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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

The 20-lb disk is mounted on the horizontal shaft AB such that its plane forms an angle of 10° with the vertical. If the shaft rotates with an angular velocity of 3 rad/s, determine the vertical
The 10-kg disk turns around the shaft AB, while the shaft rotates about BC at a constant rate of ωx = 5 rad/s. If the disk does not slip, determine the normal and frictional force it exerts on the
Two uniform rods, each having a weight of 10 lb, are pin connected to the edge of a rotating disk. If the disk has a constant angular velocity ωD = 4 rad/s, determine the angle θ made by each rod
The car travels around the curved road of radius such that its mass center has a constant speed vG. Write the equations of rotational motion with respect to the x, y, z axes.Assume that the car’s
The rod assembly has a weight of 5 lb/ft. It is supported at B by a smooth journal bearing, which develops x and y force reactions, and at A by a smooth thrust bearing, which develops x, y, and z
Four spheres are connected to shaft AB. If mc = 1 kg and mE = 2 kg, determine the mass of spheres D and F and the angles of the rods, θD and θF, so that the shaft is dynamicallybalanced, that is,
The slender rod AB has a mass m and it is connected to the bracket by a smooth pin at A. The bracket is rigidly attached to the shaft. Determine the required constant angular velocity ω of the
The 50-lb disk spins with a constant angular rate of ω1 = 50 rad/s about its axle. Simultaneously, the shaft rotates with a constant angular rate of ω2 = 10 rad/s. Determine the x, y, z components
The motor weighs 50 lb and has a radius of gyration of 0.2 ft about the z axis. The shaft of the motor is supported by bearings at A and B, and spins at a constant rate of ωs = {100k} rad/s, while
A thin rod is initially coincident with the Z axis when it is given three rotations defined by the Euler angles ϕ = 30°, θ = 45°, and ψ = 60°. If these rotations are given in the order stated,
The top consists of a thin disk that has a weight of 8 lb and a radius of 0.3 ft. The rod has a negligible mass and a length of 0.5 ft. If the top is spinning with an angular velocity ωs = 300
Solve Prob. 21–64 when θ = 90°.Solve Prob. 21–64The top consists of a thin disk that has a weight of 8 lb and a radius of 0.3 ft. The rod has a negligible mass and a length of 0.5 ft. If the
The propeller on a single-engine airplane has a mass of 15 kg and a centroidal radius of gyration of 0.3 m calculated about the axis of spin. When viewed from the front of the airplane, the propeller
The turbine on a ship has a mass of 400 kg and is mounted on bearings A and B as shown. Its center of mass is at G, its radius of gyration is kz = 0.3 m, and kx = ky = 0.5 m. If it is spinning at 200
The car travels at a constant speed of vC = 100 km/h around the horizontal curve having a radius of 80 m. If each wheel has a mass of 16 kg, a radius of gyration kG = 300 mm about its spinning axis,
The top has a mass of 90 g, a center of mass at G, and a radius of gyration k = 18 mm about its axis of symmetry. About any transverse axis acting through point O the radius of gyration is kt = 35
The 20-kg disk is spinning about its center at ωs = 20 rad/s while the supporting axle is rotating at ωy = 6 rad/s. Determine the gyroscopic moment caused by the force reactions which the pin A
The projectile shown is subjected to torque-free motion. The transverse and axial moments of inertia are I and Iz, respectively. If θ represents the angle between the precessional axis Z and the
The 1-lb top has a center of gravity at point G. If it spins about its axis of symmetry and precesses about the vertical axis at constant rates of ωs = 60 rad/s and ωp = 10 rad/s, respectively,
The projectile has a mass of 0.9 kg and axial and transverse radii of gyration of kz = 20 mm and kt = 25 mm, respectively. If it is spinning at ωs = 6 rad/swhen it leaves the barrel of a gun,
The radius of gyration about an axis passing through the axis of symmetry of the 2.5-Mg satellite is kz = 2.3 m, and about any transverse axis passing through the center of mass G, kt = 3.4 m. If the
The satellite has a mass of 1.8 Mg, and about axes passing through the mass center G the axial and transverse radii of gyration are kz = 0.8 m and kt = 1.2 m, respectively. If it is spinning at ωs =
The radius of gyration about an axis passing through the axis of symmetry of the 1.6-Mg space capsule is kz = 1.2 m, and about any transverse axis passing through the center of mass G, kt = 1.8 m. If
The satellite has a mass of 100 kg and radii of gyration about its axis of symmetry (z axis) and its transverse axes (x or y axis) of kz = 300 mm and kx = ky = 900 mm, respectively. If the satellite
A wheel of mass m and radius r rolls with constant spin ω about a circular path having a radius a. If the angle of inclination is θ, determine the rate of precession. Treat the wheel as a thin
The assembly consists of two 8-lb bars which are pin connected to the two 10-lb disks. If the bars are released from rest when θ = 60°, determine their angular velocities at the instant θ = 0°.
