I am studying for my graduate exam in physics and came across a stange phenomenon and I would like to make sure I am reasoning it correctly:(adsbygoogle = window.adsbygoogle || []).push({});

Start with a hemispherical bowl and place a small sphere (relatively) at the edge. Let the sphere roll towards the center of the bowl, thus gaining kinetic energy. At the bottom of the bowl, I have calculated the normal force the small sphere exerts on the hemispherical bowl, allowing the radius of the sphere be much less than the radius of the bowl. This force is much greater (by 17/7) than just (mass sphere) x (gravitational acceleration)!

Through my calculations I have reasoned the sphere has both translational and kinetic energy at the bottom of the bowl. From the angular speed of the sphere, I have calculated the required radial acceleration of a point on the edge of the sphere. Now I let the radius of the sphere become very small compared to the radius of the bowl it is in. Now there is a force on the bowl due to this acceleration of the sphere. From Newton's second law I finally determine that the normal force the sphere exerts on the bowl is the sum of the gravitatonal force on the sphere plus this radial acceleration due to the rotation of the sphere:

i.e. Fext = N - mg = ma

with:

a = radial acceleration of sphere

N = normal force

g = gravitational acceleration

m = mass of sphere

This analysis appears sketchy to me and I may not be explaining myself correctly, but I get the answer I am supposed to get for the normal force. Could anyone help clarify this for me? Thanks.

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# Increased normal force due to rotation

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