Symon3-11

3.11 β = \frac{π-d}{2} \frac{π-d}{2} = \frac{d}{2} D^2 = R^2 + R^2 - 2R R\cos α = 2R^2 (1 - \cos α) \rightarrow D = 2R\sqrt{\frac{1 - \cos α}{2}} D = 2R \sin \frac{d}{2} \rightarrow F = f_0 D = 2Rf_0 \sin \frac{d}{2} W_{AB} = \int_{0}^{β = \frac{d}{R}} F \cos α dα = \int_{0}^{π} 2Rf_0 \sin \frac{d}{2} \cos \frac{d}{2} dx = W_{AB} = -2Rf_0 \int \cos \frac{d}{2} dx \bigg|_{0}^{π} = \boxed{Rf_0}