Solved: A homogeneous hemisphere of radius r is placed on an incline as shown. Assuming

Determine the vertical force P that must be applied at G to maintain the equilibrium of the linkage.

Determine the vertical force P that must be applied at G to maintain the equilibrium of the linkage.

Determine the couple M that must be applied to member DEFG to maintain the equilibrium of the linkage.

Determine the couple M that must be applied to member DEFG to maintain the equilibrium of the linkage.

Determine the force P required to maintain the equilibrium of the linkage shown. All members are of the same length and the wheels at A and B roll freely on the horizontal rod.

Solve Problem 10.5 assuming that the vertical force P is applied at Point E. PROBLEM 10.5 Determine the force P required to maintain the equilibrium of the linkage shown. All members are of the same length and the wheels at A and B roll freely on the horizontal rod.

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.

Knowing that the maximum friction force exerted by the bottle on the cork is 60 lb, determine (a) the force P that must be applied to the corkscrew to open the bottle, (b) the maximum force exerted by the base of the corkscrew on the top of the bottle.

Rod AD is acted upon by a vertical force P at end A, and by two equal and opposite horizontal forces of magnitude Q at points B and C. Derive an expression for the magnitude Q of the horizontal forces required for equilibrium.

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.

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.

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.

Solve Problem 10.12 assuming that the force P applied at Point A acts horizontally to the left. 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.

The mechanism shown is acted upon by the force P; derive an expression for the magnitude of the force Q required to maintain equilibrium.

Derive an expression for the magnitude of the couple M required to maintain the equilibrium of the linkage shown.

Derive an expression for the magnitude of the couple M required to maintain the equilibrium of the linkage shown.

A uniform rod AB of length l and weight W is suspended from two cords AC and BC of equal length. Derive an expression for the magnitude of the couple M required to maintain equilibrium of the rod in the position shown.

Collar B can slide along rod AC and is attached by a pin to a block that can slide in the vertical slot shown. Derive an expression for the magnitude of the couple M required to maintain equilibrium.

For the linkage shown, determine the couple M required for equilibrium when 1.8 ft, l = 40 lb, Q = and 65 . =

For the linkage shown, determine the force Q required for equilibrium when 18 in., l = 600 lb in., M = and 70 .

A 4-kN force P is applied as shown to the piston of the engine system. Knowing that = 50 mm AB and BC 200 mm, = determine the couple M required to maintain the equilibrium of the system when (a) =30, (b) 150 . =

A couple M of magnitude 100 N m is applied as shown to the crank of the engine system. Knowing that AB 50 mm = and 200 mm,BC = determine the force P required to maintain the equilibrium of the system when (a) 60 , = (b) 120 . =

A couple M of magnitude 100 N m is applied as shown to the crank of the engine system. Knowing that AB 50 mm = and 200 mm,BC = determine the force P required to maintain the equilibrium of the system when (a) 60 , = (b) 120 . =

A slender rod of length l is attached to a collar at B and rests on a portion of a circular cylinder of radius r. Neglecting the effect of friction, determine the value of corresponding to the equilibrium position of the mechanism when l = 14 in., r = 5 in., P = 75 lb, and Q = 150 lb.

Determine the value of corresponding to the equilibrium position of the rod of Problem 10.10 when 30 in., l = 5 in., a = 25 lb, P = and 40 lb. Q = 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.

Determine the values of corresponding to the equilibrium position of the rod of Problem 10.11 when 600 mm, l = 100 mm, a = 50 N, P = and 90 N. Q = PROBLEM 10.11 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.

Determine the value of corresponding to the equilibrium position of the mechanism of Problem 10.12 when = 80 N P and 100 N. Q = 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.

Determine the value of corresponding to the equilibrium position of the mechanism of Prob. 10.14 when P = 270 N and Q = 960 N.

A load W of magnitude 600 N is applied to the linkage at B. The constant of the spring is 2.5 kN/m, k = and the spring is unstretched when AB and BC are horizontal. Neglecting the weight of the linkage and knowing that 300 mm, l = determine the value of corresponding to equilibrium.

A vertical load W is applied to the linkage at B. The constant of the spring is k, and the spring is unstretched when AB and BC are horizontal. Neglecting the weight of the linkage, derive an equation in , W, l, and k that must be satisfied when the linkage is in equilibrium.

Two bars AD and DG are connected by a pin at D and by a spring AG. Knowing that the spring is 12 in. long when unstretched and that the constant of the spring is 125 lb/in., determine the value of x corresponding to equilibrium when a 900-lb load is applied at E as shown.

