4.14. The system illustrated in Figure 4.26 is comprised of a board of length / with uniform mass per unit length of p. It sits on top of two counter-rotating cylinders, which are rotating with an angular velocity of w in the directions indicated and are separated by a distance 1/2. You may assume that w is large enough that the points of contact between the board and cylinders are always slipping and that the coefficient of dynamic friction between the board and cylinders is u. If the board is not centered on the two cylinders, then the normal force will be greater on the side to which it is displaced because more of the weight of the board will be supported on that side. For example, in the figure, the normal force between the board and cylinder will be greater at the left cylinder, and this will cause a net force to the right. Let x denote the distance that the center of the board is displaced from the center of the two cylinders, as is illustrated in the figure, and determine the differential equation for this system. Solve it if x(0) = 1/8 and x(0) = 0.

4.14. The system illustrated in Figure 4.26 is comprised of a board of length / with uniform mass per unit length of p. It sits on top of two counter-rotating cylinders, which are rotating with an angular velocity of w in the directions indicated and are separated by a distance 1/2. You may assume that w is large enough that the points of contact between the board and cylinders are always slipping and that the coefficient of dynamic friction between the board and cylinders is u. If the board is not centered on the two cylinders, then the normal force will be greater on the side to which it is displaced because more of the weight of the board will be supported on that side. For example, in the figure, the normal force between the board and cylinder will be greater at the left cylinder, and this will cause a net force to the right. Let x denote the distance that the center of the board is displaced from the center of the two cylinders, as is illustrated in the figure, and determine the differential equation for this system. Solve it if x(0) = 1/8 and x(0) = 0.

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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Question

4.14. The system illustrated in Figure 4.26 is comprised of a board of length / with
uniform mass per unit length of p. It sits on top of two counter-rotating cylinders,
which are rotating with an angular velocity of @ in the directions indicated and
are separated by a distance 1/2. You may assume that is large enough that the
points of contact between the board and cylinders are always slipping and that the
coefficient of dynamic friction between the board and cylinders is μ.
If the board is not centered on the two cylinders, then the normal force will be
greater on the side to which it is displaced because more of the weight of the board
will be supported on that side. For example, in the figure, the normal force between
the board and cylinder will be greater at the left cylinder, and this will cause a net
force to the right.
Let x denote the distance that the center of the board is displaced from the center
of the two cylinders, as is illustrated in the figure, and determine the differential
equation for this system. Solve it if x(0) = 1/8 and x(0) = 0.
μ
72
@
Fig. 4.26 System for Exercise 4.14.
1/1/2
g
3
Р
и

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