4.85) A slender rod BC of length L and weight W is held by two cables as shown.
ID: 1850283 • Letter: 4
Question
4.85) A slender rod BC of length L and weight W is held by two cables as shown. Knowing that cable AB is horizontal and that the rod forms an angle of 40 degrees with the horizontal, determine: the angle theta that cable CD forms with the horizontal and the tension in each cable.
Explanation / Answer
T1 and T2 are tensions in AB and CD respectively.
body is in equilibrium because of equlliriumin horizontal T1=T2cos(theta)................1
because of vertical equllibeium T2sin(theta)=W..........................2
moment about point B is zero
W(L/2)cos40=T2sin(theta)Lcos40-T2cos(theta)Lsin40............3
by which T2cos(theta)=(Wcot40)/2............4
divide 2 and 4
tan(theta)=2tan40
theta=inverse2tan40
therefore T2=Wcosec(THeta) and Subtitute these values in equatioon 1 to get T1=Wcot(theta)
theta=59.2 dgree
T2=1.16W and T1=0.59W
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