sigmax = # place your calculation here, equation above sigmax # display sigmax sigmay sigmax sigmaz = # place your calculation here, equation above sigmaz # display sigmaz Python Python Python Python Python Now, let's say you want to repeat the calculation for a different value of z. First, you have to note which formulas involve z. The formulas for pmax and a do not, so they don't have to be recomputed. Start by redefining z to be 0.005. Then, let's recalculate the sigma values:/nU₁₂ Poisson's ratios of the two sphere materials E,,E, Young's moduli of the two sphere materials d,,d, the two sphere diameters This material is adapted from Magrab, et al., An Engineer's Guide to MATLAB, Prentice Hall, 2000, and Shigley and Mischke, Mechanical Engineering Design, 5th Ed., McGraw-Hill, 1989. The dimensions are as follows: d1, d2, a, z: (inches) sigmax, sigmay, sigmaz: (psi) • v1, v2: (dimensionless) • E1, E2: (psi) Let's define values for the 6 parameters listed above plus the F and z input values: v1=0.3 v2=0.3 E1=3e7 E2=3e7/n2. Example Case Study Python is useful in carrying out engineering calculations, as are MATLAB, Mathcad, and Excel. Straight-through calculations occur frequently as a sequence of formulas and case studies calculate sets of results for varying input parameters. In this section, we will first lead you through a careful engineering calculation and case study and then ask you to perform another one on your own. For the next calculation it's not that important for now that you understand the formulas, just be able to compute the results correctly. If you end up in mechanical engineering, this material is in your future. When two spheres are pressed together with a force, F, the principal contact stresses in the x-, y-, and z- directions are described by: σ =σ x - Pmax Z tan a a (2)} (1+0)- 2 (1-2) (1-0) + σ + 3F Pmax E₁ E₂ 3F a=3 Pmax 8 1 1 2πα + where 1+ a d, d₂/n

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sigmax = # place your calculation here, equation above sigmax # display sigmax sigmay sigmax sigmaz = # place your calculation here, equation above sigmaz # display sigmaz Python Python Python Python Python Now, let's say you want to repeat the calculation for a different value of z. First, you have to note which formu