A thin hollow cylinder rolls without slipping from an inclined plane forming an angle 0 = 30° with the horizontal plane. At time t3D0, the cylinder is at rest and its center of mass is at height h = 2.5 m above the bottom of the incline. The axis of rotation of the cylinder is orthogonal to the incline. The cylinder has mass M = 4 kg, length L and a cross-sectional radius R<

A thin hollow cylinder rolls without slipping from an inclined plane forming an angle 0 = 30° with the horizontal plane. At time t3D0, the cylinder is at rest and its center of mass is at height h = 2.5 m above the bottom of the incline. The axis of rotation of the cylinder is orthogonal to the incline. The cylinder has mass M = 4 kg, length L and a cross-sectional radius R<

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

A thin hollow cylinder rolls without slipping from an inclined plane forming an angle 0 = 30° with the horizontal plane. At time t=0, the cylinder is at rest and
its center of mass is at height h = 2.5 m above the bottom of the incline. The axis of rotation of the cylinder is orthogonal to the incline. The cylinder has
mass M = 4 kg, length L and a cross-sectional radius R<<h. Find: (a) The velocity of the cylinders' center of mass as it reached the bottom of the incline; (b)
The rotational kinetic energy of the cylinder at the bottom of the incline; (c) Consider, now, a point particle sliding down the same incline, with initial velocity
Vin=0 and height yin=h. If the velocity of the point particle at the bottom of the incline is the same as that found for the cylinder's center of mass in part (a),
what is the value of the coefficient of kinetic friction? (Hint: in this problem, you can approximate g = 10 m/s?).

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