A square rod of length L 0 = 2.35m and sidelength d = 6.58cm is compressed with

Question

A square rod of length L0 = 2.35m and sidelength d = 6.58cm is compressed with a force of |Fc| = 87.8N in the direction of the long axis. (a) What is the magnitude of the scalar tensile stress? (b) If we assume that the area of the square rod is approximately constant and its final resting length is L = 2.25m, then what is the Young's modulus of the square rod? Now assume that the rod is stuck between two slabs that are separated by the sidelength of the rod. (c) What is the shear stress when the magnitude of the force of the top slab on the square rod in the direction of the long axis of the rod is |Fs| = 72.8N? (d) If the total distance that the top of the rod moved, as compared to the bottom of the rod, is ?x = 0.204cm, then what is the shear modulus of the rod in this geometry?

Explanation / Answer

a) tensile stress = F/A = 87.8/ 4.3*10^-3=20278.8 pa

b) Y= stress/strain = 20278.8/ (0.1/2.35) = 476551.8 pa

c) shear stress = F/A

A= 2.35 *0.0658 = 0.154

shear stress= 72.8/0.154 =470.8 pa

d) shear modulus = F/ shear strain

shear strain = distance moved bt the slab/ distance between the slab = 0.031

shear modulus = 2348.1 pa

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