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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

Determine (a) The value of α for which the reaction at A is vertical, (b) The corresponding reactions at A and E. 500 N 200 mm α 200 mm B OA D 150 mm C 30° E 200 mm
The spanner shown is used to rotate a shaft. A pin fits in a hole at A, while a flat, frictionless surface rests against the shaft at B. If the moment about C of the force exerted on the shaft at A
Determine the reactions at A and E when α = 0. 500 N 200 mm α 200 mm B OA D 150 mm C 30° E 200 mm
The semicircular rod ABCD is maintained in equilibrium by the small wheel at D and the rollers at B and C. Knowing that α = 45°, determine the reactions at B, C, and D. P В 45⁰ 45⁰
Determine the range of values of α for which the semicircular rod shown can be maintained in equilibrium by the small wheel at D and the rollers at B and C. 소 P B 45⁰ 45⁰ D
A rod AB hinged at A and attached at B to cable BD supports the loads shown. Knowing that d = 200, mm determine (a) The tension in cable BD,(b) The reaction at A.
A 12-ft ladder, weighing 40 lb, leans against a frictionless vertical wall. The lower end of the ladder rests on rough ground, 4 ft away from the wall. Determine the reactions at both ends.
A 50-lb sign is supported by a pin and bracket at A and by a cable BC. Determine the reaction at A and the tension in the cable. C A 30° 50 lb -3 ft 3 ft → B 4 ft
Determine the reactions at B and C when a = 30 mm. 60 mm 40 mm A 250 N B C 100 mm 60 mm D
Solve Prob. 4.135 when h = 10.5 ft.PROBLEM 4.135 The 8-ft rod AB and the 6-ft rod BC are hinged at B and supported by cable DE and by ball-and socket joints at A and C. Knowing that h = 3 ft,
Determine the reactions at A and E. 아옹 6 in. 4 in. C B 5 in. A 200 lb OD 10 in. - OE
One end of rod AB rests in the corner A and the other end is attached to cord BD. If the rod supports a 150-N load at its midpoint C, find the reaction at A and the tension in the cord. D A 150 N 240
A lever AB is hinged at C and attached to a control cable at A. If the lever is subjected to a 75-lb vertical force at B, draw the free-body diagram needed to determine the tension in the cable and
What will be the amplitude of steady-state vibration of the motor in Prob. 22–57 if the angular velocity of the flywheel is 20 rad/s?Prob. 22–57The electric motor turns an eccentric flywheel
The 12-kg disk has an angular velocity of ω = 20 rad/s. If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The
The 30-kg gear is subjected to a force of P = (20t) N, where t is in seconds. Determine the angular velocity of the gear at t = 4 s, starting from rest. Gear rack B is fixed to the horizontal plane,
The body and bucket of a skid steer loader has a weight of 2000 lb, and its center of gravity is located at G. Each of the four wheels has a weight of 100 lb and a radius of gyration about its center
The turntable T of a record player has a mass of 0.75 kg and a radius of gyration kz = 125 mm. It is turning freely at ωT = 2 rad/s when a 50-g record (thin disk) falls on it. Determine the final
The body and bucket of a skid steer loader has a weight of 2000 lb, and its center of gravity is located at G. Each of the four wheels has a weight of 100 lb and a radius of gyration about its center
The double pulley consists of two wheels which are attached to one another and turn at the same rate. The pulley has a mass of 15 kg and a radius of gyration of kO = 110 mm. If the block at A has a
The 10-g bullet having a velocity of 800 m/s is fired into the 5-kg disk as shown. Determine the angular velocity of the disk just after the bullet becomes embedded. Also, calculate the angle θ the
A thin rod having a mass of 4 kg is balanced vertically as shown. Determine the height h at which it can be struck with a horizontal force F and not slip on the floor.This requires that the
The platform swing consists of a 200-lb flat plate suspended by four rods of negligible weight.When the swing is at rest, the 150-lb man jumps off the platform when his center of gravity G is 10 ft
The 10-g bullet having a velocity of 800 m/s is fired into the 5-kg disk as shown. Determine the angular velocity of the disk just after the bullet becomes embedded. Also, calculate the angle θ the
