Your task is to design a light‐weight tie of length L with a circular cross‐ section of radius R. It must carry an axial force F, without stretching by more than δ. You will need to choose the material (with Young’s modulus E and density ρ) and the corresponding cross section radius to suit your choice of material, i.e. R is a “free variable”, a) Show that the extension of the tie is given by δ = FL/AE, where A =

Your task is to design a light‐weight tie of length L with a circular cross‐ section of radius R. It must carry an axial force F, without stretching by more than δ. You will need to choose the material (with Young’s modulus E and density ρ) and the corresponding cross section radius to suit your choice of material, i.e. R is a “free variable”, a) Show that the extension of the tie is given by δ = FL/AE, where A =

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.46P

See similar textbooks

Similar questions

Consider a metal bar of length L, cross-sectional area A, and Young's modulus Y. When a tension force F is applied to the bar, it causes an extension AL. Model the material as a cubic lattice, where the atoms lie at the corners of the cubes and are connected by springs with equilibrium length x. Calculate the force constant k of the atomic springs by deriving expressions for (1) the number of atoms in any cross-sectional area, (2) the number of atoms in a single chain of length L, (3) the microscopic extension Ax between atoms, (4) the tensile force f between atoms, (5) write f = kAr and show that k = Yr, (6) calculate the value of k for a typical metal such as aluminum, for which Y = 70 GN/m² and x = 0.4 nm.
The principal forces at a point p of an elastic body are o(¹)-50N/cm², o(2)=-50N/cm² and 3)-75N/cm². Find the stress vector t(n), the normal stress on, and the shear stress or for a plane that is equally inclined with respect to the principal axes. P B
The strain components εx, εy, and γxy are given for a point in a body subjected to plane strain. Determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle θp, the principal strain deformations, and the maximum in-plane shear strain distortion on a sketch. εx = -750 με, εy = -345 με, and γxy = 1250 μrad. Enter the angle such that -45°≤θp≤ +45°.
A 8-mm-thick rectangular alloy bar is subjected to a tensile load P by pins at A and B, as shown in the figure. The width of the bar is w = 35 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: & = 740 με and ε,- -270 με. (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 16 kN, what is the modulus of elasticity for this specimen? P B Answers: (a) v= i (b) Е- i GPa
Problem 11: Suppose a vertebra is subjected to a shearing force of 540 N.Randomized Variablesf = 540 Nh = 2.9 cmd = 4.3 cm Find the shear deformation in m, taking the vertebra to be a cylinder 2.9 cm high and 4.3 cm in diameter. The shear modulus for bone is 80 • 109 N/m2.
Task 8. Consider a unit cube of an isotropic solid occupying the region 0≤ x ≤ 1, 0≤ y ≤ 1, 0≤ Z ≤1. After loads are applied the displacements are given by u = ax v = By w = 72. a) Sketch the deformed shape for a = = 0.01, 3 = 0.01, y = -0.01. b) Find the volume change (the difference between the volume after de- formation and the original volume) for this unit cube.
The strain components εx, εy, and γxy are given for a point in a body subjected to plane strain. Using Mohr’s circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle θp, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch.εx = 0 με, εy = 350 με, γxy = 210 μrad. Enter the angle such that -45° ≤ θp ≤ +45°.
I need help with part B please. Thank you! In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 km and the pressure is 1.16×10^8 Pa, (about 1150 atmospheres). (A) If a cubic meter of water is taken to this depth from the surface (where the normal atmospheric pressure is about 1.0×10^5 Pa), what is the change in its volume? Assume that the bulk modulus for seawater is the same as for freshwater 2.2×10^9 Pa. Answer: -5.3E-2 m^3 (B) At the surface, seawater has a density of 1.03×10^3 kg/m^3. What is the density of seawater at the depth of the Challenger Deep? Express your answer in kilograms per cubic meter.
PROBLEM #1: A vertical force P = 20 lb is applied to the ends of the 2-ft cord AB and spring AC. If the spring has an unstretched length of 2 ft. Take k = 25 lb/ft. (see picture for illustration). Determine the: (a) forces (b) angle theta for equilibrium Note: Kindly show the complete step-by-step solution. Please make sure that your handwriting is understandable and the picture of the solution is clear. I will rate you with “like/upvote” after. I need the answer right away, thank you.
It has been suggested that a power law: dun -b dr be used to characterize the relationship between the shear stress and the velocity gradient for blood. The quantity b is a constant, and the exponent is an odd integer. A derivation of the velocity profile equation is attached. Use MATLAB to Plot several velocity distributions (all in one plot) (V/Vmax versus r/R) for n-0.1, 0.3,0.5, 0.7, 1, 3, 5, 7 to show how the profile changes with nt. The submitted file must be in a pdf format and must include: Cover page: Student(s) names and Student(s) numbers. Matlah, Code Matlab plot: the plot must have all details such as: axes names, unit, legends...th Discussion: Explanation of the obtained result, showing the differences in velocity profile for Newtonian, shear thickening, and shear thinning fluids.
For a LEHI material, the principal plane stresses and associated strains in a plane at a point are o,=36 ksi, 02=16 ksi, ɛ1=1.02 x 103, and E2=0.18 x 103. Determine the Young's modulus and Poisson ratio of the material. Hint: use the equations for principal stress for 2D plane stress for LEHI, and consider 02/01.
Prob. 4.4-6. (a) determine the maximum tensile stress, the maximum compressive stress, and the maximum shear stress; and (b) show the stresses determined in Part (a) on properly oriented stress elements (e.g., see Fig. 4.14). In solving these problems, make the sense of the stresses consistent with the sense of the torque T shown on the generic torsion member figure. T= 400 N m, d = 40 mm, and d = 0₁ 32 mm. =relative twist angle 45° (b) FIGURE 4.14 A pure- shear element, and the associ- ated maximum-normal-stress element.