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engineering
engineering mechanics statics

Engineering Mechanics Statics & Dynamics 15th Edition Russell C. Hibbeler - Solutions

At the instant shown, gear A is rotating with a constant angular velocity of ωA = 6 rad/s. Determine the largest angular velocity of gear B and the maximum speed of point C. 100 mm 00 B B -100 mm @A= 6 rad/s 100 mm 100 mm virriv
At the instant shown, the shaft and plate rotates with an angular velocity of ω = 14 rad/s and angular acceleration of α = 7 rad/s2. Determine the velocity and acceleration of point D located on the corner of the plate at this instant. Express the result in Cartesian vector form. X D 0.4
For a short time a motor of the random-orbit sander drives the gear A with an angular velocity of ωA = 40(t3 + 6t) rad/s, where t is in seconds. This gear is connected to gear B, which is fixed connected to the shaft CD. The end of this shaft is connected to the eccentric spindle EF and pad P,
If the shaft and plate rotates with a constant angular velocity of ω = 14 rad/s, determine the velocity and acceleration of point C located on the corner of the plate at the instant shown. Express the result in Cartesian vector form. X D 0.4 m B Z 0.4 m α W 0.6 m 0.3 m 0.2 m C 0.3 m y
The rod assembly is supported by ball-and-socket joints at A and B. At the instant shown it is rotating about the y axis with an angular velocity ω = 5 rad/s and has an angular acceleration α = 8 rad/s². Determine the magnitudes ofthe velocity and acceleration of point C at this instant.Solve
Rotation of the robotic arm occurs due to linear movement of the hydraulic cylinders A and B. If this motion causes the gear at D to rotate clockwise at 5 rad/s, determine the magnitudes of velocity and acceleration of the part C held by the grips of the arm. A 4 ft D 45° -B 3 ft 2 ft
Determine the velocity and acceleration of the plate at the instant θ = 30°, if at this instant the circular cam is rotating about the fixed point O with an angular velocity v = 4 rad/s and an angular acceleration a = 2 rad/s2. 120 mm 150 mm ω, α C AMA
The bar DC rotates uniformly about the shaft at D with a constant angular velocity ω. Determine the velocity and acceleration of the bar AB, which is confined by the guides to move vertically. Al @ D B
The bar DC rotates uniformly about the shaft at D with angular velocity α and angular acceleration α. Determinethe velocity and acceleration of the bar AB, which isconfined by the guides to move vertically. T A W D C T B
Determine the velocity and acceleration of the follower rod CD as a function of θ when the contact between the cam and follower is along the straight region AB on the face of the cam. The cam rotates with a constant counterclockwise angular velocity ω. О A Ө с B D
Rod CD presses against AB, giving it an angular velocity. If the angular velocity of AB is maintained at ω = 5 rad/s, determine the required magnitude of the velocity v of CD as a function of the angle θ of rod AB. DE B CI ·X W A 2 ft
Determine the velocity and acceleration of platform P as a function of the angle θ of cam C if the cam rotates with a constant angular velocity ω. The pin connection does not cause interference with the motion of P on C.The platform is constrained to move vertically by the smooth vertical guides.