Solve Problem 10.31 assuming that the 900-lb vertical force is applied at C instead of E. PROBLEM 10.31 Two bars AD and DG are connected by a pin at D and by a spring AG. Knowing that the spring is 12 in. long when unstretched and that the constant of the spring is 125 lb/in., determine the value of x corresponding to equilibrium when a 900-lb load is applied at E as shown.

Two 5-kg bars AB and BC are connected by a pin at B and by a spring DE. Knowing that the spring is 150 mm long when unstretched and that the constant of the spring is 1 kN/m, determine the value of x corresponding to equilibrium.

Rod ABC is attached to blocks A and B that can move freely in the guides shown. The constant of the spring attached at A is 3 kN/m, k = and the spring is unstretched when the rod is vertical. For the loading shown, determine the value of corresponding to equilibrium.

A vertical force P of magnitude 150 N is applied to end E of cable CDE, which passes over a small pulley D and is attached to the mechanism at C. The constant of the spring is k = 4 kN/m, and the spring is unstretched when = 0. Neglecting the weight of the mechanism and the radius of the pulley, determine the value of corresponding to equilibrium.

A horizontal force P of magnitude 40 lb is applied to the mechanism at C. The constant of the spring is 9 lb/in., k = and the spring is unstretched when 0. = Neglecting the weight of the mechanism, determine the value of corresponding to equilibrium.

Knowing that the constant of spring CD is k and that the spring is unstretched when rod ABC is horizontal, determine the value of corresponding to equilibrium for the data indicated. 300 N, 400 mm, 5 kN/m. P l k

Knowing that the constant of spring CD is k and that the spring is unstretched when rod ABC is horizontal, determine the value of corresponding to equilibrium for the data indicated. 75 lb, 15 in., 20 lb/in. P l k

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 corresponding to the position of equilibrium when 100 N, 250 mm, Pl == and 12.5 N m/rad. K =

Solve Problem 10.39 assuming that 350 N, P = 250 mm, l = and 12.5 N m/rad.K = Obtain answers in each of the following quadrants: 0 90 , 270 360,360 450 . < < < < < < PROBLEM 10.39 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 corresponding to the position of equilibrium when 100 P = N, l 250 mm, = and 12.5 N m/rad. K =

The position of boom ABC is controlled by the hydraulic cylinder BD. For the loading shown, determine the force exerted by the hydraulic cylinder on pin B when 65 . =

The position of boom ABC is controlled by the hydraulic cylinder BD. For the loading shown, (a) express the force exerted by the hydraulic cylinder on pin B as a function of the length BD, (b) determine the smallest possible value of the angle if the maximum force that the cylinder can exert on pin B is 2.5 kips.

The position of member ABC is controlled by the hydraulic cylinder CD. For the loading shown, determine the force exerted by the hydraulic cylinder on pin C when 55 . =

The position of member ABC is controlled by the hydraulic cylinder CD. Determine the angle knowing that the hydraulic cylinder exerts a 15-kN force on pin C.

The telescoping arm ABC is used to provide an elevated platform for construction workers. The workers and the platform together weigh 500 lb and their combined center of gravity is located directly above C. For the position when 20 , = determine the force exerted on pin B by the single hydraulic cylinder BD.

Solve Problem 10.45 assuming that the workers are lowered to a point near the ground so that 20 . = PROBLEM 10.45 The telescoping arm ABC is used to provide an elevated platform for construction workers. The workers and the platform together weigh 500 lb and their combined center of gravity is located directly above C. For the position when 20 , = determine the force exerted on pin B by the single hydraulic cylinder BD.

Denoting by s the coefficient of static friction between collar C and the vertical rod, derive an expression for the magnitude of the largest couple M for which equilibrium is maintained in the position shown. Explain what happens if tan . s

Knowing that the coefficient of static friction between collar C and the vertical rod is 0.40, determine the magnitude of the largest and smallest couple M for which equilibrium is maintained in the position shown, when = 35, l = 600 mm, and 300 N. P =

A block of weight W is pulled up a plane forming an angle with the horizontal by a force P directed along the plane. If is the coefficient of friction between the block and the plane, derive an expression for the mechanical efficiency of the system. Show that the mechanical efficiency cannot exceed 1 2 if the block is to remain in place when the force P is removed.

Derive an expression for the mechanical efficiency of the jack discussed in Section 8.6. Show that if the jack is to be self-locking, the mechanical efficiency cannot exceed 1 2.

Denoting by s the coefficient of static friction between the block attached to rod ACE and the horizontal surface, derive expressions in terms of P, , s and for the largest and smallest magnitude of the force Q for which equilibrium is maintained.

