The uniform rod in the figure is supported by two strings. The siring attached to the wall...
The uniform rod in the figure is supported by two strings. The siring attached to the wall ,is horizontal, and the string attached to the ceiling makes an angle of ϕ with respect to the vertical. The rod itself is tilted from the vertical by an angle θ. If ϕ = 30.0°, what is the value of θ?
Step-by-Step Solution
THINK:
The first condition for the static equilibrium:
The net force acting on the system must be zero when the system is in static equilibrium.
The second condition for the static equilibrium:
The net torque acting on the system about the pivot point must be zero when the system is in static equilibrium.
We can calculate the angle 
by using the static equilibrium conditions.
SKETCH:
The uniform rod in the figure is supported by two strings. The string attached to the wall is horizontal, and the string attached to the ceiling makes an angle of 
with respect to the vertical. The rod itself is tilted from the vertical by an angle
. It is shown in below figure.
RESEARCH:
From triangle 
in above figure, we have
From triangle 
in above figure, we have
When the rod is in equilibrium, then the net torque acting on the rod about the pivot point must be zero.
Thus the tension in the first string can be expressed as
. . . . . . (1)
When the rod is in equilibrium, then the vertical force acting on the rod must be zero.
Therefore, the weight of the rod can be written as
. . . . . . (2)
Thus,
. . . . . . (3)
CALCULATE:
Given data
The string attached to the ceiling makes an angle with vertical, 
Using the equation (3), the value of the angle 
can be calculated as
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