The man sits on the swivel chair holding two 5-lb weights with his arms outstretched. If he is rotating at 3 rad/s in this position, determine his angular velocity when the weights are drawn in and
Two children A and B, each having a mass of 30 kg, sit at the edge of the merry-go-round which is rotating at ω = 2 rad/s. Excluding the children, the merry-go-round has a mass of 180 kg and a
The Hubble Space Telescope is powered by two solar panels as shown. The body of the telescope has a mass of 11 Mg and radii of gyration kx = 1.64 m and ky = 3.85 m, whereas the solar panels can be
The cable is subjected to a force of P = (10t²) lb, where t is in seconds. Determine the angular velocity of the spool 3 s after P is applied, starting from rest. The spool has a weight of 150 lb
The 60-kg wheel has a radius of gyration about its center O of kO = 300 mm. If it is subjected to a couple moment of M = (3t2) N · m, where t is in seconds, determine the angular velocity of the
The rigid body (slab) has a mass m and rotates with an angular velocity ω about an axis passing through the fixedpoint O. Show that the momenta of all the particlescomposing the body can be
The 300-kg wheel has a radius of gyration about its mass center G of kG = 400 mm. If the wheel is subjected to a couple moment of M = 300 N·m and no slipping occurs, determine its angular velocity
At a given instant, the body has a linear momentum L = mvG and an angular momentum HG = IGω calculated about its mass center. Show that the angular momentum of the body calculated about the
The space capsule has a mass of 1200 kg and a moment of inertia IG = 900 kg · m² about an axis passing through G and directed perpendicular to the page. If it is traveling forward with a speed vG =
If rod OA of negligible mass is subjected to the couple moment M = 9 N · m, determine the angular velocity of the 10-kg inner gear t = 5s after it starts from rest. The gear has a radius of gyration
The two tugboats each exert a constant force F on the boat such that these forces are always directed perpendicular to the boat’s centerline. If the boat has a mass m and a radius of gyration kG
Show that if a slab is rotating about a fixed axis perpendicular to the slab and passing through its mass center G, the angular momentum is the same when calculated about any other point P. G P. W
The wheel having a mass of 100 kg and a radius of gyration about the z axis of kz = 300 mm rests on the smooth horizontal plane. If the belt is subjected to a force of P = 200 N, determine the
Gears A and B of mass 10 kg and 50 kg have radii of gyration about their respective mass centers of kA = 80 mm and kB = 150 mm. If gear A is subjected to the couple moment M = 10 N · m when it is at
The tire has a mass of 9kg a radius of gyration kO = 225 mm. If it is released from rest and rolls down the plane without slipping, determine the speed of its center O when t = 3 s.
The 50-kg spool is subjected to a horizontal force of P = 150 N. If the spool rolls without slipping, determine its angular velocity 3 s after it starts from rest. The radius of gyration of the spool
Determine the height h at which a bullet can strike the disk that has a weight of 15 lb and cause it to roll without slipping at A. This requires that the frictional force at A be essentially zero.
A sphere and cylinder are released from rest on the ramp at t = 0. If each has a mass m and a radius r, determine their angular velocities at time t. Assume no slipping occurs. Ө
The reel has a weight of 150 lb and a radius of gyration about its center of gravity of kG = 1.25 ft. If it is subjected to a torque of M = 25 lb · ft, and starts from rest when the torque is
Spool B is at rest and spool A is rotating at 6 rad/s when the slack in the cord connecting them is taken up. If the cord does not stretch, determine the angular velocity of each spool immediately
The 10-lb rectangular plate is at rest on a smooth horizontal floor. If it is given the horizontal impulses shown, determine its angular velocity and the velocity of the mass center. T 0.5 ft 5 20
The spool has a weight of 30 lb and a radius of gyration kO = 0.65 ft. If a force of 40 lb is applied to the cord at A, determine the angular velocity of the spool in t = 3 s starting from rest.
