Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 10.2, Problem 10.70P
To determine
Find the positions of equilibrium of the system and check whether the equilibrium is stable, unstable, or neutral.
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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.
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A spring AB of constant k is attached to two identical gears as shown. Knowing that the spring is undeformed when 0= 0, determine two values of the angle 0 corresponding to equilibrium when P= 30 lb, a= 4 in., b= 3 in., r= 6 in., and k= 5 lb/in. State in each case whether the equilibrium is stable, unstable, or neutral.
Chapter 10 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 10.1 - Determine the vertical force P that must be...Ch. 10.1 - Determine the horizontal force P that must be...Ch. 10.1 - Prob. 10.3PCh. 10.1 - Prob. 10.4PCh. 10.1 - Prob. 10.5PCh. 10.1 - A spring of constant 15 kN/m connects points C and...Ch. 10.1 - The two-bar linkage shown is supported by a pin...Ch. 10.1 - Prob. 10.8PCh. 10.1 - Prob. 10.9PCh. 10.1 - Prob. 10.10P
Ch. 10.1 - Prob. 10.11PCh. 10.1 - Prob. 10.12PCh. 10.1 - Prob. 10.13PCh. 10.1 - Prob. 10.14PCh. 10.1 - Prob. 10.15PCh. 10.1 - Prob. 10.16PCh. 10.1 - Prob. 10.17PCh. 10.1 - Prob. 10.18PCh. 10.1 - Prob. 10.19PCh. 10.1 - Prob. 10.20PCh. 10.1 - Prob. 10.21PCh. 10.1 - A couple M with a magnitude of 100 Nm isapplied as...Ch. 10.1 - Rod AB is attached to a block at A that can...Ch. 10.1 - Solve Prob. 10.23, assuming that the 800-N force...Ch. 10.1 - Prob. 10.25PCh. 10.1 - Prob. 10.26PCh. 10.1 - Prob. 10.27PCh. 10.1 - Prob. 10.28PCh. 10.1 - Prob. 10.29PCh. 10.1 - Two rods AC and CE are connected by a pin at Cand...Ch. 10.1 - Solve Prob. 10.30 assuming that force P is movedto...Ch. 10.1 - Prob. 10.32PCh. 10.1 - Prob. 10.33PCh. 10.1 - Prob. 10.34PCh. 10.1 - Prob. 10.35PCh. 10.1 - Prob. 10.36PCh. 10.1 - Prob. 10.37PCh. 10.1 - Prob. 10.38PCh. 10.1 - Prob. 10.39PCh. 10.1 - Prob. 10.40PCh. 10.1 - Prob. 10.41PCh. 10.1 - The position of boom ABC is controlled by...Ch. 10.1 - Prob. 10.43PCh. 10.1 - Prob. 10.44PCh. 10.1 - Prob. 10.45PCh. 10.1 - Prob. 10.46PCh. 10.1 - Denoting the coefficient of static friction...Ch. 10.1 - Prob. 10.48PCh. 10.1 - Prob. 10.49PCh. 10.1 - Prob. 10.50PCh. 10.1 - Prob. 10.51PCh. 10.1 - Prob. 10.52PCh. 10.1 - Prob. 10.53PCh. 10.1 - Prob. 10.54PCh. 10.1 - Prob. 10.55PCh. 10.1 - Prob. 10.56PCh. 10.1 - Prob. 10.57PCh. 10.1 - Prob. 10.58PCh. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.29....Ch. 10.2 - Prob. 10.60PCh. 10.2 - Prob. 10.61PCh. 10.2 - Prob. 10.62PCh. 10.2 - Prob. 10.63PCh. 10.2 - Prob. 10.64PCh. 10.2 - Prob. 10.65PCh. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.38....Ch. 10.2 - Prob. 10.67PCh. 10.2 - Prob. 10.68PCh. 10.2 - Prob. 10.69PCh. 10.2 - Prob. 10.70PCh. 10.2 - Prob. 10.71PCh. 10.2 - Prob. 10.72PCh. 10.2 - Prob. 10.73PCh. 10.2 - Prob. 10.74PCh. 10.2 - Prob. 10.75PCh. 10.2 - Prob. 10.76PCh. 10.2 - Prob. 10.77PCh. 10.2 - Prob. 10.78PCh. 10.2 - Prob. 10.79PCh. 10.2 - Prob. 10.80PCh. 10.2 - Prob. 10.81PCh. 10.2 - A spring AB of constant k is attached to two...Ch. 10.2 - Prob. 10.83PCh. 10.2 - Prob. 10.84PCh. 10.2 - Prob. 10.85PCh. 10.2 - Prob. 10.86PCh. 10.2 - Prob. 10.87PCh. 10.2 - Prob. 10.88PCh. 10.2 - Prob. 10.89PCh. 10.2 - Prob. 10.90PCh. 10.2 - Prob. 10.91PCh. 10.2 - Prob. 10.92PCh. 10.2 - Prob. 10.93PCh. 10.2 - Prob. 10.94PCh. 10.2 - Prob. 10.95PCh. 10.2 - Prob. 10.96PCh. 10.2 - Bars AB and BC, each with a length l and of...Ch. 10.2 - Prob. 10.98PCh. 10.2 - Prob. 10.99PCh. 10.2 - Prob. 10.100PCh. 10 - Determine the vertical force P that must be...Ch. 10 - Determine the couple M that must be applied...Ch. 10 - Prob. 10.103RPCh. 10 - Prob. 10.104RPCh. 10 - Prob. 10.105RPCh. 10 - Prob. 10.106RPCh. 10 - Prob. 10.107RPCh. 10 - Prob. 10.108RPCh. 10 - Prob. 10.109RPCh. 10 - Prob. 10.110RPCh. 10 - Prob. 10.111RPCh. 10 - Prob. 10.112RP
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- A collar B with a weight of W can move freely along the vertical rod shown. The constant of the spring is k , and the spring is unstretched when 0 = 0. (a) Derive an equation in 0, w, k, and 1 that must be satisfied when the collar is in equilibrium. (b) Knowing that W = 300 N, 1 = 500 mm, and k = 800 N/m, determine the value of 0 corresponding to equilibrium.arrow_forwardTwo uniform rods, each of mass m and length I , are attached to drums that are connected by a belt as shown. Assuming that no slipping occurs between the belt and the drums, determine the positions of equilibrium of the system and state in each case whether the equilibrium is stable, unstable, or neutral.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
- The lever AB is attached to the horizontal shaft BC that passes through a bearing and is welded to a fixed support at C . The torsional spring constant of the shaft BC is k ; that is, a couple of magnitude K is required to rotate end B through 1 rad. Knowing that the shaft is untwisted when AB is horizontal, determine the value of 0 corresponding to the position of equilibrium when P = 100 N, I= 250 mm, and K = 12.5 N.m/rad.arrow_forwardCollars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. Determine the distances x and z for which the equilibrium of the system is maintained when P=120 lb and Q=60 lb.arrow_forwardThe two-bar linkage shown is supported by a pin and bracket at B and a collar at D that slides freely on a vertical rod. Determine the force P required to maintain the equilibrium of the linkage.arrow_forward
- Using the method of Sec. 10.2C, solve Prob. 10.37.Reference to Problem 10.37:Knowing that the constant of spring CD is k and that the spring is unstretched when rod ABC is horizontal, determine the value of 0 corresponding to equilibrium for the data indicated.P=300 mm N, I=400 mm, and k =5kN/marrow_forwardShow that equilibrium is neutral in Prob. 10.1.Reference to Problem 10.1:Determine the vertical force P that must be applied at C to maintain the equilibrium of the linkage.arrow_forwardTwo 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_forward
- The T-shaped bracket shown is supported by a small wheel at E and pegs at C and D . Neglecting the effect of friction, determine (a) the smallest value of 0 for which the equilibrium of the bracket is maintained, (b) the corresponding reactions at C, D, and E.arrow_forwardTwo 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_forwardA slender rod AB is attached to two collars A and B that can move freely along the guide rods shown. Knowing that β= 30° and P = Q = 400 N, determine the value of the angle 0 corresponding to equilibrium.arrow_forward
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