Question

Please answer the following questions with work provided!

The elastic, shear and bulk moduli of steel are E = 200 GPa, G = 79.3 GPa and B = 140 GPa, respectively. Suppose you have a cylinder of steel which is 5 cm in radius and 10 cm high.

A) What is the cross sectional area of the cylinder? a) 0.00785 m2 b) 78.5 m2 c) 0.00785 cm2 d) 0.314 m2 e) 0.0025 m2

B) What is the volume of the cylinder? a) 0.000785 cm3 b) 7.85 m3 c) 0.000785 m3 d) 0.0314 m3 e) 0.00025 m3

C) If we apply shear deformation, What force is required to distort the cylinder by 0.1 mm? a) 500 MPa b) 198 KPa c) 1.10 MPa d) 1.57 MPa e) 623 KPa

D) If we apply deformation of a solid (compression) What force is required to distort the cylinder by 0.1 mm? a) 500 MPa b) 198 KPa c) 1.10 MPa d) 1.57 MPa e) 623 KPa

E) Finally, we submerge the cylinder in a high pressure fluid. What pressure is required to shrink the cylinder's volume by 0.36%? a) 500 MN b) 198 kN c) 1.10 MN d) 1.57 MN e) 623 kN

Answer 1

A) The cross sectional area of cylinder=

B)Volume of cylinder=

C) Shear modulus

Therefore

This is the force required to distort the cylinder by 0.1mm.

D)Bulk Modulus

Also

=1.1 MN.

E)We have .

Therefore