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, Problem 10.110RP
To determine
Find the positions of equilibrium of the system and state in each case whether the equilibrium is stable, unstable, or neutral.
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Determine the value of θ corresponding to the equilibrium position of the rod of Prob. 10.10 when I= 30 in., a= 5 in., P = 25 lb, and Q= 40 lb.Reference to Problem 10.10:The slender rod AB is attached to a collar A and rests on a small wheel at C . Neglecting the radius of the wheel and the effect of friction, derive an expression for the magnitude of the force Q required to maintain the equilibrium of the rod.
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.
Two uniform rods, each with a mass m , are attached to gears of equal radii as shown. Determine the positions of equilibrium of the system and 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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- Determine the value of θ corresponding to the equilibrium position of the rod of Prob. 10.12 when P = 80 N, and Q= 100 N.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_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_forwardA 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.arrow_forward
- The 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_forwardTwo rods AC and CE are connected by a pin at C and by a spring AE . The constant of the spring is k , and the spring is unstretched when θ = 30°. For the loading shown, derive an equation in P,θ ,I, and k that must be satisfied when the system is in equilibrium.arrow_forwardThe 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_forward
- Show that equilibrium is neutral in Prob. 10.7.Reference to Problem 10.7: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_forwardP A P C HINT: Collar A is in equilibrium 20.5 20 4+₂5 50 lb Free Body: Collar A 150 lb A 20 in. PROBLEM 2.63 Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the magnitude of the force P required to maintain the equilibrium of the collar when (a) x=4.5 in., (b) x=15 in. Where does N come from? What is it?arrow_forward
- Two uniform rods each with a mass m and length l are attached to gears as shown. For the range 0 < 0 < 180° determine the positions of equilibrium of the system, and state in each case whether the equilibrium is stable, unstable, or neutral.arrow_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_forwardSolve Sample Prob. 4.5, assuming that the spring is unstretched when 0 = 90°.(Reference to Sample Problem 4.5):arrow_forward
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