Knowing that the coefficient of static friction between the block attached to rod ACE and the horizontal surface is 0.15, determine the magnitude of the largest and smallest force Q for which equilibrium is maintained when 30 , 0.2 m, l == and P = 40 N.

Using the method of virtual work, determine the reaction at E.

Using the method of virtual work, determine separately the force and couple representing the reaction at H.

Referring to Problem 10.43 and using the value found for the force exerted by the hydraulic cylinder CD, determine the change in the length of CD required to raise the 10-kN load by 15 mm. PROBLEM 10.43 The position of member ABC is controlled by the hydraulic cylinder CD. For the loading shown, determine the force exerted by the hydraulic cylinder on pin C when 55 .

Referring to Problem 10.45 and using the value found for the force exerted by the hydraulic cylinder BD, determine the change in the length of BD required to raise the platform attached at C by 2.5 in. PROBLEM 10.45 The telescoping arm ABC is used to provide an elevated platform for construction workers. The workers and the platform together weigh 500 lb and their combined center of gravity is located directly above C. For the position when 20 , = determine the force exerted on pin B by the single hydraulic cylinder BD.

Determine the vertical movement of joint D if the length of member BF is increased by 1.5 in. (Hint: Apply a vertical load at joint D, and, using the methods of Chapter 6, compute the force exerted by member BF on joints B and F. Then apply the method of virtual work for a virtual displacement resulting in the specified increase in length of member BF. This method should be used only for small changes in the lengths of members.)

Determine the horizontal movement of joint D if the length of member BF is increased by 1.5 in. (See the hint for Problem 10.57.)

Using the method of Section 10.8, solve Problem 10.29. PROBLEM 10.29 A load W of magnitude 600 N is applied to the linkage at B. The constant of the spring is 2.5 kN/m, k = and the spring is unstretched when AB and BC are horizontal. Neglecting the weight of the linkage and knowing that 300 mm, l = determine the value of corresponding to equilibrium.

Using the method of Section 10.8, solve Problem 10.30. PROBLEM 10.30 A vertical load W is applied to the linkage at B. The constant of the spring is k, and the spring is unstretched when AB and BC are horizontal. Neglecting the weight of the linkage, derive an equation in , W, l, and k that must be satisfied when the linkage is in equilibrium.

Using the method of Section 10.8, solve Problem 10.31. PROBLEM 10.31 Two bars AD and DG are connected by a pin at D and by a spring AG. Knowing that the spring is 12 in. long when unstretched and that the constant of the spring is 125 lb/in., determine the value of x corresponding to equilibrium when a 900-lb load is applied at E as shown.

Using the method of Section 10.8, solve Problem 10.32. PROBLEM 10.32 Solve Problem 10.31 assuming that the 900-lb vertical force is applied at C instead of E. PROBLEM 10.31 Two bars AD and DG are connected by a pin at D and by a spring AG. Knowing that the spring is 12 in. long when unstretched and that the constant of the spring is 125 lb/in., determine the value of x corresponding to equilibrium when a 900-lb load is applied at E as shown.

Using the method of Section 10.8, solve Problem 10.33. PROBLEM 10.33 Two 5-kg bars AB and BC are connected by a pin at B and by a spring DE. Knowing that the spring is 150 mm long when unstretched and that the constant of the spring is 1 kN/m, determine the value of x corresponding to equilibrium.

Using the method of Section 10.8, solve Problem 10.35. PROBLEM 10.35 A vertical force P of magnitude 150 N is applied to end E of cable CDE, which passes over a small pulley D and is attached to the mechanism at C. The constant of the spring is k = 4 kN/m, and the spring is unstretched when = 0. Neglecting the weight of the mechanism and the radius of the pulley, determine the value of corresponding to equilibrium.

Using the method of Section 10.8, solve Problem 10.37. PROBLEM 10.37 and 10.38 Knowing that the constant of spring CD is k and that the spring is unstretched when rod ABC is horizontal, determine the value of corresponding to equilibrium for the data indicated. PROBLEM 10.37 300 N, 400 mm, 5 kN/m. P l k = = =

Using the method of Section 10.8, solve Problem 10.38. PROBLEM 10.37 and 10.38 Knowing that the constant of spring CD is k and that the spring is unstretched when rod ABC is horizontal, determine the value of corresponding to equilibrium for the data indicated. PROBLEM 10.38 75 lb, 15 in., 20 lb/in. P l k = = =

Show that equilibrium is neutral in Problem 10.1. PROBLEM 10.1 Determine the vertical force P that must be applied at G to maintain the equilibrium of the linkage.

