A 10 kN falls 30 mm on a collar rigidly attached to a vertical rod of 4 m long and section of 1000 mm². Find the instantaneous ex- tension of the bar. Use E = 210 GPa.
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- A torsion dynamometer is fitted on a turbine shaft to measure the angle of twist. It is observed that the shaft twists 1.5° in a length of 5 metres at 500 r.p.m. The shaft is solid and has a diameter of 200 mm. If the modulus of rigidity for the shaft material is 85 GPa, find the power transmitted by the turbine.A spring sustains 200 ft-lb of energy with a deflection of 3’’. Assume that the mean coil diameter is 7 times the wire diameter and that the allowable stress is 100ksi. Determine the wire diameter.A round, prismatic steel bar (E = 210 GPa) of length L = 2000 mm and diameter d = 15 mm hangs vertically from a support at its upper end (Figure on right). A sliding collar of weight W drops from a height h = 150 mm onto the flange at the lower end of the bar without rebounding. Assume W is given in Newton by W = 289. Calculate the maximum elongation of the bar due to the impact.
- A beam of mass Mv = 40 kg and length L = 3.0 m is attached to a hinge in the vertical wall. On the bar there is a block, of mass mb = 10 kg, which can be in different positions “x” on the wall. The cable that secures the end of the bar to the upper horizontal slab makes an angle θ = 45o with the bar, that is, with the horizontal (Figure).a) What are the minimum and maximum tensions in the cable as the block moves along the beam?b) If the block is at the center of the beam, what force will the hinge exert?A close-coiled helical spring is subjected to an axial pull of 600 N. The spring is made out of a 16 mm diameter rod, and has 12 complete coils, each of mean diameter 120 mm. Compute shear stress induced in the rod and the deflection under the pull. Take G = 0.85 x 105 N/mm^2.A closed-coil helical spring is to have stiffness of 900 N/m in compression with a maximum load of 45 N and a maximum shearing stress of 120 N/mm2.The length of the spring is 45 mm. find the wire diameter, mean coil radius and the number of coils. Take C= 40000 N/mm2
- a machine mass m = 500 kg is mounted on a simply supported steel beam of length l = 2 that has a rectangular cross section (thickness = 0.1 m and width 1.2 m) and whose young modulus is given by E = 2.06x10 ^ 11 N / m2. To reduce the vertical deflection of the beam, a spring of stiffness k is added in the middle of the span, as shown in the following figure. Determine the value of k necessary to reduce the deflection of the beam by: a) -25% of its original valueb) -50% of its original valuec) -75% of its original valueThe L-shaped arm ABC shown in the Fig.3 lies in a vertical plane and pivots about a horizontal pin at A. The arm has constant cross-sectional area and total weight W.A vertical spring of stiffness k supports the arm at point B. Obtain a formula for the elongation of the spring due to the weight of the arm. Then use the following numerical data for calculating the value of spring elongation. (k= 20kN/m, b=300mm1. A closed coiled helical spring, is made out of a 10mm diameter steel rod, has 10 complete coils each of mean diameter of 80mm. Calculate for force of 200N:(a) the stress induced in the section of the rod (b) the deflection under the pull (c) the amount of energy stored in the spring during extension.Take G=84GPa.
- A close-coiled helical spring is made of a wire of diameter 20 mm. The mean radius of the coils is 100 mm. Find the number of turns required and the maximum axial load permissible if the shear stress is not to exceed 100 MPa and the maximum elongation is limited to 40 mm. G = 83 GPa.A vertical shaft 25 mm diameter and 0.75 m long is mounted in long bearings and carries a pulleyof mass 10 kg midway between the bearings. The centre of pulley is 0.5 mm from the axis of theshaft. Find (a) the whirling speed, and (b) the bending stress in the shaft, when it is rotating at 1700r.p.m. Neglect the mass of the shaft and E = 200 GN/m2.A round bar of length L. modulus of elasticity E, and weight density tapers uniformly from a diameter of 3D at one end to a diameter 2D at the other end. If the bar is suspended vertically from the larger end, find the elongation of the bar caused by its own weight.