How to Determine Cable Tensions and Angles for a Suspended Leg Cast?

[elbowgrease6]

Homework Statement

Consider the two cables suspending a leg with a cast in the drawing. If the leg and cast weight 150 N, and the angle of the ankle cable is 60 degrees above the horizontal, what are the cable tensions and the angle of the knee cable from the horizontal such that the leg is supported?

Homework Equations

The Attempt at a Solution

I know it seems simple, but I don't know how to start it. Thank you for any help.

 

[SteamKing]

Since the leg is not moving, you can write the equations of statics, knowing the weight of the leg + cast, the c.g. of the leg + cast, and the tensions in the support cables. You know the angle one cable makes with the horizon, and thus can determine what the components of the unknown tension must be. For the other cable, the angle is unknown and must be solved for.

 

[elbowgrease6]

I think that is where I have gone wrong. I have written several equations:

-Tkx + Tax = 0
Tky + Tay - W = 0

-Tk(cos theta) + Ta(cos 60) = 0
Tk(sin theta) + Ta(sin 60) -150 N = 0

I think my main confusion is, is there a y term for the tensions? Because they do not tell you how much above the center of mass both cables are tied. Thanks again.

 

[elbowgrease6]

Okay, I solved it.

Theta = 33.56 degrees
Ta= 280.9 N
Tk= 168.54 N

Could anybody check and see if those seem right?

 

[SteamKing]

Not even close. Although you have written equations dealing with the components of the tensions, you have neglected to write any moment equations. Remember, for static equilibrium, Sum(forces) = 0 AND Sum (moments) = 0.

 

[yster]

hint: you must have as many equations as you have unknowns. Look at the two equations you gave. There are 3 unknowns; the angle and the two tensions. So you need at least one moment equation