The center O of the thin ring of mass m is given an angular velocity of ω0. If the ring rolls without slipping, determine its angular velocity after it has traveled a distance of s down the plane.
The rotary screen S is used to wash limestone. When empty it has a mass of 800 kg and a radius of gyration of kG = 1.75 m. Rotation is achieved by applying a torque of M = 280 N · m about the drive
The system is released from rest at θ = 0° when a constant couple moment M = 100N · m is applied. If the mass of the cable and links AB and BC can be neglected, and each pulley can be treated as a
A man having a weight of 150 lb crouches down on the end of a diving board as shown. In this position the radius of gyration about his center of gravity is kG = 1.2 ft. While holding this position at
The wheel has a mass of 100 kg and a radius of gyration of kO = 0.2 m. A motor supplies a torque M = (40θ + 900) N · m, where θ is in radians, about the drive shaft at O. Determine the speed of
The coefficient of kinetic friction between the 100-lb disk and the surface of the conveyor belt is μA = 0.2. If the conveyor belt is moving with a speed of vC = 6 ft/s when the disk is placed in
If corner A of the 60-kg plate is subjected to a vertical force of P = 500 N, and the plate is released from rest when θ = 0°, determine the angular velocity of the plate when θ = 45°. A P = 500
When a force of P = 30 lb is applied to the brake arm, the 50-lb cylinder A is descending with a speed of 20 ft/s. Determine the number of revolutions wheel B will rotate before it is brought to a
If the 50-lb bucket C is released from rest, determine its velocity after it has fallen a distance of 10 ft. The windlass A can be considered as a 30-lb cylinder, while the spokes are slender rods,
A uniform ladder having a weight of 30 lb is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle θ at which the bottom end A starts to lift
The link AB is subjected to a couple moment of M = 40 N · m. If the ring gear C is fixed, determine the angular velocity of the 15-kg inner gear when the link has made two revolutions starting from
The 50-1b cylinder A is descending with a speed of 20 ft/s when the brake is applied. If wheel B must be brought to a stop after it has rotated 5 revolutions, determine the constant force P that must
A ball of mass m and radius r is cast onto the horizontal surface such that it rolls without slipping. Determine the minimum speed vG of its mass center G so that it rolls completely around the loop
The 10-kg rod AB is pin connected at A and subjected to a couple moment of M = 15 N · m. If the rod is released from rest when the spring is unstretched at θ = 30°, determine the rod’s angular
The two 2-kg gears A and B are attached to the ends of a 3-kg slender bar. The gears roll within the fixed ring gear C, which lies in the horizontal plane. If a 10 · N m torque isapplied to the
Gears C and H each have a weight of 0.4 lb and a radius of gyration about their mass center of kA = kB = 2 in. The uniform link AB has a weight of 0.2 lb and a radius of gyration of kA = 3 in.,
Motor M exerts a constant force of P = 750 N on the rope. If the 100-kg post is at rest when θ = 0°, determine the angular velocity of the post at the instant θ = 60°. Neglect the mass of the
The spool has a mass of 100 kg and a radius of gyration of 400 mm about its center of mass O. If it is released from rest, determine its angular velocity after its center O has moved down the plane a
A ball of mass m and radius r is cast onto the horizontal surface such that it rolls without slipping. Determine its angular velocity at the instant θ = 90°, if it has an initial speed of vG as
The spool has a mass of 100 kg and a radius of gyration of 400 mm about its center of mass O.If it is released from rest, determine its angular velocity after its center O has moved down the plane a
A chain that has a negligible mass is draped over the sprocket which has a mass of 2 kg and a radius of gyration of ko = 50 mm. If the 4-kg block A is released from rest from the position s = 1 m,
The assembly consists of a 3-kg pulley A and 10-kg pulley B. If a 2-kg block is suspended from the cord, determine the block’s speed after it descends 0.5 m starting from rest. Neglect the mass of
The 6-kg rod ABC is connected to the 3-kg rod CD. If the system is released from rest when θ = 0°, determine the angular velocity of rod ABC at the instant it becomes horizontal. A 0.5 m B D 0 0.3
The assembly consists of a 3-kg pulley A and 10-kg pulley B. If a 2-kg block is suspended from the cord, determine the distance the block must descend, starting from rest, in order to cause B to have
The 25-lb slender rod AB is attached to spring BC which has an unstretched length of 4 ft. If the rod is released from rest when θ = 30°, determine its angular velocity at the instant θ = 90°.
