Chapter 1.15, Problem 29P

The figure shows a heavy weight suspended by a cable and pulled to one side by a force F. We want to know how much force F is required to hold the weight in equilibrium at a given distance x to one side (say to place a cornerstone correctly). From elementary physics, $Tcos\theta =W$, and $T\sin \theta =F$.

(a) Find F/W as a series of powers of $\theta$.

(b) Usually in a problem like this, what we know is not $\theta$, but x and l in the diagram. Find F/ W as a series of powers of x/l.