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engineering
mechanical engineering
Vector Mechanics For Engineers Statics 7th Edition R.C.Hibbeler - Solutions
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 θ corresponding to the equilibrium position of the mechanism when l = 15 in., r = 4.5 in., P = 15 lb, and Q = 30 lb.
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 θ corresponding to the equilibrium position of the mechanism when l = 14in., r = 5 in., P = 75lb, and Q = 150lb.
In Prob. 10.12, knowing that a = 42 in., b = 28 in., and W = 160lb, determine the tension T in cable AE when the door is held in the position for which BD = 42 in.Problem 10.12: An overhead garage door of weight W consists of a uniform rectangular panel AC that is supported by two sets of
The slender rod AB is attached to collar A and rests on a small wheel at C. Neglecting the radius of the wheel and the effect of friction, determine the value of θ corresponding to the equilibrium position of the mechanism when P = 75 N and Q = 135 N.
A force P is applied to slider C as shown. The constant of the spring is 1.6kN/m, and the spring is un-stretched when member BD is horizontal. Neglecting friction between the slider and the guide rod and knowing that BC = BD = 150 mm, determine the magnitude of P so that θ =25°
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 un-stretched 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.
Solve Prob. 10.30 assuming that the 900-N load is applied at C instead of E. Problem 10.30: 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 un-stretched and that the constant of the spring is 5kN/m, determine the value of x
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 un-stretched 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.
Solve Prob. 10.30 assuming that the 900-N load is applied at C instead of E. Problem 10.30: 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 un-stretched and that the constant of the spring is 5kN/m, determine the value of x
A vertical force P is applied to the linkage at B. The constant of the spring is 12.5 lb/in., and the spring is un-stretched when AB and BC are horizontal. Neglecting the weight of the linkage, determine the magnitude of P so that θ =25° when the system is in equilibrium.
A horizontal force P of magnitude 40 lb is applied to the mechanism at C. The constant of the spring is k = 9lb/in, and the spring is un-stretched when θ = 0. Neglecting the weight of the mechanism, determine the value of θ corresponding to equilibrium.
Knowing that the constant of spring CD is k and that the spring is un-stretched when θ = 0, determine the value of θ, where 0 ‰¤ θ ‰¤ 90°, corresponding to equilibrium for the given data. P = 150 lb, l = 30in., k = 40 lb/in.
Knowing that the constant of spring CD is k and that the spring is un-stretched when θ = 0, determine the value of θ, where 0 ‰¤ θ ‰¤ 90°, corresponding to equilibrium for the given data. P = 600N, l = 800 mm, k = 4kN/m
A cord is wrapped around drum A which is attached to member AB. Block D can move freely in its guide and is fastened to link CD. Neglecting the mass of AB and knowing that the spring is of constant 800 N/m and is undeformed when θ = 0, determine the value of θ
The lever AB is attached to the horizontal shaft BC which 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
Solve Prob. 10.39 assuming that P = 6.3kN, l=250 mm, and K = 225N ⋅ m/rad. Obtain answers in each of the following quadrants: 0
The position of crank BCD is controlled by the hydraulic cylinder AB. For the loading shown, determine the force exerted by the hydraulic cylinder on pin B knowing wing that θ =60°.
The position of crank BCD is controlled by the hydraulic cylinder AB. Determine the angle θ knowing that the hydraulic cylinder exerts a 105-lb force on pin B when the crank is in the position shown.
A cord is wrapped around a drum of radius a that is pinned at A. The constant of the spring is 15 lb/in., and the spring is unstretched when θ = 0. Knowing that a = 7.5 in. and neglecting the weight of the drum, determine the value of θ corresponding to equilibrium when a
For the linkage shown, determine the force P required for equilibrium when M= 320lb‹…in.
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 θ = 60°.
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 on when θ = 20°, determine the force exerted on pin B by
A block of weight W is pulled up a plane forming an angle α with the horizontal by a force P directed along the plane. If μ 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
Denoting by μs 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 μs ≥ tan θ.
Knowing that the coefficient of static friction between collar C and the vertical rod is 0.30, determine the magnitude of the largest and smallest couple M for which equilibrium is maintained in the position shown when θ = 35°, l = 500 mm, and P = 400 N. Problem 10.48: Denoting by μs
Denoting by μs the coefficient of static friction between the block attached to rod ACE and the horizontal surface, derive expressions in terms of P, μs, and θ for the largest and smallest magnitudes 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 magnitudes of the largest and smallest force Q for which equilibrium is maintained when θ = 30°, l = 200mm, and P = 40 N. Problem 10.50: Denoting by
Derive an expression for the mechanical efficiency of the jack discussed in Sec. 8.6. Show that if the jack is to be self-locking, the mechanical efficiency cannot exceed ½.
