n constructing a large mobile, Jude hangs an aluminum sphere of mass 6.0kg from a vertical steel wire 0.50m long and 2.5x10^−3 cm^2 in cross-sectional area. On the bottom of the sphere, he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0kg. For each wire, compute: (a) The tensile strain and

n constructing a large mobile, Jude hangs an aluminum sphere of mass 6.0kg from a vertical steel wire 0.50m long and 2.5x10^−3 cm^2 in cross-sectional area. On the bottom of the sphere, he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0kg. For each wire, compute: (a) The tensile strain and

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.6.7P: A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The...

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A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
The error in a measurement due to strain when using a tape measure depends on the material that it is made of. For a tape with a cross section of 10 mm by 0.7 mm, calculate how much error is introduced in inches into the measurement at a 300 ft length if the tape is pulled with 80 N and if the tape is made of: a) mild steel (E = 30 x 10^6 psi), b) polycrystalline aluminum (E = 10 x 10^6 psi) c) fiberglass composite (E = 3.5 x 10^6 psi in the long direction)
In constructing a large mobile, Jude hangs an aluminum sphere of mass 6.0kg from a vertical steel wire 0.50m long and 2.5 x10−3 cm2 in cross-sectional area. On the bottom of the sphere, he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0kg. For each wire, compute:(a) The tensile strain and(b) The elongation
A rectangular bar is notched on two sides as shown in Fig. 5.9a. The dimensions of the bar are thickness t = 0.2 cm, D = 2 cm, d = 1.8 cm, h = 0.1 cm, and r = 0.15 cm. If an elastic load of 15 kN is applied along the axis of the bar, what is the maximum stress in the vicinity of the notches? If the yield strength of the material is 950 MPa, will the material yield near the notches under this load?
A sample of silicone breast implant, polydimethylsiloxane (PDMS), is placed under unconfined compression. The magnitudes of the resulting longitudinal and transverse strains have been measured to be 2.7 and 1.341, respectively. The young's modulus of the implant is 500 kPa. Calculate the shear and bulk moduli.
An elastic rubber sphere of radius 20mm is pressed upon a rigid sphere of radius 50mm. The Young’s modulus of rubber is 0.1GPa and the Poisson’s ratio is 0.45. If the maximum allowable pressure below the indenter is 10MPa, determine the maximum contact force that we can apply and the corresponding contact radius.
9. A compressive force of 15-N is applied to a flexible poly(vinyl chloride) (CAS# 9002-86-2) wire that is 5-m long and has a diameter of 3.6-mm. If the wire contracts by 0.5-mm, calculate the compressive modulus
A rectangular steel block is 300mm in the x direction, 200mm in the y direction and 150mm in the z direction. The block is subjected to a triaxial loading consisting of three uniformly distributed forces as follows: 250kN tension in the x direction, 320kN compression in the y direction and 180kN tension in the z direction. For steel, v=0.30 and E=200,000MPa. Determine the total strain in the x direction due to the forces applied in the three directions.
A specimen of titanium alloy is tested in torsion and the shear stress–strain diagram is shown in Fig.a. Determine the shear modulus G, the proportional limit, and the ultimate shear stress. Also, determine the maximum distance d that the top of a block of this material, shown in Fig. b, could be displaced horizontally if the material behaves elastically when acted upon by a shear force V. What is the magnitude of V necessary to cause this displacement?
A 100 mm x 100 mm x 100 mm cube made with glass polymers in the y- direction is subjected to a tensile load of 100 kN along the y-direction. However, the cube is constrained against deformation in the x and z directions. Given the following properties: Ex = 20 GPa Ey = 50 GPa Ez = 20 GPa vxy = 0.25 vxz = 0.5 vyz = 0.25 (a) Compute for the change in length of the cube in the y-direction and; (b) Determine the stresses, σx, σy, σz
The data below are for a thin steel wire suitable for use as a guitar string. Ultimate tensile stress: 1.8 x 109 Pa Young Modulus: 2.2 x 1011 Pa Cross-sectional area: 2.0 x 10-7 m2 In a tensile test, a specimen of the wire, of original length 1.5 m, is stretched until it breaks. Assuming the wire obeys Hooke’s law throughout, calculate the extension of the specimen immediately before breaking.
A bar of titanium alloy of length 120mm and square cross – section, 7.5 mm x 7.5 mm, is pulled axially by a force of 15 kN. Find the percentage decrease in thickness if E = 106 GN/m2 and v = 0.33 m/s. V= velocity A bar of aluminum alloy of rectangular section75 mm x 20 mm and 800 mm long is stretched by an axial force of 150 kN. Find the volumetric strain, the actual change in volume and the percentage reduction in cross – sectional area of the bar. Take E = 70 GN/m2 and v = 0.34 m/s.V=velocity