Determine the angular velocity of rod CD at the instant θ = 30°. Rod AB moves to the left at a constant rate vAB = 5 m/s. CD 0 A 0.3 m ↓ D B VAB
At the instant shown the boomerang has an angular velocity ω = 4 rad/s, and its mass center G has a velocity vG = 6 in./s. Determine the velocity of point B at this instant. VG = 6 in./s 30° G 1.5 in. 45 5 in. B w = 4 rad/s
Determine the angular acceleration of rod CD at the instant θ = 30°. Rod AB has zero velocity, i.e., vAB = 0, and an acceleration of αAB = 2 m/s2 to the right when θ = 30°. WCD A 0.3 m L D B VAB
A bowling ball is cast on the "alley" with a backspin of ω = 10 rad/s while its center O has a forward velocity of V0 = 8 m/s. Determine the velocity of the contact point A in contact with the alley. 120 mm A 3 10 rad/s Vo = 8 m/s
If bar AB has an angular velocity ωAB = 4 rad/s, determine the velocity of the slider block C at the instant shown. 200 mm 150 mm 30° B ФАВ 60° 4 rad/s
The pinion gear A rolls on the fixed gear rack B with an angular velocity ω = 4 rad/s. Determine the velocity of the gear rack C. w ( C you A MY B 0.3 ft
Determine the angular velocity of links AB and BC at the instant θ = 30°. Also, sketch the position of link BC when θ = 55°, 45°, and 30° to show its general plane motion. 1 ft B B 3 ft vc = 6 ft/s
The pinion gear rolls on the gear racks. If B is moving to the right at 8 ft/s and C is moving to the left at 4 ft/s, determine the angular velocity of the pinion gear and the velocity of its center A. W C A. M B 0.3 ft
Knowing that the angular velocity of link AB is ωAB = 4 rad/s, determine the velocity of the collar at C and the angular velocity of link CB at the instant shown. Link CB is horizontal at this instant. 45° -350 mm- = WAB = 4 rad/s A 60° В 500 mm
At the instant shown, the truck travels to the right at 8 m/s. If the pipe does not slip at B, determine its angular velocity if its mass center G appears to remain stationary to an observer on the ground. О B -1.5 m
The inner hub of the roller bearing is rotating with an angular velocity of ωi = 6 rad/s, while the outer hub is rotating in the opposite direction at ωo = 4 rad/s. Determine the angular velocity of each of the rollers if they roll on the hubs without slipping. 50 mm w = 6 rad/s K 25 mm w = 4
The clockwise angular velocity of the link AB is 2 rad/s. Determine the angular velocity of the connecting links BC and CD at the instant shown. C - 4 in.- A WAB = 2 rad/s 90⁰ 45° 5 in. 45° B D 3 in.
The wheel rolls on its hub without slipping on the horizontal surface. If the velocity of the center of the wheel is 2 ft/s to the right, determine the velocity of points A and B at the instant shown. B 8 in. B ✈ 3 in. A 0.5 in. A 1 in.
The rod CD has a downward velocity of 6 ft/s. The rod is pinned at C to gear B. Determine the velocity of the gear rack A at the instant shown. D Oc 6ft/s 0.75 ft 1 ft мимиллии A B
Determine the velocity of the center of gravity G of the connecting rod at the instant shown. Piston Ρ is moving upward with a velocity of 300 in./s. Up = 300 in./s G 30° P O B. 5 in. 2.75 in. 1.45 in.
If the slider block A is moving downward at vA = 4 m/s, determine the velocities of blocks B and C at the instant shown. B Во 250 mm 400 mm 30° 5 3 دیا D 300 mm 300 mm E VA = 4 m/s
The gauge is used to indicate the safe load acting at the end of the boom,B, when it is in any angular position. It consists of a fixed dial plate D and an indicator arm ACE which is pinned to the plate at C and to a short link EF. If the boom is pin-connected to the trunk frame at G and is
If the slider block A is moving downward at vA = 4 m/s, determine the velocity of point E at the instant shown. Во 250 mm 400 mm 30° 5 3 D 300 mm 300 mm E VA = 4 m/s
If the link AB has an angular velocity of ω = 4 rad/s at the instant shown, determine the velocity of the slider block E at this instant. B 1 ft D 2 ft 1 ft Co 30% 30° 2 ft WAB = 4 rad/s -E
Piston P moves upward with a velocity of 300in./s at the instant shown. Determine the angular velocity of the crankshaft AB at this instant. Up = 300 in./s ↑ G- 30° P B. 5 in. 2.75 in. 1.45 in.
The pinion gear A rolls on the fixed gear rack B with an angular velocity ω = 4 rad/s Determine the velocity of the gear rack C. "↑ w = 4 rad/s m m www B 0.3 ft роботи
The planetary gear system is used in an automatic transmission for an automobile. By locking or releasing certain gears, it has the advantage of operating the car at different speeds. Consider the case where the ring gear R is held fixed, ωR = 0, and the sun gear S is rotating at ωs = 5 rad/s.
