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engineering
mechanical engineering
Vector Mechanics For Engineers Statics And Dynamics 8th Edition Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell - Solutions
The coefficients of friction are μs = 0.40 and kμ = 0.30 between all surfaces of contact. Determine the force P for which motion of the 30-kg block is impending if cable AB(a) Is attached as shown,(b) Is removed.
War air is contained a piston cylinder assembly oriented horizontally as shown in Fig.P2.31. The air cools slowly from an initial volume of 0.003 m3 to a final volume of 0.002 m3. During the process, the spring exerts a force that varies linearly from an initial value of 900 N to a final value of
Air contained within a piston-cylinder assembly is slowly heated. As shown in Fig.P2.32, m during this process the pressure first varies linearly with volume and then remains constant. Determine the total work, in kJ.
The 16-lb block A is attached to link AC and rests on the 24-lb block B. Knowing that the coefficient of static friction is 0.20 between all surfaces of contact and neglecting the mass of the link, determine the value of θ for which motion of block B is impending.
The 20-lb block A and the 40-lb block B are at rest on an incline as shown. Knowing that the coefficient of static friction is 0.25 between all surfaces of contact, determine the value of θ for which motion is impending.
A packing crate of mass 40 kg must be moved to the left along the floor without tipping. Knowing that the coefficient of static friction between the crate and the floor is 0.35, determine(a) The largest allowable value of α,(b) The corresponding magnitude of the force P.
A packing crate of mass 40 kg is pulled by a rope as shown. The coefficient of static friction between the crate and the floor is 0.35. If α =40°, determine(a) The magnitude of the force P required for impending motion of the crate,(b) Whether sliding or tipping is impending.
The cylinder shown is of weight W and radius r. Express in terms of W and r the magnitude of the largest couple M which can be applied to the cylinder if it is not to rotate assuming that the coefficient of static friction is(a) Zero at A and 0.36 at B,(b) 0.30 at A and 0.36 at B.
Carbon monoxide gas (CO) contained within a piston cylinder assembly undergoes three processes in series.Process 1-2: Expansion from P1= 5 bar, V1=0.2m3, to V2=1 m3, during which the pressure volume relationship in pV= Constant. Process 2-3: Constant volume heating from state 2 to state 3, where
A couple of magnitude 50lb ‹…ft is applied to the drum. Determine the smallest force that must be exerted by the hydraulic cylinder if the drum is not to rotate when the applied couple is directed(a) Clockwise,(b) Counterclockwise.
The hydraulic cylinder exerts on pin B a force of 600 lb directed to the right. Determine the moment of the friction force about the axle of the drum when the drum is rotating(a) Clockwise(b) Counterclockwise.
Air contained within a piston cylinder assembly undergoes three processes in series: Process 1-2: Compression at constant pressure from P1=10 lbf/in2, V1= 4ft3 to state 2. Process 2-3: Constant-volume heating to state 3, where P3= 50 lbf/in2.Process 3-1: Expansion to the initial state, during which
A cord is attached to and partially wound around a cylinder of weight W and radius r that rests on an incline as shown. Knowing that the coefficient of static friction between the cylinder and the incline is 0.35, find(a) The smallest allowable value of θ if the cylinder is to remain in
The belt sander shown in Fig.P2.35 has a belt speed of 1500 ft/min. the coefficient of friction between the sander and a plywood surface being finished is 0.2. If the downward (normal) force on the sander is 15 lbf, determine(a) The power transmitted by the belt, in Btu/s and hp, and(b) The work
A 6.5-m ladder AB of mass 10 kg leans against a wall as shown. Assuming that the coefficient of static friction μs is the same at both surfaces of contact, determine the smallest value of μs for which equilibrium can be maintained.
A 6.5-m ladder AB of mass 10 kg leans against a wall as shown. Assuming that the coefficient of static friction μs is the same at both surfaces of contact, determine the smallest value of μs for which equilibrium can be maintained.
The driveshaft of a building’s air-handling fan is turned at 300 RPM by a belt running on a 0.3 m diameter pulley,. The net force applied by the belt on the pulley is 2000 N. Determine the torque applied by the belt on the pulley, in N ∙ m, and the power transmitted, in kW.
