Maximising Tension on a Hemisphere

Classical Mechanics Level 2

A uniform rope of length l l is held motionless on a frictionless hemisphere of radius r r with one end of the rope on the top of the hemisphere. The hemisphere is fixed to the horizontal floor. Find where on the rope, from the top, maximum tensile force is developed immediately after the rope is released.

Sorry for the bad figure.

sin ⁡ − 1 [ r l ( 1 − cos ⁡ l r ) ] ) \sin^{-1}{[\frac{r}{l}(1-\cos{\frac{l}{r}})]}) sin ⁡ − 1 [ l r ( 1 − cos ⁡ r l ) ] ) \sin^{-1}{[\frac{l}{r}(1-\cos{\frac{r}{l}})]}) cos ⁡ − 1 [ l r ( 1 − cos ⁡ r l ) ] ) \cos^{-1}{[\frac{l}{r}(1-\cos{\frac{r}{l}})]}) cos ⁡ − 1 [ r l ( 1 − cos ⁡ l r ) ] ) \cos^{-1}{[\frac{r}{l}(1-\cos{\frac{l}{r}})]})

Kushal Thaman by Kushal Thaman , 18, India

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