Using the method of virtual work, determine separately the force and the couple representing the reaction at A.
Using the method of virtual work, determine the reaction at D.
Referring to Prob. 10.41 and using the value found for the force exerted by the hydraulic cylinder AB, determine the change in the length of AB required to raise the 120-lb load 1.2 in. Problem 10.41: The position of crank BCD is controlled by the hydraulic cylinder AB. For the loading shown,
Referring to Prob. 10.46 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 2.5 in. Problem 10.46: The telescoping arm ABC is used to provide an elevated platform for construction
Determine the vertical movement of joint C if the length of member FG is increased 30 mm. (Hint: Apply a vertical load at joint C, and, using the methods of Chap. 6, compute the force exerted by member FG on joints F and G. Then apply the method of virtual work for a virtual displacement resulting
Determine the horizontal movement of joint C if the length of member FG is increased by 30 mm.
Using the method of Sec. 10.8, solve Prob. 10.30. Problem 10.30: 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 5kN/m, determine the value of x corresponding to equilibrium when a
Using the method of Sec. 10.8, solve Prob. 10.31. Problem 10.31: Solve Prob. 10.30 assuming that the 900-N load is applied at C instead of E. Problem 10.30: 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
Using the method of Sec. 10.8, solve Prob. 10.32. Problem 10.32: For the mechanism shown, block A can move freely in its guide and rests against a spring of constant 2.5 kN/m that is undeformed when θ =45°. For the loading shown, determine the value of θ corresponding
Using the method Sec. 10.8, solve Prob. 10.33. Problem 10.33: A vertical force P of magnitude 150 lb is applied to the linkage at B. The constant of the spring is 12.5 lb/in., and the spring is unstretched when AB and BC are horizontal. Neglecting the weight of the linkage, determine the value of
Using the method of Sec. 10.8, solve Prob. 10.34. Problem 10.34: A vertical force P is applied to the linkage at B. The constant of the spring is 12.5 lb/in., and the spring is unstretched when AB and BC are horizontal. Neglecting the weight of the linkage, determine the magnitude of P so that
Using the method of Sec. 10.8, solve Problem 10.36. Problem 10.36: Knowing that the constant of spring CD is k and that the spring is unstretched when θ = 0, determine the value of θ, where 0‰¤Î¸ ‰¤90°, corresponding to equilibrium
Using the method of Sec. 10.8, solve Prob. 10.37. Problem 10.37: Knowing that the constant of spring CD is k and that the spring is unstretched when θ = 0, determine the value of θ, where 0 ‰¤ θ ‰¤ 90°, corresponding to equilibrium
Using the method of Sec. 10.8, solve Prob. 10.38. Problem 10.38: A cord is wrapped around drum A which is attached to member AB. Block D can move freely in its guide and is fastened to link CD. Neglecting the mass of AB and knowing that the spring is of constant 800 N/m and is undeformed when
Show that the equilibrium is neutral in Prob. 10.1. Problem 10.1: Determine the vertical force P which must be applied at G so that the linkage is in equilibrium for the position shown.
Show that the equilibrium is neutral in Prob. 10.2. Problem 10.2: Determine the vertical force P which must be applied at G so that the linkage is in equilibrium for the position shown.
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 300 and 500 mAB = g mCD = g, determine the positions of equilibrium of the system, and state in each case whether the equilibrium is stable, unstable, or neutral.
Two identical uniform rods each of weight W and length L are attached to pulleys that are connected by a belt as shown. Assuming that no slipping occurs between the belt and the pulleys, determine the positions of equilibrium of the system, and state in each case whether the equilibrium is stable,
Two uniform rods each of mass m and length l are attached to gears as shown. For the range 0 ‰¤ θ ‰¤ 180°, 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 Sec. 10.8, solve Prob. 10.39. Determine whether the equilibrium is stable, unstable, or neutral.
In Prob. 10.40, determine whether each of the positions of equilibrium is stable, unstable, of neutral.
