A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle è = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if the ramp is frictionless, so the sphere continues to rotate with its initial angular speed until it reaches its maximum height.

Answer 1

KE initial= PEfinal

1/2 mv^2+1/2 I w^2 = mgh
look up I for a sphere.

w=v/2pir
solve for h.

Answer 2

Try using conservation of energy. Be sure to include the rotational KE of the rolling sphere.

If you need additional sssistance, show your work.