Show that equilibrium is neutral in Problem 10.7. PROBLEM 10.7 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.

Two uniform rods, each of 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.

Two uniform rods, AB and CD, are attached to gears of equal radii as shown. Knowing that 8 lb =ABW and 4 lb, =CDW determine the positions of equilibrium of the system and state in each case whether the equilibrium is stable, unstable, or neutral.

Two uniform rods, each of mass m and length l, are attached to gears as shown. For the range0 180 , determine the positions of equilibrium of the system and state in each case whether the equilibrium is stable, unstable, or neutral.

Two uniform rods, each of mass m and length l, 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.

Using the method of Section 10.8, solve Problem 10.39. Determine whether the equilibrium is stable, unstable, or neutral. (Hint: The potential energy corresponding to the couple exerted by a torsion spring is 2 1 2 , K where K is the torsional spring constant and is the angle of twist.) PROBLEM 10.39 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 corresponding to the position of equilibrium when P = 100 N, l = 250 mm, and 12.5 N m/rad.

In Problem 10.40, determine whether each of the positions of equilibrium is stable, unstable, or neutral. (See hint for Problem 10.73.) PROBLEM 10.40 Solve Problem 10.39 assuming that 350 N, =P 250 mm,=l and 12.5 N m/rad. =K Obtain answers in each of the following quadrants: 0 90, 270 360, 360 450.

A load W of magnitude 100 lb is applied to the mechanism at C. Knowing that the spring is unstretched when 15 , = determine that value of corresponding to equilibrium and check that the equilibrium is stable.

A load W of magnitude 100 lb is applied to the mechanism at C. Knowing that the spring is unstretched when 30 , = determine that value of corresponding to equilibrium and check that the equilibrium is stable.

A slender rod AB, of 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 0, =y determine the value of y corresponding to equilibrium when 80 N, =W 500 mm, =l and 600 N/m. =k

A slender rod AB, of weight W, is attached to two blocks A and B that can move freely in the guides shown. Knowing that both springs are unstretched when 0, =y determine the value of y corresponding to equilibrium when 80 N, =W l = 550 mm, and 600 N/m. =k

A slender rod AB, of weight W, is attached to two blocks A and B that can move freely in the guides shown. The constant of the spring is k, and the spring is unstretched when AB is horizontal. Neglecting the weight of the blocks, derive an equation in , W, l, and k that must be satisfied when the rod is in equilibrium.

A slender rod AB, of 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 corresponding to equilibrium when 300 lb, =W 16 in., =l and 75 lb/in. =k State in each case whether the equilibrium is stable, unstable, or neutral.

A spring AB of constant k is attached to two identical gears as shown. Knowing that the spring is undeformed when 0, = determine two values of the angle 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.

A spring AB of constant k is attached to two identical gears as shown. Knowing that the spring is undeformed when 0, = and given that 60 mm, 45 mm, 90 mm, === abr and 6 kN/m, =k determine (a) the range of values of P for which a position of equilibrium exists, (b) two values of corresponding to equilibrium if the value of P is equal to half the upper limit of the range found in part a.

A slender rod AB is attached to two collars A and B that can move freely along the guide rods shown. Knowing that 30 = and P = Q = 400 N, determine the value of the angle corresponding to equilibrium.

A slender rod AB is attached to two collars A and B that can move freely along the guide rods shown. Knowing that 30 , 100 N, P = = and 25 N, =Q determine the value of the angle corresponding to equilibrium.

Cart B, which weighs 75 kN, rolls along a sloping track that forms an angle with the horizontal. The spring constant is 5 kN/m, and the spring is unstretched when 0. =x Determine the distance x corresponding to equilibrium for the angle indicated. Angle = 30 .

Cart B, which weighs 75 kN, rolls along a sloping track that forms an angle with the horizontal. The spring constant is 5 kN/m, and the spring is unstretched when 0. =x Determine the distance x corresponding to equilibrium for the angle indicated. Angle = 60.

Collar 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 corresponding to equilibrium when 50 lb, 9 in., == Wr and 15 lb/in. =k

Collar 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 corresponding to equilibrium when 50 lb, 9 in., == Wr and k = 15 lb/in.

Two bars AB and BC of negligible weight are attached to a single spring of constant k that is unstretched when the bars are horizontal. Determine the range of values of the magnitude P of two equal and opposite forces P and P for which the equilibrium of the system is stable in the position shown.

