A copper cube measures 6.40 cm on each side. The bottom face is held in place by

Question

A copper cube measures 6.40 cm on each side. The bottom face is held in place by very strong glue to a flat horizontal surface, while a horizontal force F is applied to the upper face parallel to one of the edges. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Shear stress and strain. Show that the glue exerts a force F on the bottom face that is equal but opposite to the force on the top face. How large must F be to cause the cube to deform by 0.190 mm? If the same experiment were performed on a load cube of the same size as the copper one, by what distance would it deform for the same force as in part B?

Explanation / Answer

(a)

Condition , For the block not to move,

the net force on the block must zero.

so, the glue exerts a force F on the bottom face that is equal but opposite to the force on the top face.

(b)

We know that,

shear stress = F/ A = F / (0.064)^2

shear stress = 244.14*F

shear strain = deformation / length = 0.190*10^(-3) / 0.064

strain = 0.002968

We also know that,

shear strain = shear stress / shear modulus

0.002968 =  244.14*F / 48*10^9

F = 5.84*10^5 N

(c)

For the lead cube

shear modulus = 5.6*10^9 Pa

shear stress = 5.84*10^5 / (0.064)^2 =1425.78*10^5

shear modulus = shear stress / shear strain

5.6*10^9 = 1425.78*10^5 / strain

strain = 0.02546

shear strain = deformation / length

0.02546 = deformation / 0.064

deformation = 1.63 mm

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