A thin disk of mass m has an angular velocity while rotating on a smooth surface. Determine its new angular velocity just after the hook at its edge strikes the peg P and the disk starts to rotate
The spool has a mass of 30 kg and a radius of gyration ko = 0.25 m. Block A has a mass of 25 kg, and block B has a mass of 10 kg. If they are released from rest, determine the time required for block
The space satellite has a mass of 125 kg and a moment of inertia Iz = 0.940 kg · m², excluding the four solar panels A, B, C, and D. Each solar panel has a mass of 20 kg and can be approximated as
The drum of mass m, radius r, and radius of gyration KG rolls along an inclined plane for which the coefficient of static friction is μs. If the drum is released from rest,determine the maximum
The smooth rod assembly shown is at rest when it is struck by a hammer at A with an impulse of 10 N · s. Determine the angular velocity of the assembly and the magnitude of velocity of its mass
The 50-kg cylinder has an angular velocity of 30 rad/s when it is brought into contact with the surface at C. If the coefficient of kinetic friction is μC = 0.2, determine how long it takes for the
The frame of the roller has a mass of 5.5 Mg and a center of mass at G. The roller has a mass of 2 Mg and a radius of gyration about its mass center of kA = 0.45 m. If a torque of M = 600 N · m is
The car strikes the side of a light pole, which is designed to break away from its base with negligible resistance. From a video taken of the collision it is observed that the pole was given an
A wire of negligible mass is wrapped around the outer surface of the 2-kg disk. If the disk is released from rest, determine its angular velocity in 3 s. 이 80 mm
If the boxer hits the 75-kg punching bag with an impulse of I = 20 N · s, determine the angular velocity of the bag immediately after it has been hit. Also, find the location d of point B, about
A cord of negligible mass is wrapped around the outer surface of the 50-lb cylinder and its end is subjected to a constant horizontal force of P = 2 lb. If the cylinder rolls without slipping at A,
The 200-kg satellite has a radius of gyration about the centroidal z axis of kz = 1.25 m. Initially it is rotating with a constant angular velocity of ω0 = {1500 k} rev/min. If the two jets A and B,
If the cord is subjected to a horizontal force of P = 150 N, and the gear rack is fixed to the horizontal plane, determine the angular velocity of the gear in 4 s, starting from rest. The mass of the
Gear A rotates along the inside of the circular gear rack R having a radius 2.25 ft. If A has a weight of 4 lb and a radius of gyration of kB = 0.5 ft, determine its angular momentum about point C
If the cord is subjected to a horizontal force of P = 150 N, and the gear is supported by a fixed pin at O, determine the angular velocity of the gear and the velocity of the 20-kg gear rack in 4 s,
The spool has a weight of 30 lb and a radius of gyration kO = 0.45 ft. A cord is wrapped around its inner hub and the end subjected to a horizontal force P = 5 lb. Determine the spool’s angular
The two gears A and B have weights and radii of gyration of WA = 15 lb, kA = 0.5 ft and WB = 10 lb, kB = 0.35 ft, respectively. If a motor transmits a couple moment to gear B of M = 2(1 -
Each of the two slender rods and the disk have the same mass m. Also, the length of each rod is equal to the diameter d of the disk. If the assembly is rotating with an angular velocity ω1 when the
The rod has a length L and mass m.A smooth collar having a negligible size and one-fourth the mass of the rod is placed on the rod at its midpoint. If the rod is freely rotating at ω about its end
Disk A has a weight of 20 lb. An inextensible cable is attached to the 10-lb weight and wrapped around the disk. The weight is dropped 2 ft before the slack is taken up. If the impact is perfectly
The 12-kg rod AB is pinned to the 40-kg disk. If the disk is given an angular velocity ωD = 100 rad/s while the rod is held stationary, and the assembly is then released, determine the angular
The rigid 30-lb plank is struck by the 15-lb hammer head H. Just before the impact the hammer is gripped loosely and has a vertical velocity of 75 ft/s. If the coefficient of restitution between the
A thin rod of mass m has an angular velocity ω0 while rotating on a smooth surface. Determine its new angular velocity just after its end strikes and hooks onto the peg and the rod starts to rotate
The pendulum consists of a 5-lb slender rod AB and a 10-lb wooden block. A projectile weighing 0.2 lb is fired into the center of the block with a velocity of 1000 ft/s. If the pendulum is initially
Tests of impact on the fixed crash dummy are conducted using the 300-lb ram that is released from rest at θ = 30°, and allowed to fall and strike the dummy at θ = 90°. If the coefficient of
The vertical shaft is rotating with an angular velocity of 3 rad/s when θ = 0°. If a force F is applied to the collar so that θ = 90°, determine the angular velocity of the shaft. Also, find the
The 10-lb block slides on the smooth surface when the corner D hits a stop block S. Determine the minimum velocity v the block should have which would allow it to tip over on its side and land in the
