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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

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
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
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.
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
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
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 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
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
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,
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
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
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
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 = -
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
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
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
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
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
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
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
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
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,
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
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
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
At a given instant, the cables supporting the pipe have the motions shown. Determine the angular velocity and angular acceleration of the pipe and the velocity and acceleration of point B located on
At the instant shown rod AB has an angular velocity ωAB = 4 rad/s and an angular acceleration αAB = 2 rad/s2. Determine the angular velocity and angular acceleration of rod CD at this instant.The
The 150-lb man lies against the cushion for which the coefficient of static friction is μs = 0.5. If he rotates about the z axis with a constant speed v = 30 ft/s, determine the smallest angle θ of
The 52-kg skier is coasting freely down the hill with a speed of 4 m/s at x = 10 m. Determine the normal reaction on the ground and the rate of increase in speed at the instant shown. Neglect
Prove that if the block is released from rest at point B on a smooth path of arbitrary shape, the speed it attains when it reaches point A is equal to the speed it attains when it falls freely
The rotational speed of the disk is controlled by a 30-g smooth contact arm AB which is spring mounted on the disk.When the disk is at rest, the center of mass G of the arm is located 150 mm from the
The boy of mass 40 kg is sliding down the spiral slide at a constant speed such that his position, measured from the top of the chute, has components r = 1.5 m, θ = (0.7t) rad, and z = (-0.5t) m,
The 40-kg boy is sliding down the smooth spiral slide such that z = -2 m/s when he rotates θ = 360° and his speed is 2 m/s. Determine the r, θ, z components of force the slide exerts on him at
An electron of mass m is discharged with an initial horizontal velocity of v0. If it is subjected to two fields of force for which Fx = F0 and Fy = 0.3F0, where F0 is constant, determine the equation
The 400-lb cylinder at A is hoisted using the motor and the pulley system shown. If the speed of point B on the cable is increased at a constant rate from zero to vB = 10 ft/s in t = 5 s, determine
A parachutist having a mass m opens his parachute from an at-rest position at a very high altitude. If the atmospheric drag resistance is FD = kv2, where k is a constant, determine his velocity when
The 2-kg collar C is free to slide along the smooth shaft AB. Determine the acceleration of collar C if (a) The shaft is fixed from moving, (b) Collar A, which is fixed to shaft AB, moves
The 2-kg collar C is free to slide along the smooth shaft AB. Determine the acceleration of collar C if collar A is subjected to an upward acceleration of 4 m/s2. A -45 C B
Blocks A and B each have a mass m. Determine the largest horizontal force P which can be applied to B so that A will not move relative to B. All surfaces are smooth. A А В с - р -
Determine the tension developed in the cords attached to each block and the accelerations of the blocks. Neglect the mass of the pulleys and cords. A G B 8 kg 6 kg
Blocks A and B each have a mass m. Determine the largest horizontal force P which can be applied to B so that A will not slip on B. The coefficient of static friction between A and B is μs.Neglect
A projectile of mass m is fired into a liquid at an angle θ0 with an initial velocity v0 as shown. If the liquid develops a frictional or drag resistance on the projectile which is proportional to
The rock is dropped from rest within the thick liquid. If the drag force acting on it is F = cv, where c is a constant, determine the velocity and position of the rock as a function of time. Plot the
The smooth block B of negligible size has a mass m and rests on the horizontal plane. If the board AC pushes on the block at an angle θ with a constant acceleration a0, determine the velocity of the
The block A has a mass mA and rests on the pan B, which has a mass mB. Both are supported by a spring having a stiffness k that is attached to the bottom of the pan and to the ground. Determine the
The 30-lb crate is being hoisted upward with a constant acceleration of 6 ft/s2. If the uniform beam AB has a weight of 200 lb, determine the components of reaction at A. Neglect the size and mass of
The 2-kg block B and 15-kg cylinder A are connected to a light cord that passes through a hole in the center of the smooth table. If the block is given a speed of v = 10m/s, determine the radius r of
The 2-kg block B and 15-kg cylinder A are connected to a light cord that passes through a hole in the center of the smooth table. If the block travels along a circular path of radius r = 1.5m,
The 4-Mg helicopter maneuvers a horizontal turn having a radius of curvature ρ = 400 m. Determine the lift force FL required and the angle θ of the bank when it is flying horizontally with a
The 2-kg spool S fits loosely on the inclined rod for which the coefficient of static friction is μs = 0.2. If the spool is located 0.25 m from A, determine the maximum constant speed the spool can
Determine the maximum constant speed at which the pilot can travel around the vertical curve having a radius of curvature ρ = 800 m, so that he experiences a maximum acceleration an = 8g = 78.5
At the instant θ = 60°, the boy’s center of mass G has a downward speed vG = 15 ft/s. Determine the rate of increase in his speed and the tension in each of the two supporting cords of the swing
Cartons having a mass of 5 kg are required to move along the assembly line at a constant speed of 8 m/s. Determine the smallest radius of curvature for the conveyor so the cartons do not slip. The
At the instant θ = 60°, the boy’s center of mass G is momentarily at rest. Determine his speed and the tension in each of the two supporting cords of the swing when θ = 90°. The boy has a
Calculate the constant speed of the cars on the amusementpark ride if it is observed that the cables are directed at 30° from the vertical. Each car, including its passengers, has a mass of 550 kg.
