(19%) Problem 8: A thin cylindrical ring starts from rest at a height h,-86 m. T
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(19%) Problem 8: A thin cylindrical ring starts from rest at a height h,-86 m. The ring has a radius R = 48 cm and a mass M-9 kg R: ©theexpertta.com 20% Part (a) Write an expression for the ring's initial energy at point l assuming that the gravitational potential energy at point 3 is zero 20% Part (b) If the ring rolls (without slipping) all the way to point 2 what is the ring's energy at point 2 in terms of h2 and Grade Summary 0% 100% Potential 4 5 6 1 2 3 Attempts remaining: 5 (4%per attempt) detailed view 0 END DELCLEAR Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: 4 Feedback: 2% deduction per feedback. 20% Part (c) Given h,-38 m, what is the velocity of the ring at point2 in m/s? 20% Part (d) What is the ring's rotational velocity in rad/s? 20% Part (e) After passing point 2 the hill becomes frictionless and the ring's rotational velocity remains constant. What is the linear velocity of the ring at point 3 in m/s?Explanation / Answer
(B) TE = PE + KE
= m g h2 + m v2^2 /2 + I w^2 /2
= M g h2 + M v^2 /2 + ( M R^2)(v2/R)^2 /2
= M g h2 + 3 M v2^2 / 4
(C) Applying energy conservation,
9 x 9.81 x 86 =9 x 9.81 x 38 + 3 x 9 x v^2 / 4
v2 = 25 m/s
(D) w =v2 /r = 52.2 rad/s
(E) M x 9.81 x 86 = M v^2 /2 + M x 25^2 / 4
v = 37 m/s
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