Solve 3-Force Member: Weight W=50N on Disk

[dontdisturbmycircles]

Homework Statement

http://img210.imageshack.us/img210/5118/probrb4.jpg
The weight W=50N acts at the center of the disk. Use the fact that the disk is a three force member to solve for the tension in the cable and the reactions at the pin support.

Homework Equations

The Attempt at a Solution

Okay, I realize that the forces must converge at a point directly above the center of mass of the disk, but I don't immediately see the geometrical solution. I could solve it trivially by summing the forces in the x and y and taking a moment but that's not really using the fact that the disk is a three force member. I know the direction of T (tension in rope) obviously, and this kind of gives me an indication as to the direction of the reaction at the pin support but I again, I don't think there is enough there geometrically...

 

[Astronuc]

Well, the sum of the forces in the x and y directions must equal zero, since this is a statics problem, AND the sum of the moments acting on the disc must also equal zero.

It would appear that the pivot on the left is at the same elevation as the CM of the disc? And it's moment arm is R.

The cable seems to be attached at the top vertically above the center of the disc, and there is a moment there (in the -x direction) and its moment arm is also R.

 

[ogb p]

I would approach this problem by first defining the system and identifying all of the relevant forces acting on it. In this case, the system is the disk and the forces include the weight W, the tension in the cable T, and the reactions at the pin support Rx and Ry.

Next, I would use the fact that the disk is a three force member to determine the direction of the forces. Since the disk is in equilibrium, the sum of all the forces acting on it must be equal to zero. This means that the forces must be balanced and the direction of each force can be determined based on this principle.

Using the given information, I would draw a free body diagram of the disk and apply the equations of equilibrium to solve for the unknown forces. Since the disk is a three force member, the forces must converge at a point directly above the center of mass, as mentioned in the problem statement. This means that the tension in the cable T and the reactions at the pin support Rx and Ry must all intersect at this point.

To solve for the tension in the cable T, I would use the equation ΣFy=0, which states that the sum of the forces in the y-direction must be equal to zero. This would give me the equation T + Ry - W = 0, where T is the unknown tension in the cable, Ry is the reaction at the pin support in the y-direction, and W is the weight of the disk. Solving for T, I would get T = W - Ry.

Similarly, to solve for the reactions at the pin support Rx and Ry, I would use the equations ΣFx=0 and ΣM=0. These equations state that the sum of the forces in the x-direction and the sum of the moments about any point must be equal to zero, respectively. This would give me two equations, Rx = 0 and Ry = W/2, which can be solved simultaneously.

In conclusion, by using the fact that the disk is a three force member and applying the equations of equilibrium, I can solve for the unknown forces in the system, namely the tension in the cable and the reactions at the pin support. This approach allows me to use the given information and principles of mechanics to find a geometric solution to the problem.