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 θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if : 1- the ramp is frictionless, so the sphere continues to rotate with its initial angular speed until it reaches its maximum height. → I used : Ki+Ui=Kf+Uf and concluded that Ki=7/10* m*v² =mglsinθ so l = (7/10 *m*v²)/(mg*sinθ). is it true ? 2- the ramp has enough friction to prevent the sphere from sliding so that both the linear and rotational motion stop (instantaneously). → I concluded the same as the first case : means l = (7/10 *m*v²)/(mg*sinθ). is it correct ?