In each case show graphically how to locate the instantaneous center of zero velocity of link AB. Assume the geometry is known. The disk rolls without slipping.(a)(b)(c) ( A B
Due to slipping, points A and B on the rim of the disk have the velocities shown. Determine the velocities of the center point C and point D at this instant. VB = 10 ft/s B E 45°- C 0.8 ft D 30° F V₁ = 5 ft/s
If the slider block A is moving to the right at vA = 8 ft/s, determine the velocities of blocks B and C at the instant shown. Member CD is pin connected to member ADB. 2 ft 30% AO 2 ft VA = 8 ft/s 45° 2 ft D B
Due to slipping, points A and B on the rim of the disk have the velocities shown. Determine the velocities of the center point C and point E at this instant. VB = 10 ft/s B E 45°- C 0.8 ft D 30° F VA = 5 ft/s
The conveyor belt is moving to the right at v = 8 ft/s, and at the same instant the cylinder is rolling counterclockwise at ω = 2 rad/s without slipping. Determine the velocities of the cylinder’s center C and point B at this instant. B 1 ft A @ V
The mechanism produces intermittent motion of link AB. If the sprocket S is turning with an angular velocity of ωs = 6 rad/s, determine the angular velocity of link AB at this instant. The sprocket S is mounted on a shaft which is separate from a collinear shaft attached to AB at A. The pin at C
The conveyor belt is moving to the right at v = 12 ft/s, and at the same instant the cylinder is rolling counterclockwise at ω = 6 rad/s while its center has a velocity of 4 ft/s to the left. Determine the velocities of points A and B on the disk at this instant. Does the cylinder slip on the
The transmission gear fixed onto the frame of an electric train turns with a constant rate of ωt = 30 rad/s. This gear is in mesh with the gear that is fixed to the axle of the engine. Determine the velocity of the train, assuming the wheels do not slip on the track. 10 20 30
The disk of radius r is confined to roll without slipping at A and B. If the plates have the velocities shown, determine the angular velocity of the disk. И A В 20
The mechanism shown is used in a riveting machine. It consists of a driving piston A, three members, and a riveter which is attached to the slider block D. Determine the velocity of D at the instant shown, when the piston at A is traveling at vA = 30 m/s. D 150 mm 45° 45° 60° 200 mm 300 mm VA =
The wheel of an electric train is driven by the transmission gear B, which is in mesh with the gear fixed to the wheel. If the wheel rolls without slipping, determine the angular velocity of the transmission gear needed to drive the train 40 ft/s. The transmission gear is fixed to the frame of the
In an automobile transmission the planet pinions A and B rotate on shafts that are mounted on the planet-pinion carrier CD.As shown,CD is attached to a shaft at E which is aligned with the center of the fixed sun gear S. This shaft is not attached to the sun gear. If CD is rotating at ωCD = 8
Member AB is rotating at ωAB = 6 rad/s. Determine the velocity of point P, and the angular velocity of member BPD. 200 mm B 60° -200 mm 200 mm 250 mm @AB= 6 rad/s P 60° 200 mm
As the car travels forward at 80 ft/s on a wet road, due to slipping, the rear wheels have an angular velocity ω = 100 rad/s. Determine the speeds of points A, B, and C caused by the motion. 80 ft/s 1.4 ft- B A 100 rad/s
Member AB is rotating at ωAB = 6 rad/s. Determine the velocity of point D and the angular velocity of members BPD and CD. 200 mm B 60° -200 mm 250 mm WAB= 6 rad/s P -200 mm 60° 200 mm
If C has a velocity of vc = 3 m/s, determine the angular velocity of the wheel at the instant shown. A Co Vc = 3 m/s 0.15 m TBT 0.45 m 45°
If the center O of the gear is given a velocity of vO = 10 m/s, determine the velocity of the slider block B at the instant shown. 0.125 m vo= 10 m/s ww A infr 0.175 m 0.6 m 30° 30% B
The square plate is confined within the slots at A and B. When θ = 30°, point A is moving at vA = 8 m/s. Determine the velocity of point D at this instant. B 3 0.3 m D 0.3 m 10 = 30° A- VA = 8 m/s C
