A specimen of aluminum having a rectangular cross section 9.9 mm * 12.4 mm (0.3898 in. * 0.4882 in.) is pulled in tension with 35900 N (8071 lbf) force, producing only elastic deformation. The elastic modulus for aluminum is 69 GPa (or 10 * 106 psi). Calculate the resulting strain.

Question

Physics

Johanna Fitzgerald

14 February, 01:22

A specimen of aluminum having a rectangular cross section 9.9 mm * 12.4 mm (0.3898 in. * 0.4882 in.) is pulled in tension with 35900 N (8071 lbf) force, producing only elastic deformation. The elastic modulus for aluminum is 69 GPa (or 10 * 106 psi). Calculate the resulting strain.

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Kai · Answer 1

Given:

Dimensions:

Length, l = 9.9 mm

= 0.0099 m

Width, w = 12.4 mm

= 0.0124 m

Force, f = 35900 N

Young modulus, E = 69 GPa

= 6.9 * 10^10 Pa

Young modulus, E = stress/strain

Stress = force/area

Area of a rectangle = length, l * width, w

= 0.0099 * 0.0124

= 1.2276 * 10^-4 m^2

Therefore,

Strain = stress/young modulus

= (35900/1.2276 * 10^-4) / 6.9 * 10^10

= 4.24 * 10^-3 m/m

= 0.00424 m/m