Launching a particle at the highest point inside a sphere

  • #1
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If a smooth sphere with radius a is fixed on a plane, and a particle is projected horizontally at the highest point outside/on of the sphere with speed (4ag/5)^0.5, I know that the particle will lose contact with the sphere when it makes an angle of theta with the upward vertical, where theta is cos^-1(4/5).

But what if I were to launch the particle with that speed horizontally at the highest point inside the sphere ? It seems that the particle would also lose contact at the same point ? But wouldn't the particle complete a full circle inside the sphere ?
 

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  • #2
haruspex
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It seems that the particle would also lose contact at the same point ?
Why? Which way is the normal force pointing now? What equation do you get?
 
  • #3
A.T.
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It seems that the particle would also lose contact at the same point ?
If the initial speed is such that it stays in contact outside, then it would immediately loose contact inside.
 

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