b) 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
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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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b) 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.
c) Figure Q1c shows a bracket on rollers that allow the bracket to move along a beam
in the horizontal direction. A force F₁ of 2625 N acts at point A where the angle
between F, and the x-axis is 100. If force F₂ acts at an angle a = 400 between F2
and the y-axis:
(i)
Determine the magnitude of F2 necessary to maintain bracket on horizontal
equilibrium.
(ii) Determine the vertical force at A acting along the y-axis.
Give your answers to the nearest newton (N) to 2 decimal places.
Assume coplanar forces and assume horizontal rolling is frictionless.
F1
y
α
F2
X
Transcribed Image Text:b) 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. c) Figure Q1c shows a bracket on rollers that allow the bracket to move along a beam in the horizontal direction. A force F₁ of 2625 N acts at point A where the angle between F, and the x-axis is 100. If force F₂ acts at an angle a = 400 between F2 and the y-axis: (i) Determine the magnitude of F2 necessary to maintain bracket on horizontal equilibrium. (ii) Determine the vertical force at A acting along the y-axis. Give your answers to the nearest newton (N) to 2 decimal places. Assume coplanar forces and assume horizontal rolling is frictionless. F1 y α F2 X
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