A vertical bar AD is attached to two springs of constant k and is in equilibrium in the position shown. Determine the range of values of the magnitude P of two equal and opposite vertical forces P and P for which the equilibrium position is stable if (a) , = AB CD (b) 2.

Rod AB is attached to a hinge at A and to two springs, each of constant k. If 25 in., 12 in., hd == and 80 lb, =W determine the range of values of k for which the equilibrium of the rod is stable in the position shown. Each spring can act in either tension or compression.

Rod AB is attached to a hinge at A and to two springs, each of constant k. If 45 in., 6 lb/in., == hk and 60 lb, =W determine the smallest distance d for which the equilibrium of the rod is stable in the position shown. Each spring can act in either tension or compression.

Two bars are attached to a single spring of constant k that is unstretched when the bars are vertical. Determine the range of values of P for which the equilibrium of the system is stable in the position shown.

Two bars are attached to a single spring of constant k that is unstretched when the bars are vertical. Determine the range of values of P for which the equilibrium of the system is stable in the position shown.

The horizontal bar BEH is connected to three vertical bars. The collar at E can slide freely on bar DF. Determine the range of values of Q for which the equilibrium of the system is stable in the position shown when a = 24 in., b = 20 in., and P = 150 lb.

The horizontal bar BEH is connected to three vertical bars. The collar at E can slide freely on bar DF. Determine the range of values of P for which the equilibrium of the system is stable in the position shown when a = 150 mm, b = 200 mm, and Q = 45 N.

Bars AB and BC, each of length l and of negligible weight, are attached to two springs, each of constant k. The springs are undeformed, and the system is in equilibrium when 1 = 2 = 0. Determine the range of values of P for which the equilibrium position is stable.

Solve Problem 10.97 knowing that l = 800 mm and k = 2.5 kN/m. PROBLEM 10.97* Bars AB and BC, each of length l and of negligible weight, are attached to two springs, each of constant k. The springs are undeformed, and the system is in equilibrium when 1 = 2 = 0. Determine the range of values of P for which the equilibrium position is stable.

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 1 = 2 = 0 is stable.

Solve Problem 10.99 knowing that k = 20 lb/in., r = 3 in., l = 6 in., and (a) W = 15 lb, (b) W = 60 lb. PROBLEM 10.99* 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 1 = 2 = 0 is stable.

Determine the horizontal force P that must be applied at A to maintain the equilibrium of the linkage.

Determine the couple M that must be applied to member ABC to maintain the equilibrium of the linkage.

A spring of constant 15 kN/m connects Points C and F of the linkage shown. Neglecting the weight of the spring and linkage, determine the force in the spring and the vertical motion of Point G when a vertical downward 120-N force is applied (a) at Point C, (b) at Points C and H.

Derive an expression for the magnitude of the force Q required to maintain the equilibrium of the mechanism shown.

Derive an expression for the magnitude of the couple M required to maintain the equilibrium of the linkage shown.

Two 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 30 . = For the loading shown, derive an equation in P, , l, and k that must be satisfied when the system is in equilibrium.

A force P of magnitude 240 N is applied to end E of cable CDE, which passes under pulley D and is attached to the mechanism at C. Neglecting the weight of the mechanism and the radius of the pulley, determine the value of corresponding to equilibrium. The constant of the spring is 4 kN/m, k = and the spring is unstretched when 90 . =

Two identical rods ABC and DBE are connected by a pin at B and by a spring CE. Knowing that the spring is 4 in. long when unstretched and that the constant of the spring is 8 lb/in., determine the distance x corresponding to equilibrium when a 24-lb load is applied at E as shown.

Solve Problem 10.108 assuming that the 24-lb load is applied at C instead of E. PROBLEM 10.108 Two identical rods ABC and DBE are connected by a pin at B and by a spring CE. Knowing that the spring is 4 in. long when unstretched and that the constant of the spring is 8 lb/in., determine the distance x corresponding to equilibrium when a 24-lb load is applied at E as shown.

Two bars AB and BC are attached to a single spring of constant k that is unstretched when the bars are vertical. Determine the range of values of P for which the equilibrium of the system is stable in the position shown.

A homogeneous hemisphere of radius r is placed on an incline as shown. Assuming that friction is sufficient to prevent slipping between the hemisphere and the incline, determine the angle corresponding to equilibrium when 10 . =

A homogeneous hemisphere of radius r is placed on an incline as shown. Assuming that friction is sufficient to prevent slipping between the hemisphere and the incline, determine (a) the largest angle for which a position of equilibrium exists, (b) the angle corresponding to equilibrium when the angle is equal to half the value found in part a.