A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed ν = 3.00 m/s when it encounters a ramp that is at an angle θ = 23.0° above the horizontal. Find the maximum distance that the sphere travels up the ramp in each case:
a) The ramp is frictionless, so the sphere continues to rotate with its initial angular speed until it reaches its maximum height.
b) The ramp provides enough friction to prevent the sphere from sliding, so both the linear and rotational motion stop (instantaneously).
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