A string AB of unstretched length L is stretc | vedclass

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(C) Let $T$ be the tension in the string segments $AC$ and $BC$. Applying the equilibrium condition at point $C$ in the vertical direction:$F = 2T \si

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$K L(1-\cos 	heta) 	an 	heta$

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(C) Let $T$ be the tension in the string segments $AC$ and $BC$. Applying the equilibrium condition at point $C$ in the vertical direction:$F = 2T \sin 	heta$The length of each segment $AC$ and $BC$ in the stretched state is $L' = \frac{L/2}{\cos 	heta}$.The elongation in each segment is $\Delta L = L' - \frac{L}{2} = \frac{L}{2} \left( \frac{1}{\cos 	heta} - 1 ight) = \frac{L}{2} \left( \frac{1 - \cos 	heta}{\cos 	heta} ight)$.Given the force to elongation ratio $K$, the tension $T$ is $T = K \Delta L = K \frac{L}{2} \left( \frac{1 - \cos 	heta}{\cos 	heta} ight)$.Substituting $T$ into the force equation:$F = 2 \left[ K \frac{L}{2} \left( \frac{1 - \cos 	heta}{\cos 	heta} ight) ight] \sin 	heta$$F = K L (1 - \cos 	heta) \frac{\sin 	heta}{\cos 	heta}$$F = K L (1 - \cos 	heta) 	an 	heta$.

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