3) A hinge is a double constraint which restraints: a) a translation and a rotation in the plane; b) a rotation in the plane; c) two translations in the plane. 4) The Mohr's arbelos is the region in the plane of the special stress components σ- which defines: a) all and the only possible stress states in the neighborhood of a point of a continuum, at varying normal vector in that point; b) among the possible stress states defined in the neighborhood of a point of a continuum, only those which are principal; c) all the possible stress states in the neighborhood of a point of a continuum for which the stress tensor is diagonal. 5) The first invariant of the stress tensor is a measure of: a) the volume deformation about a point of a body; b) the deviatoric component of the stress tensor in a point of a body; c) the average normal stress component in a point of a body.

For the machine element shown, locate the y coordinate of the center of gravity.

Compute the line energy of dislocation in fcc, diamond. The shear modulus of carbon is 462 GNm 2. The diameter of carbon atom in diamond is 1.54Å. Answer: 1.46 x 10-3J/m

Prob. 4.4-6. (a) determine the maximum tensile stress, the maximum compressive stress, and the maximum shear stress; and (b) show the stresses determined in Part (a) on properly oriented stress elements (e.g., see Fig. 4.14). In solving these problems, make the sense of the stresses consistent with the sense of the torque T shown on the generic torsion member figure. T= 400 N m, d = 40 mm, and d = 01 32 mm. =relative twist angle 45° (b) FIGURE 4.14 A pure- shear element, and the associ- ated maximum-normal-stress element.

Give me the right solution, Strictly avoid Ai answer.

In the methane molecule, CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the C-H is in the direction of and an adjacent C-H bond is at the direction . results to an angular bond of approximately 109o for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A = 0.93i + 0.91j + 1.09k B = 1.02i + -0.99j + -1.08k

suppose S and T are infinite sets and Φ : S→T is a function that is not onto have S and T the same cardinality? prove (use mapping)

During a dunk, a basketball player will elevate theircenter of mass 70 cm (or more) while jumping off of one leg. What is the strain energy contribution to the energy required to elevate the center of mass given the following parameters? How much energy has to be contributed by active muscle contraction? mass = 82 kg, K leg = 35000N/m, dispacement = 0.11 m.

A high-carbon steel with a fully pearlitic microstructure was used to form a high-strength bolt (H.-C. Lee et al., J. Mater. Proc. Tech. 211, 1044 (2011)). It was found that the bolt head had an average interlamellar spacing of 257 nm whereas the average spacing in the body of the bolt was 134 nm. Assuming that dislocation pileup is the primary mechanism responsible for the strength of this alloy, what ratio of strength (or hardness) might be expected in the head and body of the bolt?