The 2-kg spool S fits loosely on the inclined rod for which the coefficient of static friction μs = 0.2. is If the spool is located 0.25 m from A, determine the minimum constant speed the spool can
The 5-lb packages ride on the surface of the conveyor belt. If the belt starts from rest and its speed increases to 2 ft/s in 2s, determine the maximum angle θ so that none of the packages slip on
A girl having a mass of 25 kg sits at the edge of the merrygo- round so her center of mass G is at a distance of 1.5 m from the axis of rotation. If the angular motion of the platform is slowly
The plane is traveling at a constant speed of 800 ft/s along the curve y = 20(10-6)x2 + 5000, where x and y are in feet. If the pilot has a weight of 180 lb, determine the normal and tangential
The jet plane is traveling at a constant speed of 1000 ft/s along the curve y = 20(10-6)x2 + 5000, where x and y are in feet. If the pilot has a weight of 180 lb, determine the normal and tangential
A motorcyclist in a circus rides his motorcycle within the confines of the hollow sphere. If the coefficient of static friction between the wheels of the motorcycle and the sphere is μs = 0.4,
A sled and rider, weighing 30 lb and 150 lb, respectively, travel down a smooth slope that has the shape shown. If the rider does not hold on to the sides of the sled, determine the normal force
The collar has a mass of 2 kg and is free to slide along the smooth rod, which rotates in the horizontal plane. The attached spring has a stiffness k = 1 kN/m, and when no force is applied to the
The collar has a mass of 2 kg and is free to slide along the smooth rod, which rotates in the horizontal plane. The attached spring has a stiffness k = 1 kN/m, and when no force is applied to the
A small, 6-lb collar slides along the vertical, circular, smooth rod. If the collar is released from rest when θ = 10°, determine the normal force which it exerts on the rod when it arrives at
The 2-lb collar is released from rest at A and slides down along the smooth rod. If the attached spring has a stiffness k = 2 lb/ft, determine its unstretched length so that it does not allow the
The 150-lb man lies against the cushion for which the coefficient of static friction μs = 0.5 is Determine the resultant normal and frictional forces the cushion exerts on him due to rotation about
If the bicycle and rider have a total weight of 180 lb, determine the resultant normal force acting on the bicycle when it is at point A while it is freely coasting at vA = 6 ft/s. Also, calculate
The 2-kg pendulum bob moves in the vertical plane with a velocity of 6 m/s when θ = 0°. Determine the angle θ where the tension in the cord becomes zero. -2m-
The collar has a mass of 5 kg and is confined to move along the smooth circular rod which lies in the horizontal plane. The attached spring has an unstretched length of 200 mm. If at the instant θ =
The cyclist is coasting freely down the hill with a speed of 15 m/s at y = 0.2 m. Determine the resultant normal reaction on the bicycle and the rate of increase in speed at the instant shown. The
The airplane, traveling at a constant speed 50 m/s, of is executing a horizontal turn. If the plane is banked at θ = 15°, when the pilot experiences only a normal force on the seat of the plane,
The “eggbeater” wind turbine is stopped by using spoilers which consist of 20-lb blocks that slide out along the blades when the blades are turning. As the spoilers travel along the blade, they
The 600-kg wrecking ball is suspended from the crane by a cable having a negligible mass. If the ball has a speed v = 8 m/s at the instant it is at its lowest point, θ = 0°, determine the tension
The 2-kg pendulum bob moves in the vertical plane with a velocity of 8 m/s when θ = 0°. Determine the initial tension in the cord and also at the instant the bob reaches θ = 30°. Neglect the size
