Concept explainers
Solve Prob. 10.99, assuming that the vertical force applied at B is increased to 5P.
*10.99 Bars AB and CD, each of length l and of negligible weight, are attached to a spring of constant k. The spring is undeformed and the system is in equilibrium when θ1 = θ2 = 0. Determine the range of values of P for which the equilibrium position is stable.
Fig. P10.99
Find the range of values of P for which the equilibrium of the system is stable.
Answer to Problem 10.100P
The range of values of P for which the equilibrium position is stable is
Explanation of Solution
Given information:
The system is in equilibrium, when
Calculation:
Show the free-body diagram of the arrangement as in Figure 1.
Find the horizontal distance
Find the horizontal distance
Find the vertical distance
Find the vertical distance
When the values are small,
Find the potential energy (V) using the relation.
Here, the spring constant is k.
Substitute
Substitute
Differentiate the Equation (1) with respect to
Differentiate the Equation (2).
Differentiate the equation (2) with
Differentiate the Equation (1) with respect to
Differentiate the Equation;
Condition 1:
When the equilibrium is stable,
Substitute 0 for
Substitute 0 for
The condition is satisfied. The equilibrium is stable.
Condition 2:
Check the condition,
Substitute
Condition 3:
Refer to all the conditions,
The minimum value of P is 0.
The maximum value of P is
Therefore, the range of values of P for which the equilibrium position is stable is
Want to see more full solutions like this?
Chapter 10 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- Two uniform rods Ab and CD. of the same length I. are attached to gears as shown. Knowing that rod AB weighs 3 lb and that rod CD weighs 2 lb. determine the positions ol equilibrium of the svstem and state in each ease whether the equilibrium is stable, unstable, or neutral.Fig. P10 70arrow_forwardProblem # 8: The five forces acting at the end of the boom satisfy the condition of equilibrium. Determine the values of T_{1} and T_{2} .arrow_forwardSolve Prob. 10.32 assuming that the 900-N vertical force is applied at C instead of E.Reference to Problem 10.32:Two bars AD and DG are connected by a pin at D and by a spring AG . Knowing that the spring is 300 mm long when unstretched and that the constant of the spring is 5 kN/m, determine the value of x corresponding to equilibrium when a 900-N load is applied at E as shown.arrow_forward
- Two rods of negligible weight are attached to drums of radius r that are connected by a belt and spring of constant k . Knowing that the spring is undeformed when the rods are vertical, determine the range of values of P for which the equilibrium position 01=02 =0 = 0 is stable.arrow_forward/determine-tension-developed-cord-required-equilibrium-20-kg-lamp-q8388573arrow_forwardA slender rod AB with a weight W is attached to two blocks A and B that can move freely in the guides shown. Knowing that the spring is unstretched when AB is horizontal, determine three values of 0 corresponding to equilibrium when W = 300 lb, I= 16 in., and k= 75 lb/in. State in each case whether the equilibrium is stable, unstable, or neutral.arrow_forward
- C. Determine the force in the 197 N/m stiffness spring when the system is in equilibrium.(include units with answer) D. Determine the force in the 328 N/m stiffness spring when the system is in equilibrium.(include units with answer) E. Determine the deflection of the 328 N/m stiffness spring when the system is in equilibrium.(include units with answer)arrow_forwardProblem 1: The bar shown is in equilibrium. Determine force P, T, and R.arrow_forwardUsing the principles of equilibrium of Non-concurrent forces.arrow_forward
- Solve Prob. 10.12 assuming that the force P applied at point A acts horizontally to the left.Reference to Problem 10.12:Knowing that the line of action of the force Q passes through point C , derive an expression for the magnitude of Q required to maintain equilibrium.arrow_forwardCollar A can slide freely on the semicircular rod shown. Knowing that the constant of the spring is k and that the unstretched length of the spring is equal to the radius r , determine the value of 0 corresponding to equilibrium when w= 50 lb, r= 9 in., and k= 15 lb/in.arrow_forwardA 120kg block is supported by a rope which is wrapped 1 1/2 times around a horizontal rod. knowing that the coefficient of static friction between the rope and the rod is 0.15, determine the range of values of P for equilibrium is maintained.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY