Problem #4 The figure below shows two collars having masses mi and m2. The collar having mass m2 is free to slide without friction only in the vertical direction which the collar having mass mi is free to slide without friction only in the horizontal direction. m, L Figure for Problem #4 Both collars are connected by a rigid hinged rod of mass m and length L and the horizontally moving collar is connected to a spring having stiffness constant k. The spring is at its natural length when m; is either directly above or directly below m. so that in the figure, the spring is stretched by an amount x beyond its natural length. Use the principle of virtual work to determine all possible static equilibrium points for all possible values of mi, m2, m, L, k and g. That is, consider both cases when (2m2 + m)g 2kL (2m2 + m)g. 2kL > 1 and < 1. Assume that the horizontal rail and the spring is not in the way of m2 so that m2 can fall below the horizontal rail.

Problem #4 The figure below shows two collars having masses mi and m2. The collar having mass m2 is free to slide without friction only in the vertical direction which the collar having mass mi is free to slide without friction only in the horizontal direction. m, L Figure for Problem #4 Both collars are connected by a rigid hinged rod of mass m and length L and the horizontally moving collar is connected to a spring having stiffness constant k. The spring is at its natural length when m; is either directly above or directly below m. so that in the figure, the spring is stretched by an amount x beyond its natural length. Use the principle of virtual work to determine all possible static equilibrium points for all possible values of mi, m2, m, L, k and g. That is, consider both cases when (2m2 + m)g 2kL (2m2 + m)g. 2kL > 1 and < 1. Assume that the horizontal rail and the spring is not in the way of m2 so that m2 can fall below the horizontal rail.

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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Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.

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Problem #4
The figure below shows two collars having masses m1 and m2. The collar having mass m2
is free to slide without friction only in the vertical direction which the collar having mass
mi is free to slide without friction only in the horizontal direction.
m, L
Figure for Problem #4
Both collars are connected by a rigid hinged rod of mass m and length L and the
horizontally moving collar is connected to a spring having stiffness constant k. The spring
is at its natural length when m; is either directly above or directly below m1. so that in the
figure, the spring is stretched by an amount x beyond its natural length. Use the principle
of virtual work to determine all possible static equilibrium points for all possible values of
m1, m2, m, L, k and g. That is, consider both cases when
(2m2 + m)g , 1
2kL
(2m2 + m)g < 1.
2kL
and
Assume that the horizontal rail and the spring is not in the way of m2 so that m2 can fall
below the horizontal rail.

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