2. Fig. 2 shows a solid sphere of mass 2 kg and a massless string of total length 4 meters which is wrapped around the equator of the sphere (total length includes the length of wrapped string and the length of the string hanging from the ceiling). The sphere then falls vertically while rolling down (without slipping) the whole wrapped string and falls on top of an inclined plane. Due to the collision with the inclined plane, it loses all its kinetic energy within a very short time and starts rolling along the inclined plane with zero initial velocity. Consider that a total of 10 Joules of energy is lost during the motion of the sphere along the planes. The magnitude of gravitational acceleration g = 9.8 m/s². 1 m 3 m 2 m 30 Fig. 2 (a) Find the value of the moment of inertia of the sphere about its axis of rotation. (b) inclined plane? What is the magnitude of angular velocity of the sphere when it touches the (c) How far along the second inclined plane (45°) on the right will the center of the sphere travel before it comes to a stop?

2. Fig. 2 shows a solid sphere of mass 2 kg and a massless string of total length 4 meters which is wrapped around the equator of the sphere (total length includes the length of wrapped string and the length of the string hanging from the ceiling). The sphere then falls vertically while rolling down (without slipping) the whole wrapped string and falls on top of an inclined plane. Due to the collision with the inclined plane, it loses all its kinetic energy within a very short time and starts rolling along the inclined plane with zero initial velocity. Consider that a total of 10 Joules of energy is lost during the motion of the sphere along the planes. The magnitude of gravitational acceleration g = 9.8 m/s². 1 m 3 m 2 m 30 Fig. 2 (a) Find the value of the moment of inertia of the sphere about its axis of rotation. (b) inclined plane? What is the magnitude of angular velocity of the sphere when it touches the (c) How far along the second inclined plane (45°) on the right will the center of the sphere travel before it comes to a stop?

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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Concept explainers

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.

Question

2. Fig. 2 shows a solid sphere of mass
2 kg and a massless string of total
length 4 meters which is wrapped
around the equator of the sphere (total
length includes the length of wrapped
string and the length of the string
hanging from the ceiling). The sphere
then falls vertically while rolling down
(without slipping) the whole wrapped
string and falls on top of an inclined
plane. Due to the collision with the
inclined plane, it loses all its kinetie
energy within a very short time and
starts rolling along the inclined plane with zero initial velocity. Consider that a total of 10 Joules
of energy is lost during the motion of the sphere along the planes. The magnitude of gravitational
acceleration g = 9.8 m/s².
1 m
3 m
2 m
30
Fig. 2
(a)
Find the value of the moment of inertia of the sphere about its axis of rotation.
(b)
inclined plane?
What is the magnitude of angular velocity of the sphere when it touches the
(c)
How far along the second inclined plane (45°) on the right will the center of the
sphere travel before it comes to a stop?

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