A 49° 1.8 C 44 lb DI
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Cable AB passes over the small ideal pulley C without a change in its tension. What length of cable CD is required for static equilibrium in the position shown? What is the tension T in cable CD?
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- The bar ABC is supported by three identical, ideal springs. Note that the springs are always vertical because the collars to which they are attached are free to slide on the horizontal rail. Find the angle at equilibrium if W = kL. Neglect the weight of the bar.Find the equilibrium positions of the 30-lb homogeneous bar and investigate their stability.The uniform bar AB of weight W and length L is pinned to a sliding collar at A and to the sliding rod BD at B. The spring wound around rod BD has a stiffness k and is undeformed when rod AB is in the position =0. Determine the expression for the angle (other than =90 ) at equilibrium and investigate the stability of equilibrium for this position.
- Find the smallest value of P for which the crate in the Prob. 4.34 will be in equilibrium in the position shown. (Hint: A rope can only support a tensile force.)Draw the FBDs for the entire structure and the member BDE. Count the total number of unknowns and the total number of independent equilibrium equations. Note that the cable that supports the 1200-lb weight runs over a smooth peg at D.Draw the FBDs for the beam ABC and the segments AB and BC. Note that the two segments are joined by a pin at B. Count the total number of unknowns and the total number of independent equilibrium equations.
- The center of gravity of the nonhomogeneous bar AB is located at G. Find the angle at which the bar will be in equilibrium if it is free to slide on the frictionless cylindrical surface.The stiffness of the ideal spring that is compressed by the slider C is k = 250 N/m. The spring is unstretched when =20. When the mass m is suspended from A, the system is in equilibrium at =60. Determine the value of m and whether the equilibrium position is stable or unstable.For Probs. 4.61–4.68, (a) draw the free-body diagrams for the entire assembly (or structure) and each of its parts. Neglect friction and the weights of the members unless specified otherwise. Be sure to indicate all relevant dimensions. For each problem, (b) determine the total number of unknown forces and the total number of independent equilibrium equations.
- The spring is connected to a rope that passes over the cylindrical surface and is attached to corner A of the rocker. The spring has a stiffness k and is undeformed when =0. When the weight W is suspended from A, the equilibrium position of the rocker is =30. Determine if this equilibrium position is stable. Neglect the weight of the rocker.The two uniform cylinders, each of weight W, are resting against inclined surfaces. Neglecting friction, draw the free-body diagrams for each cylinder and for the two cylinders together. Count the total number of unknowns and the total number of independent equilibrium equations.The spring attached to the homogenous bar of weight W is undeformed when =0. Determine the smallest spring stiffness k for which the =0 equilibrium position will be stable. Use W = 10 lb, a = 24 in., and b = 6 in. Assume that the spring remains horizontal, which is a valid approximation if is small.