A solid spherical ball of mass 2.74 kg and radius 0.15 m rolls along a smooth, l

Question

A solid spherical ball of mass 2.74 kg and radius 0.15 m rolls along a smooth, level surface with a speed of 2 m/s. The ball rolls up an inclined plane. How far up the plane does the ball go? Express your answer as the vertical height from the level surface

Explanation / Answer

(a) If the surface is frictionless:- =>Let the block go L meter up the plane =>The vertical height (h) gained by the block = Lsin22* =>By the law of energy conservation =>PE(gained) = KE(initial) =>mgh = 1/2mv^2 =>2g x Lsin22* = v^2 =>L = v^2/[2gsin22*] =>L = (3)^2/[2 x 9.8 x 0.37] =>L = 1.23 m (b) By v = u -at =>0 = 3 - gsin22* x t =>t = 3/[9.8 x 0.37] =>t = 0.81 sec =>Total time to return to its starting point (T) = 2 x t = 2 x 0.82 = 1.64 sec

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