A square plate is 2.2 × 10 -2 m thick, measures 3.4 × 10 -2 m on a side, and has

Question

A square plate is 2.2 × 10-2 m thick, measures 3.4 × 10-2 m on a side, and has a mass of 7.2 × 10-2 kg. The shear modulus of the material is 2.6 × 1010 N/m2. One of the square faces rests on a flat horizontal surface, and the coefficient of static friction between the plate and the surface is 0.83. A force is applied to the top of the plate, as in Figure (a). Determine (a) the maximum possible amount of shear stress, (b) the maximum possible amount of shear strain, and (c) the maximum possible amount of shear deformation ?X (see Figure (b)) that can be created by the applied force just before the plate begins to move.

Explanation / Answer

a) shear stress = F / A

= (7.2 * 10-2 * 9.8 * 0.83) / (3.4 * 10-2 * 3.4 * 10-2) = 506.61 N/m2

b) shear strain = stress / shear modulus

= 506.61 / (2.6 * 1010) = 1.95 * 10-8 m

c) delta x = strain * l

= 1.95 * 10-8 * 2.2 * 10-2 = 4.28 * 10-10 m

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