Two forces of the same magnitude 46 106 N but with opposite direction are applie

Question

Two forces of the same magnitude 46 106 N but with opposite direction are applied to parallel faces of a metal block as shown in the Active Figure. The shear modulus of the block is S = 9 1010 N/m2. The two faces that sustain the shearing force are a distance h = 0.10 m apart, and have cross-sectional area A = 0.020 m2. Find the value of the displacement x between the edges of the block. Conceptualize The forces applied along opposite faces of the block result in a distortion of the block that is similar to the deformation you can observe in a book when it is pushed on its upper surface across a table top, as illustrated in the Active Figure. Categorize The problem asks for the temporary change in shape from applying a force. It is a problem of the elastic properties of solids. Analyze The relation between the force applied per unit area and the displacement x that it produces divided by the fractional separation of the two faces is S = F/A x/h or equivalently S = hF Ax which can be rearranged to give the desired displacement: x = m.

Explanation / Answer

F = 46*10^6 N
S = 9*10^10 N/m^2
h = 0.1 m
A = 0.02 m^2
dx = ?
now, phi = dx/h
and
S = F*h/A*dx
hence
9*10^10 = 46*10^6*0.1/0.02*dx
dx = 2.5555 mm

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