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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

Determine the angular velocity of link BC and velocity of the piston C at the instant shown. A @AB = 12 rad/s B -0.6 m -1.2 m-
Determine the maximum angular displacement of the pendulum in Prob. 16–24.Prob. 16–24.A pendulum has a swinging motion such that θ = [ - 0.101 sin(4.95t) + 0.3 cos(4.95t) ] rad, where t is in
The pinion gear A on the motor shaft is given a constant angular acceleration α = 3 rad/s². If the gears A and Bhave the dimensions shown, determine the angular velocityand angular displacement of
Determine the distance the load W is lifted in t = 5 s using the hoist. The shaft of the motor M turns with an angular velocity ω = 100(4 + t) rad/s, where t is in seconds. 50 mm B 300 mm 30
The disk starts at ω0 = 1 rad/s when θ = 0, and is given an angular acceleration α = (0.3θ) rad/s2, where θ is in radians. Determine the magnitudes of the normal and tangential components of
If cable AB is unwound with a speed of 3 m/s, and the gear rack C has a speed of 1.5 m/s, determine the angular velocity of the gear and the velocity of its center O. 1.5 m/s ().3 m រ -- ឧស 3
If the center O of the gear is moving with a speed of vo = 6 m/s, determine the velocity of point A on the gear. The gear rack B is fixed. 0.6 m² A w frrrrrrrrrr min gr 0.3 m 6 m/s B
The disk starts from rest and is given an angular acceleration α = (5t1/2) rad/s2, where t is in seconds. Determine the magnitudes of the normal and tangential components of acceleration of a point
The disk starts from rest and is given an angular acceleration α = (2t²) rad/s², where t is in seconds. Determine the angular velocity of the disk and its angular displacement when t = 4 s. 0.4 m P
Determine the angular velocity of link BC and the velocity of the piston C at the instant shown. 0.2 m T B 0.8 m = 6 rad/s C 130⁰
A motor gives gear A an angular acceleration of αA = (2 + 0.006 θ2) rad/s2, where θ is in radians. If this gear is initially turning at ωA = 15 rad/s, determine the angular velocity of gear B
Determine the angular velocity of links BC andCD at the instant shown. 0.2 m B 130⁰ @AB = 10 rad/s 0.4 m DO 0.2 m
A motor gives gear A an angular acceleration of αA = (2t3) rad/s2, where t is in seconds. If this gear is initially turning at ωA = 15 rad/s, determine the angular velocity of gear B when t = 3 s.
At the instant shown, end A of the rod has thevelocity and acceleration shown. Determine the angularacceleration of the rod and acceleration of end B of the rod. 4 m A |a₁ = 5 m/s² VA = 6 m/s 5m B
The gear rolls on the fixed rack with an angular velocity of ω = 12 rad/s and angular acceleration of α = 6 rad/s². Determine the horizontal and vertical components of acceleration of point A. 0.3
A motor gives gear A an angular acceleration of αA = (4t3) rad/s2, where t is in seconds. If this gear is initially turning at (ωA)0 = 20 rad/s, determine the angular velocity of gear B when t = 2
The vacuum cleaner’s armature shaft S rotates with an angular acceleration of α = 4ω3/4 rad/s2, where ω is in radωs. Determine the brush’s angular velocity when t = 4 s, starting from ω0 = 1
At the instant shown, the horizontal portion of the belt has an angular acceleration of 3 m/s2, while points in contact with the outer edge of the pulleys have an acceleration magnitude of 5 m/s2. If
The gear rolls on the fixed rack B. At the instant shown, the center O of the gear moves with a velocity of vo = 6 m/s and acceleration of ao = 3 m/s². Determine the angular acceleration of the gear
At the instant shown, cable AB has a velocity of 3 m/s and acceleration of 1.5 m/s², while the gear rack has a velocity of 1.5 m/s and acceleration of 0.75 m/s². Determine the angular acceleration
If the motor turns gear A with an angular acceleration of αA = 3 rad/s² when the angular velocity is ωA = 60 rad/s, determine the angular acceleration and angular velocity of gear D. A B -100
If the motor turns gear A with an angular acceleration of αA = 2 rad/s² when the angular velocity is ωA = 20 rad/s, determine the angular acceleration and angular velocity of gear D. B -100
At the instant shown, the wheel rotates with an angular velocity of ω = 12 rad/s and an angularacceleration of α = 6 rad/s². Determine the angularacceleration of link BC at the instant shown. 0.3
At the instant shown, wheel A rotates with an angular velocity of ω = 6 rad/s and an angular accelerationof α = 3 rad/s². Determine the angular acceleration oflink BC and the acceleration of
A pendulum has a swinging motion such that θ = [ - 0.101 sin(4.95t) + 0.3 cos(4.95t) ] rad, where t is in seconds, and the arguments for the sine and cosine are in radians. Determine the magnitudes
Morse Industrial manufactures the speed reducer shown. If a motor drives the gear shaft S with an angular acceleration of α = (0.4et) rad/s2, where t is in seconds, determine the angular velocity of
Due to an increase in power, the motor M rotates the shaft A with an angular acceleration of α = (0.060²) rad/s², where θ is in radians. If the shaft is initially turning at ω0 = 50 rad/s,
The gear A on the drive shaft of the outboard motor has a radius rA = 0.7 in. and the meshed pinion gear B on the propeller shaft has a radius rΒ = 1.4 in. Determine the angular velocity of the
The gear A on the drive shaft of the outboard motor has a radius rA = 0.7 in. and the meshed pinion gear B on the propeller shaft has a radius rΒ = 1.4 in. Determine the magnitudes of the velocity
The turntable T is driven by the frictional idler wheel A, which simultaneously bears against the inner rim of the turntable and the motor-shaft spindle B. Determine the required diameter d of the
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
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
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
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 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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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.
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
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
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
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
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
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 =
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
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 =
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
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
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

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