The tube rotates in the horizontal plane at a constant rate of θ̇ = 4 rad/s. If a 0.2-kg ball B starts at the origin O with an initial radial velocity of ṙ = 1.5 m/s and moves outward through the
The 2-kg rod AB moves up and down as its end slides on the smooth contoured surface of the cam, where r = 0.1 m and z = (0.02 sin 2θ) m. If the cam is rotating at a constant rate of 5 rad/s,
The smooth pin P has a mass of 80 g. It is attached to an elastic cord extending from O to P and, due to the slotted arm guide, moves along the horizontal circular path r = (0.8 sin θ) m. If the
Using a forked rod, a 0.5-kg smooth peg P is forced to move along the vertical slotted path r = (0.5 θ) m, where θ is in radians. If the angular position of the arm is u = (π/8 t2) rad, where t is
Using air pressure, the 0.5-kg ball is forced to move through the tube lying in the horizontal plane and having the shape of a logarithmic spiral. If the tangential force exerted on the ball due to
A boy standing firmly spins the girl sitting on a circular "dish" or sled in a circular path of radius r0 = 3 m such that her angular velocity is θ̇0 = 0.1 rad/s. If the attached cable OC is drawn
Determine the magnitude of the resultant force acting on a 5-kg particle at the instant t = 2 s, if the particle is moving along a horizontal path defined by the equations r = (2t + 10) m and θ =
The collar, which has a weight of 3 lb, slides along the smooth rod lying in the horizontal plane and having the shape of a parabola, r = [4/(l - cosθ)] ft, where θ is in radians. If the collar’s
If the coefficient of static friction between the conical surface and the block is μs = 0.2, determine the maximum constant angular velocity without causing the block to slide upwards. 45° -300
The path of motion of a 5-lb particle in the horizontal plane is described in terms of polar coordinates as r = (2t + 1) ft and θ = (0.5t² - t) rad, where t is in seconds. Determine the magnitude
If the coefficient of static friction between the conical surface and the block of mass m is μs = 0.2, determine the minimum constant angular velocity so that the block does not slide downwards.
For a short time, the 250-kg roller-coaster car with passengers is traveling along the spiral track at a constant speed of v = 8 m/s. If the track descends d = 12 m for every full revolution, θ =
The 2-lb spool slides along the smooth horizontal spiral rod, r = (2 θ) ft, where θ is in radians. If its angular rate of rotation is constant and equals θ̇ = 4 rad/s, determine the
If the position of the 3-kg collar C on the smooth rod AB is held at r = 720 mm, determine the constant angular velocity θ̇ at which the mechanism is rotating about the vertical axis. The spring
The amusement park ride rotates with a constant angular velocity of θ̇ = 0.8 rad/s. If the path of the ride is defined by r = (3 sinθ + 5)m and z = (3 cos θ)m, determine the r, θ, and z
For a short time, the 250-kg roller-coaster car with passengers is traveling along the spiral track at a constant speed such that its position measured from the top of the track has components r = 10
The smooth surface of the vertical cam is defined in part by the curve r = (0.2 cos θ + 0.3) m. The forked rod is rotating with an angular acceleration of θ̈ = 2 rad/s², and when θ = 45°,
Using air pressure, the 0.5-kg ball is forced to move through the tube lying in the horizontal plane and having the shape of a logarithmic spiral. If the tangential force exerted on the ball due to
The forked rod is used to move the smooth 2-lb particle around the horizontal path in the shape of a limaçon, r = (2 + cos θ) ft. If θ = (0.5t2) rad, where t is in seconds, determine the force
The collar has a mass of 2 kg and travels along the smooth horizontal rod defined by the equiangular spiral r = (eθ) m, where is in radians. Determine the tangential force F and the normal force N

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