The crankshaft AB rotates at ωAB = 50 rad/s about the fixed axis through point A, and the disk at C is held fixed in its support at E. Determine the angular velocity of rod CD at the instant shown. B 40 mm, 300 mm E 60° -100 mm- 75 mm F 75 mm D -WAB = 50 rad/s
The drums have the angular velocities at the instant shown. Determine the angular velocity of the pulley C and the velocity of the load D. 0.15 m- A 4 rad/s 0.3 m G D 8 rad/s C B 0.2 m
The square plate is confined within the slots at A and B. When θ = 30°, point A is moving at vA = 8 m/s. Determine the velocity of point C at this instant. B 3 0.3 m D 0.3 m 10 = 30° A- VA = 8 m/s C
The mechanism used in a marine engine consists of a crank AB and two connecting rods BC and BD. Determine the velocity of the piston at D the instant the crank is in the position shown and has an angular velocity of 5 rad/s. 45° 0.4 m 60° 0.2 m 30° 0.4 m 5 rad/s C 45°
The mechanism used in a marine engine consists of a single crank AB and two connecting rods BC and BD. Determine the velocity of the piston at C the instant the crank is in the position shown and has an angular velocity of 5 rad/s. 45° 0.4 m 60° 0.2 m CO B 30° 0.4 m 5 rad/s 45°
At a given instant A has the motion shown. Determine the acceleration of point C at this instant. B C 3 ft -1.5 ft- VA= 3 ft/s A/a₁= aA = 6 ft/s²
The disk is rotating at a constant rate of 4 rad/s as it falls freely, its center having an acceleration of 32.2 ft/s2. Determine the accelerations of points A and B on the rim of the disk at the instant shown. W = 4 rad/s = A 1.5 ft B
At a given instant A has the motion shown. Determine the acceleration of B and the angular acceleration of the bar at this instant. B - 3 ft -1.5 ft- VA = 3 ft/s A|aA= aA = 6 ft/s²
The ends of bar AB are confined to move along the paths shown. At a given instant, A has a velocity of 8 ft/s and an acceleration of 3 ft/s². Determine the angular velocity and angular acceleration of AB at this instant. 4 ft B 4 ft 30° 30° O ft/s VA = 8 a₁ = 3 ft/s²
At a given instant the slider block A is moving to the right with the motion shown. Determine the angular acceleration of link AB and the acceleration of point B at this instant. B 2 m 30° 2 m VA = 4 m/s a₁ = 6 m/s²
At a given instant the roller A on the bar has the velocity and acceleration shown. Determine the velocity and acceleration of the roller B, and the bar’s angular velocity and angular acceleration at this instant. 4 m/s 6 m/s² A 30° $30⁰ 0.6 m B
If member AB has the angular motion shown, determine the angular velocity and angular acceleration of member CD at the instant shown. A 300 mm- @AB = 3 rad/s AB = 8 rad/s2 200 mm 0 = 60° 500 mm B
The hoop is cast on the rough surface such that it has an angular velocity ω = 4 rad/s and an angular acceleration α = 5 rad/s². Also, its center has a velocity vo = 5 m/s and a deceleration ao = 2 m/s². Determine the acceleration of point A at this instant. ao = 2 m/s²/ A 0.3 m w = 4 rad/s α
Determine the angular acceleration of link AB if link CD has the angular velocity and angular deceleration shown. 0.6 m 0.3 m B 0.6 m D OC acD = 4 rad/s² @CD = 2 rad/s
At a given instant the slider block B is moving to the right with the motion shown. Determine the angular acceleration of link AB and the acceleration of point A at this instant. 3 ft 5 ft OB VB = 6 ft/s aB = 2 ft/s²
Determine the angular acceleration of link CD if link AB has the angular velocity and angular acceleration shown. A 0.5 m C AB D а AB = 6 rad/s2 3 rad/s ш 1 m- 0.5 m B 1 m
The hydraulic cylinder D extends with a velocity of vB = 4 ft/s and an acceleration of αB = 1.5 ft/s2. Determine the acceleration of C at the instant shown. 1 ft VB = 4 ft/s aB = 1.5 ft/s² D B 2 ft 30%
The hoop is cast on the rough surface such that it has an angular velocity ω = 4 rad/s and an angular acceleration α = 5 rad/s². Also, its center has a velocity of Vo = 5 m/s and a deceleration αo = 2 m/s². Determine the acceleration of point B at this instant. ao = 2 m/s² A 0 0.3 m w = 4
