Which faces of an infinitesimal element (aligned with the cartesian coordinate s

Question

Which faces of an infinitesimal element (aligned with the cartesian coordinate system) can x_1 momentum be transported across? A. The x_2 faces (i.e. the faces perpendicular to the x_2 direction but parallel to the x1 direction) B. The x_3 faces (i.e. the faces perpendicular to the x_3 direction but parallel to the x_1 direction) C. All of the faces D. The x_1 faces (i.e. the faces perpendicular to the x_1 direction) E. The x_2 and x_3 faces (i.e. the faces perpendicular to the x_2 and x_3 directions but parallel to the x_1 direction)

Explanation / Answer

Ans:- D is the ans. As per Cartesian coordinate system is aligned with x1 is momentum of transported across the infinitesimal element. that faces is initial from a linear proportionality of respective normal stress with surface element. that infinitesimal relation is momentum of transport & the component of id direction of cosign

the stress vector is acting on the surface element normal to the coordinate axis x2

dFi = D dAn x2x and also denoted as dF =dA *

so that the stress force dF is effecting on the infinitesimal element area dA. so the directly proportionality factor x2 is stands form the x1-component of the surface force/unit area . so the area is perpendicularto the x2 axis. the infinitesimal element is called a stress tensor. The element is associated with the surfaces are displayed

So that stresses in the (x1 * x2) infinitesimal element plan on the above diagram convention for x3. so we assume we should take different look at all the element surface forces that are exist base on cubical element of the size x1, x2= - X3 . We properly insure here that x3 = 1. so The momentum of transported force on the x2 is constant on a plane is related to x3 is negligible and the tangential force on a plane x1=constant plane in the x2 ,x3 is not constant plan direction. so we prove that the x1 faces ( the face perpendicular to the x1 direction).

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