight of the rod, w. Therefore, T = w.

In conclusion, the problem at hand is to determine the value of theta and the corresponding tension in the cord BC in a static friction situation involving a leaning stick. However, the setup may need to be revised in order to solve for theta.