Torque and tension question

1. Jul 25, 2006

kankerfist

The picture I attached to this thread is a system that I came across while studying for my final exam today. It is a system that is in equilibrium, and the only numerical values are:

Angle of wire/ground: 30
Angle of strut/ground: 45
Mass of hanging weight: 500 lb
Mass of strut: 100 lb (uniform mass)

I have written out all the forces that I can find, several of which are couples that cancel out, but I cannot find a numerical value for the tension in the cable T. The question asks what the tension is, and I have begun to think there is no way to describe tension numerically from the given data. Can someone please help me out by confirming that there isn't enough data here to describe tension numerically? Thanks a lot!

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2. Jul 25, 2006

Staff: Mentor

Seems like there's enough information to me. Have you applied the equilibrium conditions to the strut? (What's the net torque on the strut due to all the forces on it?)

3. Jul 25, 2006

kankerfist

The net torque at P has to be zero. I guess my problem is that I haven't figured out how to numerically describe the positions of the forces relative to P. For instance, one of the torque forces is the 500 lb weight. I know the direction of the force is straight down, but I'm not sure how to numerically find its position vector relative to P. If I did, then I could calculate the cross product to find the torque due to the 500 lb weight. Thanks for the reply!

4. Jul 25, 2006

Staff: Mentor

Perhaps you are thinking that you need the length of the strut? If that's the problem, just call the length "L". You'll find that you don't need the numerical value: when you write the torque equation, the length will cancel out.

(Tip: Try to solve the problem symbolically. Wait until the last step before reaching for the calculator.)

5. Jul 25, 2006

PPonte

The torque force of the 500 lb weight is applied at the top of the strut and the direction of this force is as you said straight down. Then, you need to find the lever arm.

The lever arm is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force.

Once you know the lever-arm, you may find the torque.
You may follow the same strategy to find the other torques.

Remember Doc Al's hints!

6. Jul 25, 2006

kankerfist

You guys are about 10x as helpful as my teacher! Here is where I have gotten:
Grav Torques from the masses + Torque from wire's tension = 0,
so:
x_strut is distance from P to the 500lb mass lever arm
x_wire is distance from where the wire is grounded to P
h is the height of where the wire and strut meet

(226.8)(9.8)(x_strut) + (45.36)(9.8)(x_strut / 2) = (Tension)(x_wire)

Then geometrically I know that:
Sin[30] = h/(x_strut + x_wire)
Sin[45] = h/x_strut

so:
h = (x_strut + x_wire)Sin[30] = (x_strut)Sin[45]

Solving for x_wire:
x_wire = 0.414 x_strut

Then plugging into the original torque equation gives me:
(226.8)(9.8)(x_strut) + (45.36)(9.8)(x_strut / 2) = (Tension)(0.414 x_strut)

Solving this for Tension yields 5905 N of tension in the wire. Any hints on whether or not I'm approaching this correctly would be greatly appreciated!

Last edited: Jul 26, 2006
7. Jul 26, 2006

kankerfist

Actually, I got the lever arm on tension messed up there. Looks like the lever arm of tension is actually (0.414)(x_strut)Sin(30)

This fix yields a tension of 11816 N of tension in the wire

8. Jul 26, 2006

To provide a clearer definition, it would be better to say that $$x_{strut}$$ is the HORIZONTAL distance from P to the vertical wire connecting the 500lb mass. Also, h is the height of the point where the wire and strut meet.

Really? Check again!

Last edited: Jul 26, 2006
9. Jul 26, 2006

Staff: Mentor

Looks like you have things a bit messed up. Let's do it step by step. (I'll use "L" as the length of the strut.) First, let's find the clockwise torques about point P:
-due to the weight of the strut: (L/2)*(100 lbs)* sin(45)
-due to the hanging mass: (L)*(500 lbs)* sin(45)

Now find the counterclockwise torque about point P, which is due to the tension in the wire. To do that you need to figure out the angle that the wire makes with the strut. It's easy--just use what you know about triangles. I'll call that angle "theta":
-due to wire: (L)*(T) sin(theta)

Once you figure out theta, just set total torque equal to zero (or clockwise torques equal to counterclockwise torques -- same thing) and solve for T.