The 25-lb slender rod AB is attached to spring BC which has an unstretched length of 4 ft. If the rod is released from rest when θ = 30°, determine the angular velocity of the rod the instant the
Solve Prob. 18–38 if the chain has a mass of 0.8 kg/m. For the calculation neglect the portion of the chain that wraps over the sprocket.Solve Prob. 18–38A chain that has a negligible mass is
The two bars are released from rest at the position θ = 90°. B Determine their angular velocities at the instant they become horizontal. Neglect the mass of the roller at C. Each bar has a mass m
The tire has a mass of 8 kg a radius of 0.3 m and a radius of gyration about its center of gravity G of kG = 0.25 m. If it is released from rest at the top of the hill, determine the velocity of its
The uniform 150-lb stone (rectangular block) is being turned over on its side by pulling the vertical cable slowly upward until the stone begins to tip. If it then falls freely (T = 0) from an
The assembly consists of two 8-lb bars which are pin connected to the two 10-lb disks. If the bars are released from rest when θ = 60°, determine their angular velocities at the instant θ = 30°.
The two bars are released from rest at the position θ. Determine their angular velocities at the instant they become horizontal. Neglect the mass of the roller at C. Each bar has a mass m and length
The pavement compactor is traveling down the incline at vG = 5 ft/s when the motor is disengaged. Determine the angular velocity of the roller B when the compactor has traveled 20 ft down the plane.
The 40-kg wheel has a radius of gyration about its center of gravity G of kG = 250 mm. If it rolls without slipping, determine its angular velocity when it has rotated clockwise 90° from the
If the 250-lb block is released from rest when the spring is unstretched, determine the velocity of the block after it has descended 5 ft.The drum has a weight of 50 lb and a radius of gyration of kO
The uniform garage door has a mass of 150 kg and is guided along smooth tracks at its ends. Lifting is done using the two springs, which are attached to the anchor bracket at A and to the
The pendulum of the Charpy impact machine has a mass of 50 kg and a radius of gyration of kA = 1.75 m. If it is released from rest when θ = 0°, determine its angular velocity just before it strikes
The two 12-kg slender rods are pin connected and released from rest at the position θ = 60°. If the spring has an unstretched length of 1.5 m, determine the angular velocity of rod BC, when the
A large roll of paper having a mass of 20 kg and a radius r = 150 mm is resting over the edge of a corner, such that the end of the paper on the roll is attached to the horizontal surface. If the
At a given instant the body of mass m has an angular velocity ω and its mass center has a velocity vG. Show that its kinetic energy can be represented as T = 1/2IICω2, where IIC is the moment
The 50-kg flywheel has a radius of gyration of kO = 200 mm about its center of mass. If it is subjected to a torque of M = (9θ¹/2+1) N-m, where θ is in radians, determine its angular velocity when
The slender 15-kg bar is initially at rest and standing in the vertical position when the bottom end A is displaced slightly to the right. If the track in which it moves is smooth, determine the
The uniform 50-lb slender rod is subjected to a couple moment of M = 100 lb ft. If the rod is at rest when θ = 0°, determine its angular velocity when θ = 90°. O M=100 lb-ft 5 ft
The 80-kg wheel has a radius of gyration about its mass center O of ko = 400 mm. Determine its angular velocity after it has rotated 20 revolutions starting from rest. 0.6 m P = 50 N
Each gear has mass of 2 kg and a radius of gyration about its pinned mass center A or B, respectively of kg = 40 mm. Each link has a mass of 2 kg and a radius of gyration about its pinned end A or B,
The spool has a mass of 60 kg and a radius of gyration kG = 0.3 m. If it is released from rest, determine how far its center descends down the smooth plane before it attains an angular velocity of ω
The uniform 50-kg slender rod is at rest in the positionshown when P = 600 N is applied. Determine the angularvelocity of the rod when the rod reaches the vertical position. 4 m 5 m P = 600 N B
The spool has a mass of 40 kg and a radius of gyration of kO = 0.3 m. If the 10-kg block is released from rest, determine the distance the block must fall in order for the spool to have an angular
The drum has a mass of 50 kg and a radius of gyration about the pin at O of kO = 0.23 m. Starting from rest, the suspended 15-kg block B is allowed to fall 3 m without applying the brake ACD.