Angle θ is equal to 45° after a block of weight W is hung from member AB as shown. Neglecting the weight of AB and knowing that the spring is unstretched when θ =20°, determine the value of W, and state whether the equilibrium is stable, unstable, or neutral.
A block of weight W is hung from member AB as shown. Neglecting the weight of AB and knowing that the spring is unstretched when θ = 20°, determine the value of θ corresponding to equilibrium when W = 6.6 lb. State whether the equilibrium is stable, unstable, or neutral.
The slender rod AB of negligible weight is attached to two 10-lb blocks A and B that can move freely in the guides shown. Knowing that the constant of the springs is 1 lb/in. and that the unstretched length of each spring is 7.5 in., determine the value of x corresponding to equilibrium.
A slender rod AB of mass m is attached to two blocks A and B which can move freely in the guides shown. Knowing that the spring is unstretched when y = 0, determine the value of y corresponding to equilibrium when m = 12 kg, l = 750 mm, and k = 900 N/m.
The constant of spring AB is k, and the spring ring is unstretched when θ = 0. (a) Neglecting the weight of the rigid arm BCD, derive an equation in terms of θ, k, a, l, and W that is satisfied when the arm is in equilibrium. (b) Determine three values of θ corresponding to equilibrium
Spring AB of constant 2kN/m is attached to two identical drums as shown. Knowing that the spring is unstretched when en θ = 0, determine(a) The range of values of the mass m of the block for which a position of equilibrium exists,(b) The range of values of θ for which the equilibrium is
Spring AB of constant 2kN/m is attached to two identical drums as shown. Knowing that the spring is unstretched when θ = 0 and that m = 20 kg, determine the values of θ less than 180° corresponding to equilibrium. State in each case whether the equilibrium is stable unstable, or
Bar ABC is attached to collars A and B that can move freely on the rods shown. The constant of the spring is k, and the spring is unstretched when θ = 0.(a) Neglecting the mass of bar ABC, derive an equation in terms of θ, m, g, k, and l that is satisfied when bar ABC is in
A slender rod AB of negligible mass 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 θ corresponding to equilibrium.
A slender rod AB of negligible mass is attached to two collars A and B that can move freely along the guide rods shown. n. Knowing that β =30°, P = 100 N, and Q = 25 N, determine the value of angle θ corresponding to equilibrium.
The 25-lb block D can slide freely on the inclined surface. Knowing that the constant of the spring is 2.5 lb/in. and that the spring is unstretched when θ = 0, determine the value of θ corresponding to equilibrium.
Cable AB is attached to two springs and passes through a ring at C. Knowing that the springs are unstretched when y = 0, determine the distance y corresponding to equilibrium.
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 θ corresponding to equilibrium when m = 20kg, r = 180mm, and k = 3kN/m.
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 θ corresponding to equilibrium when m = 20kg, r = 180 mm, and k = 3 kN/m.
Rod AB is attached to a hinge at A and to two springs of constant k that are unstretched in the position shown. If 50 h = in., d = 24 in., and W = 160 lb, determine the range of values of k for which the equilibrium of the rod is stable in the given position. Each spring can act in either tension
Rod AB is attached to a hinge at A and to two springs of constant k that are unstretched in the position shown. If h = 30 in., k = 4 lb/in., and W = 40 lb, determine the smallest distance d for which the equilibrium of the rod is stable in the given position. Each spring can act in either tension
The uniform plate ABCD of negligible mass is attached to four springs of constant k and is in equilibrium in the position shown. Knowing that the springs can act in either tension or compression and are undeformed in the given position, determine the range of values of the magnitude P of two equal
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.
Bar AC is attached to a hinge at A and to a spring of constant k that is undeformed when the bar is vertical. Knowing that the spring can act in either tension or compression, determine the range of values of P for which the equilibrium of the system is stable in the position shown.
Bars BC and EF are connected at G by a pin that is attached to BC and that can slide freely in a slot cut in EF. Determine the smallest mass m1 for which the equilibrium of the mechanism is stable in the position shown.
The horizontal bar BEH is pinned to collar E and to vertical bars AC and GI. The collar 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 = 480mm, b = 400 mm, and P = 600 N.
Bars AB and BC each of length l and of negligible weight are attached to two spring each of constant k. The springs are 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.