End A of a slender, uniform rod of weight W and length L bears on a horizontal surface as shown, while end B is supported by a cord BC of length L. Knowing that the coefficient of static friction is 0.40, determine(a) The value of θ for which motion is impending,(b) The corresponding value of
A 10-V battery supplies a constant current of 0.5amp to a resistance for 30 min(a) Determine the resistance, in ohms,(b) For the battery, determine the amount of energy transfer by work, in kJ.
A slender rod of length L is lodged between peg C and the vertical wall and supports a load P at end A. Knowing that θ =35° and that the coefficient of static friction is 0.20 at both B and C, determine the range of values of the ratio L/a for which equilibrium is maintained.
The shear shown is used to cut and trim electronic-circuit-board laminates. Knowing that the coefficient of kinetic friction between the blade and the vertical guide is 0.20, determine the force exerted by the edge E of the blade on the laminate.
A 12-V automotive storage battery is charged with a constant current of 2amp for 24h. If electricity costs $0.08 per kW ∙ h, determine the cost of recharging the battery
The basic components of a clamping device are bar AB, locking plate CD, and lever EFG; the dimensions of the slot in CD are slightly larger than those of the cross section of AB. To engage the clamp, AB is pushed against the work piece, and then force P is applied. Knowing that P = 40 lb and
As shown in Fig.P2.39, a steel wire suspended vertically having a cross-section area A and an initial length X0 is stretched by a downward force F applied to the end of the wire. The normal stress in the wire varies linearly according to σ= C ε, where ε is the strain, given by
The friction tongs shown are used to lift a 750-lb casting. Knowing that 36 h = in., determine the smallest allowable value of the coefficient of static friction between the casting and blocks D and D′.
A soap film is suspended on a wire frame, as shown in Fig.2.10. The movable wire is displaced by an applied force F. If the surface tension remains constant (a) Obtain an expression for the work done in stretching the film in terms of the surface tension τ, length ℓ, and displacement
The steel-plate clamp shown is used to lift a steel plate H weighing 550 lb. Knowing that the normal force exerted on steel cam EG by pin D forms an angle of 40° with the horizontal and neglecting the friction force between the cam and the pin, determine the smallest allowable value of the
The steel-plate clamp shown is used to lift a steel plate H weighing 550 lb. Knowing that the normal force exerted on steel cam EG by pin D forms an angle of 40° with the horizontal and neglecting the friction force between the cam and the pin, determine the smallest allowable value of the
The lift-tong mechanism shown consists of twin four-bar linkages and is used to lift a 40-kg machine component. Knowing that LAB = 36 mm, determine the smallest allowable value of the coefficient of static friction between the component and the gripping pads when(a) α = 0,(b) α =30°.
As shown in Fig. P2.41, a spring having an initial unscratched length of ℓ0 is stretched by a force F applied at its end. The stretched length is ℓ. By Hooke€™s law, the force is linearly related to the spring extension by F = k (ℓ - ℓ0), where k is the stiffness.
A flat surface having an area of 2m2 and a temperature of 350K is cooled convectively by a gas at 300K. Using data from Table 2, 1, determine the largest and smallest heat transfer rates, in kW, that might be encountered for(a) Free convection,(b) Forced convection.
A pipe of diameter 60 mm is gripped by the Still son wrench shown. Portions AB and DE of the wrench are rigidly attached to each other and portion CF is connected by a pin at D. If the wrench is to grip the pipe and be self-locking, determine the required minimum coefficients of friction at A and C.
A 0.2-m-thick plane wall is constructed of concrete. At steady state, the energy transfer rate by conduction through a 1-m2 area of the wall is 0.15kW. If the temperature distribution is linear through the wall, what is the temperature difference across the wall, in K?
