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Question

a uniform rod of weight 80 Newtons is suspended from the ceiling by string attached to its ends. The rod is in equilibrium at an angle 10 degrees to the horizontal and the string attached to the higher end is at an angle 40 degrees to the vertical. Find the angle which the other string makes with the vertical. Find also the tension in the two strings.

Answer 1

Here's a diagram for my solution

http://i142.photobucket.com/albums/r88/odu83/rod.jpg

The rod has length L

the sum of forces in the vertical equal zero

T1*cos(40)+T2*cos(th)-80=0

doing a bit of algebra
T2*cos(th)=80-T1*cos(40)

the sum of forces in the horizontal equal zero

T1*sin(40)-T2*sin(th)=0

doing a bit of algebra
T2*sin(th)=T1*sin(40)

divide the two equations to get
tan(th)=T1*sin(40)/(80-T1*cos(40))

Summing torques about the connection of T2 (left end of the rod)

80*cos(10)*L/2-T1*sin(40)*L=0
T1=80*cos(10)/(2*sin(40))
T1=61.3 N

using our equation of tan(th)
tan(th)=T1*sin(40)/(80-T1*cos(40))
th=50 degrees

T2=51.4 N

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