A square plate is 1.0 ×10^-2 m thick, measures 3.0 ×10^-2 m on a side, and has a mass of 7.2 ×

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A square plate is 1.0 ×10^-2 m thick, measures 3.0 ×10^-2...

A square plate is $1.0 \times 10^{-2} \mathrm{~m}$ thick, measures $3.0 \times 10^{-2} \mathrm{~m}$ on a side, and has a mass of $7.2 \times 10^{-2} \mathrm{~kg}$. The shear modulus of the material is $2.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$. One of the square faces rests on a flat horizontal surface, and the coefficient of static friction between the plate and the surface is $0.90 .$ A force is applied to the top of the plate, as in Figure $10-32 a$. 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 $\Delta X$ (see Figure $10-32 b$ ) that can be created by the applied force just before the plate begins to move.

Key Concepts

Shear Deformation

Shear deformation refers to the displacement or change in position of one part of a material relative to another due to an applied shear force. It is typically quantified by the product of shear strain and a characteristic dimension of the material (such as its thickness), providing a measure of the overall distortion experienced by the material under load.

Shear Modulus

The shear modulus, also known as the modulus of rigidity, is an intrinsic property of a material that relates shear stress to shear strain. It is defined as the ratio of shear stress to shear strain in the elastic (reversible) deformation region, and it provides a measure of the material's resistance to shape changes when subjected to tangential forces.

Static Friction

Static friction is the frictional force that resists the initiation of sliding motion between two surfaces in contact. It is characterized by a coefficient of static friction which, when multiplied by the normal force between the surfaces, gives the maximum friction force available to counteract any applied tangential forces before motion begins.

Shear Stress

Shear stress is defined as the force per unit area acting parallel to the surface of a material. It quantifies how the material responds to forces that tend to cause layers of the material to slide relative to one another, which is essential in understanding material deformation under tangential loads.

Shear Strain

Shear strain is the measure of deformation representing the angular change or displacement between layers of a material when subjected to shear stress. It is a dimensionless quantity that indicates how much a material has deformed from its original shape as a result of an applied tangential force.

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