Determine the height h of the bumper of the pool table, so that when the pool ball of mass m strikes it, no frictional force will be developed between the ball and the table at A. Assume the bumper
The pendulum consists of a 15-kg solid ball and 6-kg rod. If it is released from rest when θ1 = 90°, determine the angle θ2 after the ball strikes the wall, rebounds, and the pendulum swings
The 4-lb rod AB is hanging in the vertical position. A 2-lb block, sliding on a smooth horizontal surface with a velocity of 12 ft/s, strikes the rod at its end B. Determine the velocity of the block
The hammer consists of a 10-kg solid cylinder C and 6-kg uniform slender rod AB. If the hammer is released from rest when θ = 90° and strikes the 30-kg block D when θ = 0º, determine the velocity
The 20-kg disk strikes the step without rebounding. Determine the largest angular velocity ω1 the disk can have without losing contact with the step A. 200 mm A 130 mm
The solid ball of mass m is dropped with a velocity v1 onto the edge of the rough step. If it rebounds horizontally off the step with a velocity v2, determine the angle θ at which contact
The uniform rod assembly rotates with an angular velocity of ω0 on the smooth horizontal plane just before the hook strikes the peg P without rebound. Determine the angular velocity of the assembly
The ladder of the fire truck rotates around the z axis with an angular velocity ω₁ = 0.15 rad/s, which is increasing at 0.8 rad/s². At the same instant it is rotating upward at a constant rate
A 50-g pencil (uniform slender rod) falls down onto the table with a velocity of 0.2 m/s just before impact. If it is at an angle of 60° with the horizontal, and it does not slip during the impact,
The rod of mass m and length L is released from rest without rotating. When it falls a distance L, the end A strikes the hook S, which provides a permanent connection. Determine the angular velocity
The 15-lb rod AB is released from rest in the vertical position. If the coefficient of restitution between the floor and the cushion at B is e = 0.7 determine how high the end of the rod rebounds
A ball having a mass of 8 kg and initial speed of v1 = 0.2 m/s rolls over a 30-mm-long depression.Assuming that the ball rolls off the edges of contact, first A then B, without slipping, determine
The 2-kg disk is thrown down onto the rough surface with the velocity and angular velocity shown. If there is no slipping, and the coefficient of restitution is e = 0.5, determine the velocity of the
The ladder of the fire truck rotates around the z axis with an angular velocity of ω₁ = 0.15 rad/s, which is increasing at 0.2 rad/s². At the same instant it is rotating upward at ω2 = 0.6 rad/s
The disk rotates about the z axis at a constant rate ωz = 0.5 rad/s without slipping on the horizontal plane. Determine the velocity and the acceleration of point A on the disk. x w₂ = 0.5
The cone rolls in a circle and rotates about the z axis at a constant rate ωz = 8 rad/s. Determine the angular velocity and angular acceleration of the cone if it rolls without slipping. Also, what
The pendulum consists of a 10-lb solid ball and 4-lb rod. If it is released from rest when θ = 0°, determine the angleθ₁ of rebound after the ball strikes the wall and thependulum swings up to
The propeller of an airplane is rotating at a constant speed ωxi, while the plane is undergoing a turn at a constant rate ωt. Determine the angular acceleration of the propeller if(a) The turn is
The antenna is following the motion of a jet plane. At the instant θ = 25° and ϕ = 75°, the constant angular rates of change are θ̇ = 0.4 rad/s and ϕ̇ = 0.6 rad/s. Determine the velocity and
The disk rotates about the shaft S, while the shaft is turning about the z axis at a rate of ωz = 4 rad/s, which is increasing at 2 rad/s2. Determine the velocity and acceleration of point B on the
At a given instant, the antenna has an angular motion ω₁ = 3 rad/s and ω̇₁ = 2 rad/s² about the z axis. At this same instant, θ = 30°, the angular motion about the x axis is ω₂ = 1.5
The disk rotates about the shaft S, while the shaft is turning about the z axis at a rate of ωz = 4 rad/s, which is increasing at 2 rad/s2. Determine the velocity and acceleration of point A on the
The telescope is mounted on the frame F that allows it to be directed to any point in the sky. At the instant θ = 30°, the frame has an angular acceleration of αy′ = 0.2 rad/s² and an angular
The bevel gear A rolls on the fixed gear B. If at the instant shown the shaft to which A is attached is rotating at 2 rad/s and has an angular acceleration of 4 rad/s2, determine the angular velocity
The truncated double cone rotates about the z axis at ωz = 0.4 rad/s without slipping on the horizontal plane. If at this same instant ωz is increasing at ω̇z = 0.5 rad/s², determine the
The electric fan is mounted on a swivel support such that the fan rotates about the z axis at a constant rate of ωz = 1 rad/s and the fan blade is spinning at a constant rate ωs = 60 rad/s. If ϕ =
The electric fan is mounted on a swivel support such that the fan rotates about the z axis at a constant rate of ωz = 1 rad/s and the fan blade is spinning at a constant rate ωs = 60 rad/s. If at

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