A hollow steel strut has a square cross-section whose outer dimension is 27 mm and whose wall thickness is 10 mm. Calculate its radius of gyration for use in buckling theory. Input your value in units of mm to 1 decimal place.
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- Shown is a lightweight plank supported at its right end by a 7.0-mm-diameter rope with a tensile strength of 6.0 x 107 N/m2.a. What is the maximum force that the rope can support?b. What is the greatest distance, measured from the pivot, that the center of gravity of an 800 kg piece of heavy machinery can be placed without snapping the rope?A satellite similar to the Tethered Satellite in the figure below has a mass of 550 kg and is at the end of a 19.2 km long, 2.90 mm diameter cable with the tensile strength of steel. (a)How much does the cable stretch (in m) if a 108 N force is exerted to pull the satellite in? (Assume the satellite and shuttle are at the same altitude above the Earth. Young's modulus for steel is 210 ✕ 109 N/m2.) m (b)What is the effective force constant of the cable (in N/m)? N/m (c)How much energy (in J) is stored in it when stretched by the 108 N force? JFind τF the torque about point P due to the force applied by the Achilles' tendon. Express your answer in terms of F, ϕ, and x.
- Consider a nanotube with a Youngs modulus of 2.130 1012 N/m2 that experiences a tensile stress of 5.3 1010 N/m2. Steel has a Youngs modulus of about 2.000 1011 Pa. How much stress would cause a piece of steel to experience the same strain as the nanotube?The 37-kg homogeneous smooth sphere rests on the ( 2.9/1.1 ) incline A and bears against the smooth vertical wall B. Calculate the contact forces at A and B.Note: slope y/In the following mechanism, T1 torque and F1 force act on the AB link. Equilibrium conditionSCD according to the superposition principle, the magnitude of torque required to be applied to the CB.obtain by making drawings? (F1 is vertical from mid point of ABIt is applied directly) O=40⁰, CB=3m, AB=2m
- Do the dimensional analysis of the torque (f = rXF).A strut of lengthL = 3.00 m and mass m =16.0 kg is held by a cableat an angle of θ = 30.0°with respect to the horizontalas shown in FigureP8.30. (a) Sketch a forcediagram, indicating allthe forces and their placementon the strut. (b) Why is the hinge a good place to usefor calculating torques? (c) Write the condition for rotationalequilibrium symbolically, calculating the torques around thehinge. (d) Use the torque equation to calculate the tension in the cable. (e) Write the x- and y-components of Newton’ssecond law for equilibrium. (f) Use the force equation tofind the x- and y -components of the force on the hinge.(g) Assuming the strut position is to remain the same, wouldit be advantageous to attach the cable higher up on the wall?Explain the benefit in terms of the force on the hinge andcable tension.Three forces are applied to a square plate as shown in the figure. Find the modulus, direction, and the point of application of the resultant force, if this point is taken on the side BC. Determine the resul- tant torque with respect to the center O of the square.
- Which of the following statements ARE true? a.)If a force passes through the pivot point, its torque is zero b.)If a force passes through the pivot point, its torque is infinitely large c.)Under equilibrium conditions, you have complete freedom to specify any point as the pivot point d.)Under equilibrium conditions, the pivot point is uniquely determined, and you can't change it.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 painter climbs a ladder leaning against a smoothwall. At a certain height, the ladder is on the verge of slipping.(a) Explain why the force exerted by the vertical wall on theladder is horizontal. (b) If the ladder of length L leans at anangle u with the horizontal, what is the lever arm for this horizontalforce with the axis of rotation taken at the base of theladder? (c) If the ladder is uniform, what is the lever arm forthe force of gravity acting on the ladder? (d) Let the mass ofthe painter be 80 kg, L = 4.0 m, the ladder’s mass be 30 kg,θ = 53°, and the coefficient of friction between ground andladder be 0.45. Find the maximum distance the painter canclimb up the ladder.