Problem 2. The tensors a and b, are specified by: Determine the following quantities: (a) aiibjbj (b) bmanm (c) aijaipajp aij ГО 1 0 2 = 1 LO 07 1 1 b₁ = 2
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- Transforming the coordinates of the shear stress from cartesian to spherical coordinate system allows to better visualize the dynamics of the tensor on a spherical geometry. True or FalseThe following are stress and strain tensors at any point. Determine the principalstresses or strains and the maximum shear stress or strain at the point.The stress tensor below is given for x, y, z coordinate system. Find the stress tensor if x, ycoordinates are rotated 45° clockwise.[?] = 4 1 2 1 6 0 2 0 8
- The stress tensor at a point is given below. Determine: a) All principal stresses. b) Unit normal vectors in all principal directions. c) The maximum shear stress. d) 3D Mohr's circle with calculations and labelling key values.Show with tensors and in three-dimensional space that all directions are principal axes for the stress state at a point where τ1=τ2=τ3How would the last part of this problem be solved (finding the magnitude of the resultant vector in terms of the two constants given the normalizing term n)?
- 2.) We are on the space station, so there is no effective gravity. In a small fluid experiment, a small spherical bacteria of 1 mm radius is moving at a speed of +1.50 mm/second horizontally in the fluid. The bacteria has a density of 1500. kg/m^3. (3a) Draw a free-body diagram, labeling all forces and show the likely direction of Fnet (3b) What is the mass of the bacteria? (3c) If the value of the viscosity is 1.25 kg/m/s, then what is the net acceleration experienced by the bacteria at that moment.A tank is filled with fluid under prcssurc anti the prcssurc gauge fixcd at the top indicatcs a prcssurc of 21 kPa. The curved surfacc of the top is quarter of a circular part of radius 2.6 m. calculate the magnitude (N) and direction (degree) of the resultant force on the cun'ed surface. (p=950kg./m³for fluid)The surface tensions of mercury and water at 60 degrees Celcius are 0.47N/m and 0.0662 N/m, respectively. What capillary height changes will occur in these two fluids when they are in contact with air in a glass tube of radius 0.30mm? Use θ = 130° for mercury, and 0° for water; y = 132.3 kN/m3 for mercury and 9.650 kN/m3 for water. Provide the given along with its solution.