Rank Designs A-F: Largest to Smallest Tension

[wanamaa]

Homework Statement

A sign is to be hung from the end of a thin pole, and the pole supported by a single cable. Your design firm brainstorms the six scenarios shown below. In scenarios A, B, and D, the cable is attached halfway between the midpoint and end of the pole. In C, the cable is attached to the mid-point of the pole. In E and F, the cable is attached to the end of the pole.

Rank the design scenarios (A through F) on the basis of the tension in the supporting cable.
Rank from largest to smallest. To rank items as equivalent, overlap them.

Homework Equations

tau = rFsin(theta) ,where r is the distance from the hinge to the force and theta is the angle of the force relative to the pole.

The Attempt at a Solution

Well, the tension of design E is equal to the weight of the sign, since it is in the same location. C and F are equal in torque because rFsin(30) = 1/2 r. Both A and B have the cable attached at the same point and, since A is at an angle less than 90 degrees, A requires more tension than B. On that same note, A has a greater angle than D, so A requires less tension.

I've only got one shot at this and I would like it figured out by Friday. My educated guess is that C = F > A > D > B > E, but I want to make sure before I submit my answer. I'm horrible with problems with only variables. Could someone verify if I'm right/close/wrong? Any help would be awesome.

 

[nvn]

wanamaa: You are currently close. Also, it appears you have the wrong formula for cable tension T. Review your trigonometry.

 

[anphys32]

the ranking order is: C=F>D>A>B>E