A light metal panel is welded to two short sleeves of l-in. inside diameter that can slide on a horizontal rod. The coefficients of friction between the sleeves and the rod are μs = 0.40 and μk = 0.30. A cord attached to corner C is used to move the panel along the rod. Knowing that the cord
(a) Solve Prob. 8.32 assuming that the cord is attached at point E at a distance x = 4 in. from corner C.(b) Determine the largest value of x for which the panel can be moved to the right.Problem 8.32: A light metal panel is welded to two short sleeves of l-inside diameter that can slide on a
As shown in Fig. P2.44, the 6-in-thick exterior wall of a building has an average thermal conductivity of 0.32Btu/h ∙ ft ∙ oR. At steady state, the temperature of the wall decreases linearly from T1 = 70oF on the inner surface to T2 on the outer surface. The outside ambient air
A collar B of mass m is attached to the spring AB and can move along the rod shown. The constant of the spring is 1.5kN/m and the spring is unscratched when θ = 0. Knowing that the coefficient of static friction between the collar and the rod is 0.40, determine the range of values of m for
A collar B of mass m is attached to the spring AB and can move along the rod shown. The constant of the spring is 1.5kN/m and the spring is unscratched when θ = 0. Knowing that the coefficient of static friction between the collar and the rod is 0.40, determine the range of values of m for
As shown in Fig. P2.45, an oven wall consists of a 0.25-in-thick layer of steel (ks = 8.7Btu/h ∙ft∙ oR) and a layer of thick (kb = 0.42Btu/h ∙ ft ∙ oR). At steady state, a temperature decrease of 1.2oF occurs over the steel layer. The inner temperature of the steel layer is
Denoting by μs the coefficient of static friction between the collar C and the horizontal rod, determine the largest magnitude of the couple M for which equilibrium is maintained. Explain what happens if μs ≥ tan θ.
Bar AB rests on the two quarter-circle surfaces shown. A force P is applied at point C which is located at a distance a from end A. Neglecting the weight of the bar and knowing that the coefficient of static friction between the bar and each of the surfaces is 0.35, determine the smallest value of
The 9-lb block A and the 6-lb block B are connected by a slender rod of negligible mass. The coefficient of static friction is 0.40 between all surfaces of contact. Knowing that for the position shown the rod is horizontal determine the range of values of P for which equilibrium is maintained.
Two rods are connected by a collar at B. A couple MA of magnitude 12lb‹…ft is applied to rod AB. Knowing that μs = 0.30 between the collar and rod AB, determine the largest couple MC for which equilibrium will be maintained.
Slider A is pinned to flywheel B and slides in the slot of yoke CD. Neglecting friction in bearings E and F and knowing that P = 8 lb and μs = 0.25 between the slider and the yoke, determine(a) The largest couple MB for which equilibrium can be maintained,(b) The smallest couple MB
The 12-lb slender rod AB is pinned at A and Knowing that the diameter of the cylinder is 12.5 in. and that the coefficient of static friction is 0.35 between all surfaces of contact, determine the largest magnitude of the force P for which equilibrium is maintained.
The masses of blocks A and C are 2.4 kg and 6 kg respectively. Knowing that μs = 0.50 between block A and the incline and μs = 0.30 between block C and the horizontal surface, determine(a) The smallest value of the mass of block B for which the blocks are in equilibrium,(b) The largest value
Blocks A, B, and C having the weights shown are at rest on an incline. Denoting by μs the coefficient of static friction between all surfaces of contact, determine the smallest value of μs for which equilibrium is maintained.
A slender, uniform steel rod of length 9 in. is placed inside a pipe as shown. Knowing that the coefficient of static friction between the rod and the pipe is 0.20, determine the largest value of θ for which the rod will not fall into the pipe.
Two slender rods of negligible weight are pin-connected at A and attached to the 18-lb block B and the 80-lb block C as shown. The coefficient of static friction is 0.55 between all surfaces of contact. Determine the range of values of P for which equilibrium is maintained.
Two 8° wedges of negligible weight are used to move and position a 530-lb block. Knowing that the coefficient of static friction is 0.40 at all surfaces of contact, determine the magnitude of the force P for which motion of the block is impending.
Two 8° wedges of negligible weight are used to move and position a 530-lb block. Knowing that the coefficient of static friction is 0.40 at all surfaces of contact, determine the magnitude of the force P for which motion of the block is impending.
