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

weight-of-the-frame

#1

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.)

Answer:

Tension in the wires (T) = 0.75W
Let q be the angle of wires with vertical.
So, Total Force in vertical direction from the wires = 2T
cos(q)
which must be equal to the weight of picture frame (W).
2Tcos(q) = W
2
0.75Wcos(q) = W
cos(q) = 1/1.5 = 2/3
So, the angle(q) is 48.2 degrees