Problem involving Torque and a Derrick from Feynman Exercises

AI Thread Summary
The discussion revolves around solving a torque problem involving a derrick, where the user initially calculated the tension T using torque equations based on the components of tension and weight. The user derived T as T = (L/x) W tan(θ) and confirmed this using the principle of virtual work. However, confusion arose regarding the book's answer, which includes an additional term of W/2, indicating the weight of the boom. The clarification highlights that the boom's weight must be considered alongside the block's weight in the torque calculations. Understanding this relationship resolves the discrepancy in the tension equation.
suh112
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Homework Statement
2.17 A derrick is made of a uniform boom of length L and weight w, pivoted at its lower end, as shown in Fig. 2-15. It is supported at an angle with the vertical by a horizontal cable attached at a point a distance x from the pivot, and a weight W is slung from its upper end. Find the tension T in the horizontal cable.
Relevant Equations
##\tau = F_{\perp}r##
Work = Fd
I attempted to solve this problem by considering the torque caused by the perpendicular components of the tension and weight with respect to the derrick. $$ Tcos\theta x = Wsin\theta L$$ $$T = \frac L x Wtan\theta$$ Using the principle of virtual work I also arrived at the same answer by considering the derrick falling a distance y. $$Wsin\theta y = Tcos\theta \frac x L y $$The answer listed in the book is ##T = \frac L x (W + \frac W 2 )tan\theta ## and I can't figure out where the ##\frac W 2 ## term comes from. Thank you in advance for helping me.
 

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In addition to the weight W of the block, the boom has weight w.
 
TSny said:
In addition to the weight W of the block, the boom has weight w.
Ok I see now. Thanks for pointing that out.
 
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