Derive the expression for the largest angle θ for which the homogeneous block stays in equilibrium.
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Derive the expression for the largest angle θ for which the homogeneous block stays in equilibrium.
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- Determine the largest force P for which the 16-kg uniform bar remains in equilibrium.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.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 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.Neglecting friction, determine the relationship between P and Q, assuming that the mechanism is in equilibrium in the position shown.
- The homogeneous 240-lb bar is supported by a rough horizontal surface at A, a smooth vertical surface at B, and the cable BC. Draw the FBD of the bar and count the unknowns.Determine the ratio P/Q of the forces that are required to maintain equilibrium of the mechanism for an arbitrary angle . Neglect the weight of the mechanism.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 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.The uniform bar of weight W is held in equilibrium by the couple C0. Find C0 in terms of W, L, and .Find the equilibrium positions of the 30-lb homogeneous bar and investigate their stability.