An 18-kg mass is hung from a lever which rests against a 10° wedge at A and is supported by a frictionless hinge at C. Knowing that the coefficient of static friction is 0.25 at both surfaces of the wedge and that for the position shown the spring is stretched 100 mm, determine(a) The magnitude
Solve Prob. 8.48 assuming that force P is directed to the left. Problem 8.48: An 18-kg mass is hung from a lever which rests against a 10° wedge at A and is supported by a frictionless hinge at C. Knowing that the coefficient of static friction is 0.25 at both surfaces of the wedge and that for
The elevation of the end of a steel beam supported by a concrete floor is adjusted by means of the steel wedges E and F. The base plate CD has been welded to the lower flange of the beam, and the end reaction of the beam is known to be 90 KN. The coefficient of static friction is 0.30 between the
The elevation of the end of a steel beam supported by a concrete floor is adjusted by means of the steel wedges E and F. The base plate CD has been welded to the lower flange of the beam, and the end reaction of the beam is known to be 90 KN. The coefficient of static friction is 0.30 between the
A 16° wedge A of negligible weight is placed between two 175-lb blocks B and C which are at rest on inclined surfaces as shown. The coefficient of static friction is 0.40 between both the wedge and the blocks and block C and the incline. Determine the magnitude of the force P for which motion
A 16° wedge A of negligible weight is placed between two 175-lb blocks B and C which are at rest on inclined surfaces as shown. The coefficient of static friction is 0.40 between both the wedge and the blocks and block C and the incline. Determine the magnitude of the force P for which motion
To level a wood deck, wood wedges A and B are placed under a corner of the deck. Wedge B rests on a wood board as shown, and a bar clamp is used to apply equal and opposite forces to the wedges. Knowing that θ =18° and that the coefficient of static friction between all wood surfaces is
To level a wood deck, wood wedges A and B are placed under a corner of the deck, and wedge B rests on a wood board as shown. Knowing that the coefficient of static friction between all wood surfaces is 0.35 and 0.60 between the board and the ground, determine the maximum value of the wedge angle
A 12° wedge is to be forced under the corner B of the 250-lb quarter cylinder shown. Knowing that the coefficient of static friction between the cylinder and the wedge is 0.35 and 0.50 between the wedge and the floor, determine the magnitude of the force P required for impending motion of the
A small screwdriver is used to pry apart the two coils of a circular key ring. The wedge angle of the screwdriver blade is 16° and the coefficient of static friction is 0.12 between the coils and the blade. Knowing that a force P of magnitude 3.5 N was required to insert the screwdriver to the
A conical wedge is placed between two horizontal plates that are then slowly moved toward each other. Indicate what will happen to the wedge(a) If μs = 0.20,(b) If μs = 0.30.
A 6° steel wedge is driven into the end of an ax handle to lock the handle to the ax head. The coefficient of static friction between the wedge and the handle is 0.35. Knowing that a force P of magnitude 60 lb was required to insert the wedge to the equilibrium position shown, determine the
A 10° wedge is forced under an 80-kg cylinder as shown. Knowing that the coefficient of static friction at all surfaces is 0.25, determine the force P for which motion of the wedge is impending.
A 10° wedge is forced under an 80-kg cylinder as shown. Knowing that the coefficient of static friction between the cylinder and the vertical wall is 0.30, determine the smallest coefficient of static friction between the wedge and the cylinder for which shipping can be impending at B.
