Problem involving Torque and a Derrick from Feynman Exercises

[suh112]

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.

 

[TSny]

In addition to the weight W of the block, the boom has weight w.

 

[suh112]

In addition to the weight W of the block, the boom has weight w.

Ok I see now. Thanks for pointing that out.