A square plate is 1.8 times 10-2 m thick, measures 3.3 times 10-2 m on a side, a

Question

A square plate is 1.8 times 10-2 m thick, measures 3.3 times 10-2 m on a side, and has a mass of 7.3 times 10-2 kg. The shear modulus of the material is 5.0 times 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 0.87. A force is applied to the top of the plate, as in figure (a). Determine the maximum possible amount of shear stress, the maximum possible amount of shear strain, and 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. the maximum possible amount of shear stress the maximum possible amount of shear strain the maximum possible amount of shear deformation ?X that can be created by the applied force just before the plate begins to move

Explanation / Answer

Maximum Shear stress = F / A

F = 7.3 * 10^-3 * 9.81*0.87

A = 3.3 * 3.3 * 10^-4

a)Max shear stress = 572.11 N/m^2

b)Maximum shear strain = Shear stress / shear modulus = 572.11/ (5*10^10) = 1.144 * 10^-8 m

c)shear strain = delta x / l

delta x = 1.144*10^-8 * 1.8*10^-2 =2.05 8 10^-10 m

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