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
The angle
Answer to Problem 10.62P
The value ofangle at the stable equilibrium positions is
Explanation of Solution
Given Information:
The weight of the load = W
The stiffness of each spring = k
Given that
The following figure is given,
Calculation:
Consider the following figure,
To calculate the angle for the equilibrium position, let us calculate the potential energy of the system. The total potential energy of the system consists of potential energy of the weight (Vg) and the potential energy of the springs (Ve)
The total potential energy =
Putting the value of Yg and s in equation (1)
The potential energy of the system comes out to be
Now, let us take the first derivative of the total potential energy of the system,
Now, the principle of minimum potential energy can be used to find the value of angle
The roots of equation
Now, differentiating equation 3 again to get
Thus, system is at unstable equilibrium at
Thus, system is at stable equilibrium at
Conclusion:
Therefore, the value ofangle at the stable equilibrium positions is
Want to see more full solutions like this?
Chapter 10 Solutions
International Edition---engineering Mechanics: Statics 4th Edition
- 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.arrow_forwardThe 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.)arrow_forwardThe 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.arrow_forward
- The uniform bar of weight W is held in equilibrium by the couple C0. Find C0 in terms of W, L, and .arrow_forwardThe 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.arrow_forwardThe 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.arrow_forward
- The homogeneous plate of weight W is suspended from two cables. Determine the force P that is necessary to keep the plate in the position shown.arrow_forwardFind 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.)arrow_forwardDraw 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.arrow_forward
- 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.arrow_forwardThe homogeneous 80-kg sign is suspended from a ball-and-socket joint at O, and cables AD and BC. Determine the forces in the cables.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L