There is a six-sided die on the next page. a) Draw x-, y-, and z-axes in...

  

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There is a six-sided die on the next page. a) Draw x-, y-, and z-axes in the top-left corner (away from the die) such that Face "3" has a normal +, Face "5" has a normal +, and Face "6" has a normal +2. (Hint: In this perspective, your axes should resemble an upside-down "Y".) b) Six-sided dice have the property that opposite faces add up to 7. So, the unseen Face "1" must be opposite Face "6" and has a normal -2. What are the normal vectors for the remaining two unseen faces, "2" and "4"? The die is dropped into water, which exerts forces (pressure, a.k.a. normal force; and shear force). The die resists the forces with stress, so it doesn't deform. c) Write the stress tensor 7 in matrix form, labeling each element in the 3 3 matrix with one of the nine stress tensor components Tij, i = {x, y, z}, j = {x, y, z}. d) Which of these components corresponds to normal stress? Shear stress? e) On Face "3", Face "5", and Face "6", draw and label an arrow for each of the nine stress tensor components Tij. (Hint: Each of the faces should have three arrows assembling to resemble an upside-down "Y". You can redraw the die without the dots if it helps make the figure less cluttered.) There is a six-sided die on the next page. a) Draw x-, y-, and z-axes in the top-left corner (away from the die) such that Face "3" has a normal +, Face "5" has a normal +, and Face "6" has a normal +2. (Hint: In this perspective, your axes should resemble an upside-down "Y".) b) Six-sided dice have the property that opposite faces add up to 7. So, the unseen Face "1" must be opposite Face "6" and has a normal -2. What are the normal vectors for the remaining two unseen faces, "2" and "4"? The die is dropped into water, which exerts forces (pressure, a.k.a. normal force; and shear force). The die resists the forces with stress, so it doesn't deform. c) Write the stress tensor 7 in matrix form, labeling each element in the 3 3 matrix with one of the nine stress tensor components Tij, i = {x, y, z}, j = {x, y, z}. d) Which of these components corresponds to normal stress? Shear stress? e) On Face "3", Face "5", and Face "6", draw and label an arrow for each of the nine stress tensor components Tij. (Hint: Each of the faces should have three arrows assembling to resemble an upside-down "Y". You can redraw the die without the dots if it helps make the figure less cluttered.)