What Is the Tension in the Top Cables of the Sculpture?

[mandi182]

Homework Statement

An abstract sculpture is constructed by suspending a sphere of polished rock along the vertical with four cables connected to a square wooden frame 1.7 m. If the stone has mass m = 5.2 kg, and the bottom two cables are under a tension of 25 N each, what is the tension in each top cable?

The picture just shows a square with a ball in the middle and 4 cables on each side.

Homework Equations

I don't know what equation to use. I know that it is not accelerating but that is all the I know.

The Attempt at a Solution

I thought that it may be the tension given because the top would hold more. I also tried half that and quadruple that. None of the other people in my class were able to figure it out.

I really just need someone to explain it to me.

Thanks!

 

[PhanthomJay]

Without a picture, I'm envisioning a square open frame standing vertically, with the sphere suspended in the center, supported by 4 cables, each of which is attached to the corners of the frame, making an X pattern Is this correct?

 

[mandi182]

Yes, it is basically an X with a ball in the middle.

 

[PhanthomJay]

OK. Draw a free body diagram of the sphere (isolate it to draw the forces acting on it). It's weight will act veritically down, acting away from the sphere, and the 2 lower tension forces as given (25 N each) pull away from the sphere, each at a 45 degree angle, left or right of the vertical. The 2 unknown top tension forces also pull away from the sphere, at a 45 degree angle, left or right of the vertical. Since, as you have noted, the sphere is in equilibrium, use Newton's 1st law in both the x and y directions to solve for the value of the tensions in the upper cords (you can make use of the symmetry of the problem to make it even easier).