**50. A person starts from rest at the top of a large frictionless spherical surface, and slides into the water below (see the drawing). At what angle q does the person leave the surface? (Hint: When the person leaves the surface, the normal force is zero.)

 

Free Body Diagram at top

Free Body Diagram at loss of contact point (N = 0)

Sum of radial forces at the point contact is lost

 

Solving for

Now again with no non-conservative forces, we can conserve mechanical energy

 

Person starts from rest, so no kinetic energy before.

 

 

 

Consider what Dh is

 

Now substitute forthat we found above

 

Multiply by 2

 

Canceling like terms on both sides

Solve q

 

 

 

 

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This page last updated on January 11, 2020