If member AB has the angular motion shown, determine the velocity and acceleration of point C at the instant shown. A - 300 mm @AB = 3 rad/s AB = 8 rad/s² 200 mm 0 = 60° 500 mm B
The hydraulic cylinder D extends with a velocity of vB = 4 ft/s and an acceleration of αB = 1.5 ft/s2. Determine the acceleration of A at the instant shown. C 1 ft VB = 4 ft/s aB = 1.5 ft/s²| D B 2 ft 30%
Pulley A rotates with the angular velocity and angular acceleration shown. Determine the acceleration of block E at the instant shown. 50 mm = WA 40 rad/s %₁ = 5 rad/s² E A 50 mm B 125 mm
If member AB has the angular motion shown, determine the angular velocity and angular acceleration of member CD at the instant shown. A - 300 mm @AB = 3 rad/s AB = 8 rad/s² 200 mm 0 = 60° 500 mm B
Gear A is held fixed, and arm DE rotates clockwise with an angular velocity of ωDE = 6 rad/s and an angular acceleration of αDE = 3 rad/s². Determine the angular acceleration of gear B at the instant shown. A D 0.3 m 30° B 0.2 m E
Pulley A rotates with the angular velocity and angular acceleration shown. Determine the angular acceleration of pulley B at the instant shown. 50 mm WA 40 rad/s α₁ = 5 rad/s² E A 50 mm 'B 125 mm
The hydraulic cylinder extends with a velocity of vA = 1.5 m/s and an acceleration of aA = 0.5 m/s2. Determine the angular acceleration of link ABC and the acceleration of end C at the instant shown. Point B is pin connected to the slider block. C 0.5 m7 VA = 1.5 m/s a = 0.5 m/s² 90° B 60° A 0.6
The slider block moves with a velocity of vB = 5 ft/s and an acceleration of aB = 3 ft/s2. Determine the angular acceleration of rod AB at the instant shown. A 1.5 ft 30° 2 ft B VB = 5 ft/s aB = 3 ft/s²
Gear A rotates counterclockwise with a constant angular velocity of ωA = 10 rad/s, while arm DE rotates clockwise with an angular velocity of ωDE = 6 rad/s and an angular acceleration of αDE = 3 rad/s². Determine the angular acceleration of gear B at the instant shown. D 0.3 m 30% B 0.2 m E
The slider block moves with a velocity of vB = 5 ft/s and an acceleration of aB = 3 ft/s2. Determine the acceleration of A at the instant shown. A 1.5 ft 30° 2 ft B UB=5 ft/s aB = 3 ft/s²
The disk rolls without slipping such that it has an angular acceleration of α = 4 rad/s2 and angular velocity of ω = 2 rad/s at the instant shown. Determine the acceleration of points A and B on the link and the link’s angular acceleration at this instant. Assume point A lies on the periphery
The flywheel rotates with an angular velocity ω = 2 rad/s and an angular acceleration α = 6 rad/s2. Determine the angular acceleration of links AB and BC at this instant. w = 2 rad/s α = 6 rad/s², 0.3 m A 0.5 m C B 0.4 m
The man stands on the platform at O and runs out toward the edge such that when he is at A, y = 5 ft,his mass center has a velocity of 2 ft/s and an acceleration of 3 ft/s2, both measured relative to the platform and directed along the positive y axis. If the platform has the angular motions shown,
Solve Prob. 16-131 assuming that at the instant x = 0.1 m, ẋ = -3m/s, ẍ = 1.25 m/s², ωD = 2 rad/s, and the disk has an angular deceleration αD = 4 rad/s².Solve Prob. 16-131The slider block B, which is attached to a cord, moves along the slot of the horizontal circular disk. If the cord is
Water leaves the impeller of the centrifugal pump with a velocity of 25m/s and acceleration of 30m/s2, both measured relative to the impeller along the blade line AB. Determine the velocity and acceleration of a water particle at A as it leaves the impeller at the instant shown. The impeller
Block A, which is attached to a cord, moves along the slot of a horizontal forked rod. At the instant shown, the cord is pulled down through the hole at O with an acceleration of 4 m/s2 and its velocity is 2 m/s. Determine the acceleration of the block at this instant. The rod rotates about O with