Solve Prob. 10.97 knowing that 400 l = mm and k = 1.25kN/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 θ1 =θ2 =0. Determine the
Bar ABC of length 2a and negligible mass is hinged at C to a drum of radius a as shown. Knowing that the constant of each spring is k and that the springs are undeformed when θ1 = θ2 = 0, determine the range of values of P for which the equilibrium position θ1 = θ2 = 0 is
Solve Prob. 10.99 knowing that 2 kN/k = m and a = 350 mm. Problem 10.99: Bar ABC of length 2a and negligible mass is hinged at C to a drum of radius a as shown. Knowing that the constant of each spring is k and that the springs are undeformed when θ1 = θ2 = 0, determine the range of
Knowing that the maximum friction force exerted by the bottle on the cork is 300 N, determine(a) The force P which 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.
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 θ =70°.
Determine the vertical force P which must be applied at G so that the linkage is in equilibrium for the position shown.
Determine the couple M which must be applied to member DEFG so that the linkage is in equilibrium for the position shown.
Derive an expression for the magnitude of the couple M so that the linkage is in equilibrium for the position shown.
Two rods AC and CE are connected by a pin at C and by a spring AE. The constant of the spring is 1.5 lb/in., and the spring is unstretched when θ = 30°. Knowing that l = 10 in. and neglecting the weight of the rods, determine the value of θ corresponding to equilibrium
For the linkage shown, determine the couple M required for equilibrium when l = 1.8 ft, Q = 40 lb, and θ = 65°.
Determine the vertical force P which must be applied at G so that the linkage is in equilibrium for the position shown.
Determine the vertical movement of joint D if the length of member BF is increased by 75 mm. (Hint: Apply a vertical load at joint D, and, using the methods of Chap. 6, compute the force exerted by member BF on joints B and F. Then apply the method of virtual work for a virtual displacement
Determine the horizontal movement of joint D if the length of member BF is increased by 75 mm.
Two uniform rods, AB and CD, are attached to gears of equal radii as shown. Knowing that 3.5 kg mAB = and 1.75 kg, CD m = determine the positions of equilibrium of the system, and state in each case whether the equilibrium is stable, unstable, or neutral.
A slender rod AB of mass m 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 θ corresponding to equilibrium when m = 125kg, l = 320 mm, and k = 15kN/m. State in each case
A 13.2-N force P is applied to the lever which controls the auger of a snow blower. Determine the moment of P about A when α is equal to 30°.
The force P is applied to the lever which controls the auger of a snow blower. Determine the magnitude and the direction of the smallest force P which has a 2.20- N m ⋅ counterclockwise moment about A.
A 13.1-N force P is applied to the lever which controls the auger of a snow blower. Determine the value of α knowing that the moment of P about A is counterclockwise and has a magnitude of 1.95 N ⋅ m.
A foot valve for a pneumatic system is hinged at B. Knowing that α = 28°, determine the moment of the 4-lb force about point B by resolving the force into horizontal and vertical components.
A foot valve for a pneumatic system is hinged at B. Knowing that α = 28°, determine the moment of the 4-lb force about point B by resolving the force into components along ABC and in a direction perpendicular to ABC.
It is known that a vertical force of 800 N is required to remove the nail at C from the board. As the nail first starts moving, determine (a) The moment about B of the force exerted on the nail, (b) The magnitude of the force P which creates the same moment about B if α = 10°, (c)
A sign is suspended from two chains AE and BF. Knowing that the tension in BF is 45 lb, determine(a) The moment about A of the force exert by the chain at B,(b) The smallest force applied at C which creates the same moment about A.
A sign is suspended from two chains AE and BF. Knowing that the tension in BF is 45 lb, determine(a) The moment about A of the force exerted by the chain at B,(b) The magnitude and sense of the vertical force applied at C which creates the same moment about A,(c) The smallest force applied at B
The tailgate of a car is supported by the hydraulic lift BC. If the lift exerts a 125-N force directed along its center line on the ball and socket at B, determine the moment of the force about A.
The tailgate of a car is supported by the hydraulic lift BC. If the lift exerts a 125-N force directed along its center line on the ball and socket at B, determine the moment of the force about A.
A winch puller AB is used to straighten a fence post. Knowing that the tension in cable BC is 260 lb, length a is 8 in., length b is 35 in., and length d is 76 in., determine the moment about D of the force exerted by the cable at C by resolving that force into horizontal and vertical components
It is known that a force with a moment of 7840 lb ⋅in. about D is required to straighten the fence post CD. If a = 8 in., b = 35 in., and d = 112 in., determine the tension that must be developed in the cable of winch puller AB to create the required moment about point D.
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