Bags of grass seed are stored on a wooden plank as shown. To move the plank, a 9° wedge is driven under end A. Knowing that the weight of the grass seed can be represented by the distributed load shown and that the coefficient of static friction is 0.45 between all surfaces of contact,(a)
Solve Prob. 8.62 assuming that the wedge is driven under the plank at B instead of at A. Problem 8.62: Bags of grass seed are stored on a wooden plank as shown. To move the plank, a 9° wedge is driven under end A. Knowing that the weight of the grass seed can be represented by the distributed
The 10-kg block A is at rest against the 50-kg block B as shown. The coefficient of static friction μs is the same between blocks A and B and between block B and the floor, while friction between block A and the wall can be neglected. Knowing that 150 P = N, determine the value of μs for
Solve Prob. 8.64 assuming that μs is the coefficient of static friction between all surfaces of contact. Problem 8.64: The 10-kg block A is at rest against the 50-kg block B as shown. The coefficient of static friction μs is the same between blocks A and B and between block B and the floor,
Derive the following formulas relating the load W and the force P exerted on the handle of the jack discussed in Section 8.6. (a) P = (Wr/a) tan (θ + φs), to raise the load; (b) P = (Wr/a) tan (φs + θ), to lower the load if the screw is self-locking; (c) P = (Wr/a) tan
The square-threaded worm gear shown has a mean radius of 1.5 in. and a lead of 0.375 in. The larger gear is subjected to a constant clockwise couple of 7.2 kip ⋅in. Knowing that the coefficient of static friction between the two gears is 0.12, determine the couple that must be applied to shaft
In Prob. 8.67, determine the couple that must be applied to shaft AB to rotate the gear clockwise. Problem 8.67: The square-threaded worm gear shown has a mean radius of 1.5 in. and a lead of 0.375 in. The larger gear is subjected to a constant clockwise couple of 7.2 kip ⋅in. Knowing that the
High-strength bolts are used in the construction of many steel structures. For a 1-in.-nominal-diameter bolt the required minimum bolt tension is 47.25 kips, assuming the coefficient of friction to be 0.35, determine the required couple that should be applied to the bolt and nut. The mean diameter
The position of the automobile jack shown is controlled by a screw ABC that is single-threaded at each end (right-handed thread at A, left-handed thread at C). Each thread has a pitch of 2 mm and a mean diameter of 7.5 mm. If the coefficient of static friction is 0.15, determine the magnitude of
For the jack of Prob. 8.70, determine the magnitude of the couple M that must be applied to lower the automobile. Problem 8.70: The position of the automobile jack shown is controlled by a screw ABC that is single-threaded at each end (right-handed thread at A, left-handed thread at C). Each thread
The vise shown consists of two members connected by two double-threaded screws of mean radius 6 mm and pitch 2 mm. The lower member is threaded at A and B (μs =0.35), but the upper member is not threaded. It is desired to apply two equal and opposite forces of 540 N on the blocks held
(a) Which screw should be adjusted first?(b) The maximum couple applied in tightening the second screw.
In the gear-pulling assembly shown, the square-threaded screw AB has a mean radius of 0.9375 in. add a lead of 0.25 in. Knowing that the coefficient of static friction is 0.10, determine the couple which must be applied to the screw to produce a force of 1000 lb on the gear. Neglect friction at end
A hot-metal ladle and its contents have a mass of 50 Mg. Knowing that the coefficient of static friction between the hooks and the pinion is 0.30, determine the tension in cable AB required to start tipping the ladle. Note: the simplification sin (tan−1 μ) ≈ μ is NOT used in the
A windlass of 10-in. diameter is used to raise or lower a 160-lb load. The windlass is supported by two poorly lubricated bearings of 3-in. diameter. Knowing that the coefficient of static friction between the shaft and the bearings is 0.50, determine the magnitude of the force P required for
A windlass of 10-in. diameter is used to raise or lower a 160-lb load. The windlass is supported by two poorly lubricated bearings of 3-in. diameter. Knowing that the coefficient of static friction between the shaft and the bearings is 0.50, determine the magnitude of the force P required for
A windlass of 10-in. diameter is used to raise or lower a 160-lb load. The windlass is supported by two poorly lubricated bearings of 3-in. diameter. Knowing that the coefficient of static friction between the shaft and the bearings is 0.50, determine the magnitude of the smallest force P required
A windlass of 10-in. diameter is used to raise or lower a 160-lb load. The windlass is supported by two poorly lubricated bearings of 3-in. diameter. Knowing that the coefficient of static friction between the shaft and the bearings is 0.50, determine the magnitude of the smallest force P required
Control lever ABC fits loosely on an 18-mm-diameter shaft at support B. Knowing that 130 P = N for impending clockwise rotation of the lever, determine(a) The coefficient of static friction between the shaft and the lever,(b) The magnitude of the force P for which counterclockwise rotation of the
The block and tackle shown are used to raise a 600-N load. Each of the 60-mm-diameter pulleys rotates on a 10-mm-diameter axle. Knowing that the coefficient of kinetic friction is 0.20, determine the tension in each portion of the rope as the load is slowly raised.