The ball B of negligible size rolls through the tube such that at the instant shown it has a velocity of 5 ft/s and an acceleration of 3 ft/s2, measured relative to the tube. If the tube has an angular velocity of ω = 3 rad/s and an angular acceleration of α = 5 rad/s2 at this same instant,
The slider block B, which is attached to a cord, moves along the slot of the horizontal circular disk. If the cord is pulled down through the central hole A in the disk at a constant rate of ẋ = - 3 m/s, measured relative to the disk, determine the acceleration of the block at the instant x = 0.1
At the instant θ = 60°, link CD has an angular velocityωCD = 4 rad/s and an angular acceleration αCD = 2 rad/s². Determine the angular velocity and angular acceleration of rod AB at this instant. The collar at C is pin connected to DC and slides over AB. -2 ft B 2 ft 0= 60°, @CD= 4 rad/s αCD
Rod AB rotates counterclockwise with a constant angular velocity ω = 3 rad/s. Determine the velocity of point C located on the double collar when θ = 30°. The collar consists of two pin-connected slider blocks which are constrained to move along the circular path and the rod AB. A 0 w = 3
Rod AB rotates counterclockwise with a constant angular velocity ω = 3 rad/s. Determine the velocity and acceleration of point C located on the double collar when θ = 45°. The collar consists of two pin-connected slider blocks which are constrained to move along the circular path and the rod AB.
At the instant shown, rod AB has an angular velocity ωAB = 3 rad/s and an angular acceleration αAB = 5 rad/s2. Determine the angular velocity and angular acceleration of rod CD at this instant. The collar at C is pin connected to CD and slides over AB. A 60° @AB = 3 rad/s AB = 5 rad/s² 0.75
The block B of the “quick-return” mechanism is confined to move within the slot in member CD. If AB is rotating at a constant rate of ωAB = 3 rad/s determine the angular velocity and angular acceleration of member CD at the instant shown. C A- 30° WAB = 3 rad/s B 30° 50 mm 200 mm D
The disk rotates with the angular motion shown. Determine the angular velocity and angular acceleration of the slotted link AC at this instant. The peg at B is fixed to the disk. w = 6 rad/s 10 rad/s² α = 30° 0.3 m 30° 0.75 m B C
The wheel is rotating with the angular velocity and angular acceleration at the instant shown. Determine the angular velocity and angular acceleration of the rod at this instant. The rod slides freely through the smooth collar. 300 mm, A O w = 8 rad/s a = 4 rad/s² -720 mm- C B
A ride in an amusement park consists of a rotating platform P, having a constant angular velocity ωP = 1.5 rad/s and four cars, C, mounted on the platform, which have constant angular velocities ωC/P = 2 rad/s measured relative to the platform. Determine the velocity and acceleration of the
A ride in an amusement park consists of a rotating arm AB having a constant angular velocity ωAB = 2 rad/s. The car mounted at the end of the arm has a constant angular velocity ω' = {-0.5k} rad/s, measured relative to the arm. At the instant shown, determine the velocity and acceleration of the
A ride in an amusement park consists of a rotating arm AB that has an angular acceleration of αAB = {1k] rad/s² when ωAB = {2k] rad/s at the instant shown. Also at this instant the car mounted at the end of the arm has an angular acceleration of α = {-0.6k) rad/s² and angular velocity of ω' =
Peg B on the gear slides freely along the slot in link AB. If the gear’s center O moves with the velocity and acceleration shown, determine the angular velocity and angular acceleration of the link at this instant. 150 mm vo = 3 m/s ao = 1.5 m/s 150 mm แบบ บ 600 mm บบบบบบ
If the slider block C is fixed to the disk that has a constant counterclockwise angular velocity of 4 rad/s, determine the angular velocity and angular acceleration of the slotted arm AB at the instant shown. 180 mm 60° 40 mm 'C B 60 mm 30⁰% w = 4 rad/s W

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