The uniform bar AB shown in Fig has a mass of 20 kg and a length of 2 m. If the spring is un- stretched at an angle e = 30°, determine the spring constant 4 for equilibrium at an angle 0- 60°.
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- The weight of the uniform bar AB is W. The stiffness of the ideal spring attached to B is k, and the spring is unstretched when =80. If W=kL, the bar has three equilibrium positions in the range 0, only one of which is stable. Determine the angle at the stable equilibrium position.The 14-kN weight is suspended from a small pulley that is free to roll on the cable. The length of the cable ABC is 20 m. Determine the horizontal force P that would hold the pulley in equilibrium in the position x=5m.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.
- Find the stable equilibrium position of the system described in Prob. 10.56 if m = 2.06 kg.The cable of mass 1.8 kg/m is attached to a rigid support at A and passes over a smooth pulley at B. If the mass M = 40 kg is attached to the free end of the cable, find the two values of H for which the cable will be in equilibrium. (Note: The smaller value of H represents stable equilibrium.)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.
- The 40-kghomogeneous disk is placed on a frictionless inclined surface and held in equilibrium by the horizontal force P and a couple C (C is not shown on the figure). Find P and C.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 weightless bars AB and CE, together with the 5-lb weight BE, form a parallelogram linkage. The ideal spring attached to D has a free length of 2 in. and a stiffness of 7.5 lb/in. Find the two equilibrium positions that are in the range 0/2, and determine their stability. Neglect the weight of slider F.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.