The block and tackle shown is used to lower a 600-N load. Each of the 60-mm-diameter pulleys rotates on a 10-mm-diameter axle. Knowing that the coefficient of kinetic friction is 0.20, determine the tension in each portion of the rope as the load is slowly lowered.
The link arrangement shown is frequently used in highway bridge construction to allow for expansion due to changes in temperature. At each of the 3-in.-diameter pins A and B the coefficient of static friction is 0.20. Knowing that the vertical component of the force exerted by BC on the link is 50
A gate assembly consisting of a 24-kg gate ABC and a 66-kg counterweight D is attached to a 24-mm-diameter shaft B which fits loosely in a fixed bearing. Knowing that the coefficient of static friction is 0.20 between the shaft and the bearing, determine the magnitude of the force P for which
A gate assembly consisting of a 24-kg gate ABC and a 66-kg counterweight D is attached to a 24-mm-diameter shaft B which fits loosely in a fixed bearing. Knowing that the coefficient of static friction is 0.20 between the shaft and the bearing, determine the magnitude of the force P for which
A gate assembly consisting of a 24-kg gate ABC and a 66-kg counterweight D is attached to a 24-mm-diameter shaft B which fits loosely in a fixed bearing. Knowing that the coefficient of static friction is 0.20 between the shaft and the bearing, determine the magnitude of the force P for which
A gate assembly consisting of a 24-kg gate ABC and a 66-kg counterweight D is attached to a 24-mm-diameter shaft B which fits loosely in a fixed bearing. Knowing that the coefficient of static friction is 0.20 between the shaft and the bearing, determine the magnitude of the force P for which
A 500-lb crate rests on a dolly as shown. The dolly has four 5-in.-diameter wheels with 0.5-in.-diameter axles. Knowing that the coefficients of friction are μs = 0.12 and μk = 0.08, determine the magnitude of the horizontal force P required(a) For impending motion of the dolly,(b) To keep
A scooter is designed to roll down a 3 percent slope at a constant speed. Assuming that the coefficient of kinetic friction between the 25-mm-diameter axles and the bearing is 0.12, determine the required diameter of the wheels. Neglect the rolling resistance between the wheels and the ground.
A 7-in.-diameter buffer weighs 10.1 lb. The coefficient of kinetic friction between the buffing pad and the surface being polished is 0.60. Assuming that the normal force per unit area between the pad and the surface is uniformly distributed, determine the magnitude Q of the horizontal forces
The pivot for the seat of a desk chair consists of the steel plate A, which supports the seat, the solid steel shaft B which is welded to A and which turns freely in the tubular member C, and the nylon bearing D. If the weight W of a scatted 80-kg person acts directly above the pivot, determine the
As the surfaces of a shaft and a bearing wear out, the frictional resistance of a thrust bearing decreases it is generally assumed that the wear is directly proportional to the distance traveled by any given point of the shaft and thus to the distance r from the point to the axis of the shaft.
Assuming that bearings wear out as indicated in Prob. 8.92, show that the magnitude M of the couple required to overcome the frictional resistance of a worn-out collar bearing is M = 1/2 μk P (R1 + R2) where P = magnitude of the total axial force R1, R2 = inner and outer radii of collar
Assuming that the pressure between the surfaces of contact of the conical bearing shown is uniform, show that the magnitude M of the couple required to overcome frictional resistance is
Solve Prob. 8.90 assuming that the normal force per unit area between the pad and the surface varies linearly from a maximum at the center to zero at the circumference of the pad. Problem 8.90: A 7-in.-diameter buffer weighs 10.1 lb. The coefficient of kinetic friction between the buffing pad and
The pivot for the seat of a desk chair consists of the steel plate A, which supports the seat, the solid steel shaft B which is welded to A and which turns freely in the tubular member C, and the nylon bearing D. If the weight W of a scatted 80-kg person acts directly above the pivot, determine the
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