Tension problem involving picture frame

[Chandasouk]

Homework Statement

A picture frame hung against a wall is suspended by two wires attached to its upper corners.

If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame? (Neglect any friction between the wall and the picture frame.)

I have no idea what to do except for to draw a free body diagram.

 

[rl.bhat]

Find the vertical and horizontal components of both the tensions.
Horizontal components cancel each other. Net horizontal components = ...?

 

[Chandasouk]

the X components would be cos\theta*.75 ?You mean the vertical components cancel each other out right?

 

[rl.bhat]

the X components would be cos\theta*.75 ?


You mean the vertical components cancel each other out right?

Sorry. I mean net vertical component.
If θ is the angle of T with vertical, then check the x component.
What is y component?

 

[Chandasouk]

Sin\theta*.75 ?

If I broke the tension into components, I get a triangle with theta above the horizontal

 

[rl.bhat]

In the problem it is stated that "If the two wires make the same angle with the vertical'
If you call this angle as θ, then
vertical component is T*cosθ and horizontal component is T*sinθ.
Horizontal components are equal in magnitude and opposite in direction. Hence they cancel each other.
The net vertical component is the weight of the frame.

 

[Chandasouk]

okay, I understand that now, but how do I find the angle? The tension on both wires are .75 of the weight, so could I substitute

vertical component is .75w*cosθ

 

[rl.bhat]

Two vertical components are there. Find net vertical component and equate it to the weight of the frame w. And solve for θ.