BSL uses the sign convention that Tij has a positive value if i) the force by the surroundings acting on the surface with outward normal - points in the + direction, or ii) the force by the surroundings acting on the surface with outward normal + points in the - direction. And Tij has a negative value if i) the force by the surroundings acting on the surface with outward normal + points in the + direction, or ii) the force by the surroundings acting on the surface with outward normal - points in the- direction. Note that a force in a negative direction is considered a negative force, and a force in the positive direction is considered a positive force. In the derivation of the motion equation we did in class (9/21/23), we drew the arrows so the x-directional forces were all considered to be "IN" terms in the force balance, but the definition of "IN" got confusing. Let's do the same example but with a different approach and see that we get the same results. Let's draw all forces pointing in the + direction. a) Draw a diagram of a differential volume cube centered at (xo, yo, Zo) with dimensions Ax, Ay, Az. Label each face (left, right, bottom, top, back, front) with its outward normal (, +, , +, -2, +2), and draw appropriate axes. d) What is its outward normal? e) For a + direction force, will tij be positive or negative? f) Let's figure out the magnitude of the force. F; = TijAi, where Tij is the stress and A{ is the area with normal i. Calculate Tij|surface, doing a first-order Taylor expansion from Tij at (xo, Yo, Zo). Then calculate the area with the cube's dimensions. g) Let's adjust the direction of the force if necessary, based on (d). Do we need to multiply with a negative sign? h) Repeat (b)(f) for the other five faces. (You can just show the final results for each face).