Solve Prob. 18–2 if the coefficient of kinetic friction between the spool and plane at A is μk = 0.2.Solve Prob. 18–2The spool has a mass of 60 kg and a radius of gyration kG = 0.3 m .If it is
The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration of k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0,
The 50-kg wheel is subjected to a force of 50 N. If the wheel starts from rest and rolls without slipping, determine its angular velocity after it has rotated 10 revolutions. The radius of gyration
The spool weighs 20 lb and has a radius of gyration of kG = 3 in. If it is released from rest, determine how far it must drop before the velocity of its center becomes 20 ft/s. The cable is wrapped
If the uniform 30-kg slender rod starts from rest at the position shown, determine its angular velocity after it has rotated 4 revolutions. The forces remain perpendicular to the rod. 30 N 10.5 m 0.5
A force of P = 20 N is applied to the cable, which causes the 175-kg reel to turn since it is resting on the two rollers A and B of the dispenser. Determine the angular velocity of the reel after it
The compound disk pulley consists of a hub and attached outer rim. If it has a mass of 3 kg and a radius of gyration of kG = 45 mm, determine the speed of block A after A descends 0.2 m from rest.
A force of P = 20 N is applied to the cable, which causes the 175-kg reel to turn without slipping on the two rollers A and B of the dispenser. Determine the angular velocity of the reel after it has
The 20-kg wheel has a radius of gyration about its center G of kG = 300 mm. When it is subjected to a couple moment of M = 50 N · m, it rolls without slipping. Determine the angular velocity of the
The system consists of a 20-lb disk A, 4-lb slender rod BC, and a 1-lb smooth collar C. If the disk rolls without slipping, determine the velocity of the collar at the instant the rod becomes
If the 30-kg disk is released from rest when θ = 0°,determine its angular velocity when θ = 90°. Jo G 0.3 m
The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a radius of gyration about its center of kO = 0.6 ft and is turning with an angular velocity of
At the instant the spring becomes undeformed, the center of the 40-kg disk has a speed of 4 m/s. From this point determine the distance d the disk moves down the plane before momentarily stopping.
The 60-kg rod OA is released from rest when θ = 0°. Determine its angular velocity when θ = 45°. The spring remains vertical during the motion and is unstretched when θ = 0°. 3 m k = 150 N/m
The 50-kg reel has a radius of gyration about its center G of kG = 300 mm. If it is released from rest, determine its angular velocity when its center G has traveled 6 m down the smooth inclined
The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a centroidal radius of gyration of kO = 0.6 ft and is turning with an angular velocity of 20 rad
The 30-kg rod is released from rest when θ = 0°.Determine the angular velocity of the rod when θ = 90°.The spring is unstretched when θ = 0°. 1.5 m -2 m- wwwwwwww k = 80 N/m
The disk, which has a mass of 20 kg, is subjected to the couple moment of M = (2θ + 4) N · m, where θ is in radians. If it starts from rest, determine its angular velocity when it has made two
A motor delivers 50 lb · ft of torque to the pinion gear D, which is in mesh with the larger gear A and the attached drum over which the cable winds. If A has a weight of 120 lb and a radius of
The 30-kg rod is released from rest when θ = 45°. Determine the angular velocity of the rod when θ = 0°. The spring is unstretched when θ = 45°. B 1.5 m k = 300 N/m A
The revolving door consists of four doors which are attached to an axle AB. Each door can be assumed to be a 50-lb thin plate. Friction at the axle contributes a moment of 2 lb · ft which resists
The 20-kg rod is released from rest when θ = 0°. Determine its angular velocity when θ = 90°. The spring has an unstretched length of 0.5 m. A W 2m -2m- B 1 m k = 100 N/m
The 10-kg uniform slender rod is suspended at rest from the pin at 0 when the force of F = 150 N is applied to its end. Determine the angular velocity of the rod when it has rotated 90° clockwise
The 10-kg uniform slender rod is suspended at rest from the pin at O when the force of F = 150 N is applied to its end. Determine the angular velocity of the rod when it has rotated 180° clockwise
The pendulum consists of a 10-kg uniform disk and a 3-kg uniform slender rod. If it is released from rest in the position shown, determine its angular velocity when it rotates clockwise 90°. M = 30

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