A 1.25 m long cable has a diameter 3.50 mm with a Young's Modulus, E, of 9.75 x 10⁹ N/m². When the wire is placed under tension, it experiences a stress of 202.52 x 106 N/m², the length of the cable extends by 36.35 mm. Calculate the force that the cable experiences under tension and the strain energy density (U/V) due to deformation. Give your answers in newtons (N) to 2 decimal places for the force; and in joules per cubic metre (J/m³) for the strain energy density to 2 decimal places. Assume the cable is solid and the material is homogeneous.

A 1.25 m long cable has a diameter 3.50 mm with a Young's Modulus, E, of 9.75 x 10⁹ N/m². When the wire is placed under tension, it experiences a stress of 202.52 x 106 N/m², the length of the cable extends by 36.35 mm. Calculate the force that the cable experiences under tension and the strain energy density (U/V) due to deformation. Give your answers in newtons (N) to 2 decimal places for the force; and in joules per cubic metre (J/m³) for the strain energy density to 2 decimal places. Assume the cable is solid and the material is homogeneous.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.6.13P: A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean...

See similar textbooks

Similar questions

A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?
A light wire 1.75 m long has a cross-sectional area of 2.3 mm². It is hung vertically and stretches 0.31 mm when a 10.0 kg block is attached to it. Find the stress, the strain and the Young's modulus for the wire. Take the acceleration due to gravity to be 9.80 ms Give your answers correct to two significant figures. Stress = MPa. Strain = Young's modulus = GPa.
A rectangular block is 7 cm long in the x-direction, 5 cm in the y-direction, and 9 cm long in the z-direction. The block is subjected to a triaxial loading of three uniformly distributed forces as follows: 15 kN in the x- direction, 21 kN in the y-direction, and 18 kN in the z-direction. Calculate the strain in the direction y if Poisson's ratio v = 0.30 and having a modulus of elasticity of E = 150 GPa. y 7 cm 9 cm 21 kN 15 kN 5 cm 18 kN
Use the principle of Strain energy due to direct stresses strength of materials 2
2. The tires of an agricultural tractor shown below are assumed to be 25 cm wide for the front tires and 40 cm at the rear tires. Ground contact of each tire is 15 cm. Calculate the compressive stress between each tire and the ground surface. Weight = 2,500 kg 15 cm 1.3m Point A 2.2 m 2R 2F
A wire 2 m long and 2 mm in diameter, when stretched by weight of 8 kg has its length increased by 0.24 mm. Find the stress, strain and Young’s modulus of the material of the wire. (Note: g = 9.8 m/s2). Answers: (2.5 x 107 N/m2, 1.2 x 10-4 m/m, 2.08 x 1011 N/m2)
A steel plate is subjected to a state of plane stress (E = 200 GPa and v = 0.29) of Oxx = 105 MPa, Oyy = -19 MPa and Oyy = 96 MPa. Calculate the axial strain, ɛ77, at this point in the z direction, normal to the plate's surface. Provide your answer in microstrain, pɛ. You do not need to type the units.
A solid bar of length L = 4 m and diameter 200 mm is heated from 20 to 320 degrees celsius and restrained between two solid immovable walls. Young's modulus of the material is 90 GPa and the coefficient of thermal expansion is 22 x 10-6/°C. →Calculate the thermal strain, e, in micro-strain correct to two decimal places. micro-strain. Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places. E: σ: MPa. Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places: F MN. L
prove that : TL strain Energy = 2 %3D -x Volume 4G %3D 2GJ
After a fall, a 98 kg rock climber finds himself dangling from the end of a rope that had been 17 m long and 9.8 mm in diameter but has stretched by 3.1 cm. For the rope, calculate (a) the strain, (b) the stress, and (c) the Young's modulus. (a) Number i Units This answer has no units (b) Number i Units N/m^2 or Pa (c) Number i Units N/m^2 or Pa > >
One spring is placed inside the other, not touching each other, and compressed between a pair of parallel plates until the distance between the plates is 40 mm. Make a neat detailed sketch of the spring and plate assembly. If G = 83 GPa for both springs, calculate the following: 1. The force applied to the spring assembly. 2. The shear stress induced in each spring. 3. The total strain energy stored in the spring assembly. 4. The stiffness of each spring. 5. The equivalent stiffness of a single spring that can be substituted in place of these springs.
The figure shows the stress-strain curve for a rectangular steel test piece in tension. The test piece is loaded up to point B and then released. If the test piece was originally 58.9 mm long, estimate its new length (in mm) after it is released? State your answer in mm without including the units. Stress (MPа) Elastic Inclastic strain strain 473 - В 408 - 340 272 - Unload 204 - Reload 136 - Plastic Elastic 68 - deformation recovery 0.0020 0.0060 0.0100 0.0000 0.0040 0.0080 0.0120 Strain (mm/mm) Answer: