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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

Determine the frequency of oscillation of the cylinder of mass m when it is pulled down slightly and released. Neglect the mass of the small pulley.
Determine the natural period of vibration of the 10-lb semicircular disk. 0.5 ft
A torsional spring of stiffness k is attached to a wheel that has a mass of M. If the wheel is given a small angular displacement of θ about the z axis, determine the natural period of oscillation.
If the lower end of the 6-kg slender rod is displaced a small amount and released from rest, determine the natural frequency of vibration. Each spring has a stiffness of k = 200 N/m and is
Determine the differential equation of motion of the 15-kg spool. Assume that it does not slip at the surface of contact as it oscillates. The radius of gyration of the spool about its center of mass
The 5-lb sphere is attached to a rod of negligible mass and rests in the horizontal position. Determine the natural frequency of vibration. Neglect the size of the sphere. -1 ft -0.5 ft- k = 10 lb/ft
Determine the natural period of vibration of the disk having a mass m and radius r. Assume the disk does not slip on the surface of contact as it oscillates. k wwww-of
Without an adjustable screw, A, the 1.5-lb pendulum has a center of gravity at G. If it is required that it oscillates with a period of 1 s, determine the distance a from pin O to the screw. The
If the block-and-spring model is subjected to the periodic force F = F0cos ot, show that the differential equation ofmotion is ẍ + (k/m)x= (F0/m) cos ωt, where x ismeasured from the equilibrium
The bar has a mass of 8 kg and is suspended from two springs such that when it is in equilibrium, the springs make an angle of 45° with the horizontal as shown. Determine the natural period of
If the wheel is given a small angular displacement of θ and released from rest, it is observed that it oscillates with a natural period of τ. Determine the wheel’s radius of gyration about its
A block which has a mass m is suspended from a spring having a stiffness k. If an impressed downward vertical force F = FO acts on the weight, determine the equation which describes the position of
A 5-kg block is suspended from a spring having a stiffness of 300 N/m. If the block is acted upon by a vertical force F = (7 sin 8t) N, where t is in seconds, determine the equation which describes
If the dashpot has a damping coefficient of c = 50 N · s/m, and the spring has a stiffness of k = 600 N/m, show that the system is underdamped, and then find the pendulum's period of oscillation.
A 4-lb weight is attached to a spring having a stiffness k = 10 lb/ft. The weight is drawn downward a distance of 4 in. and released from rest. If the support moves with a vertical displacement δ =
The 30-lb block is attached to two springs having a stiffness of 10 lb/ft. A periodic force F = (8 cos 3t) lb, where t is in seconds, is applied to the block. Determine the maximum speed of the block
A 4-kg block is suspended from a spring that has a stiffness of k = 600 N/m. The block is drawn downward 50 mm from the equilibrium position and released from rest when t = 0. If the support moves
Find the differential equation for small oscillations in terms of θ for the uniform rod of mass m. Also show that if c < √mk/2, then the system remains underdamped. The rod is in a horizontal
The barrel of a cannon has a mass of 700 kg, and after firing it recoils a distance of 0.64 m. If it returns to its original position by means of a single recuperator having a damping coefficient of
The light elastic rod supports a 4-kg sphere. When an 18-N vertical force is applied to the sphere, the rod deflects 14 mm. If the wall oscillates with harmonic frequency of 2 Hz and has an amplitude
If the 30-kg block is subjected to a periodic force of P = (300 sin 5t) N, k = 1500 N/m, and c = 300 N · s/m, determine the equation that describes the steady-state vibration as a function of time.
The fan has a mass of 25 kg and is fixed to the end of a horizontal beam that has a negligible mass.The fan blade is mounted eccentrically on the shaft such that it is equivalent to an unbalanced
Use a block-and-spring model like that shown in Fig. 14a but suspended from a vertical position and subjected to a periodic support displacement of δ = δ0 cos ω0t determine the equation of motion
The engine is mounted on a foundation block which is spring supported. Describe the steady-state vibration if the block and engine have a total weight of 1500 lb, and the engine, when running,
In Prob. 22–53, determine the amplitude of steady-state vibration of the fan if its angular velocity is 10 rad/s.Prob. 22–53The fan has a mass of 25 kg and is fixed to the end of a horizontal
The electric motor turns an eccentric flywheel which is equivalent to an unbalanced 0.25-lb weight located 10 in. from the axis of rotation. If the static deflection of the beam is 1 in. because of
What will be the amplitude of steady-state vibration of the fan in Prob. 22-53 if the angular velocity of the fan blade is 18 rad/s?Prob. 22-53The fan has a mass of 25 kg and is fixed to the end of a
The 450-kg trailer is pulled with a constant speed over the surface of a bumpy road, which may be approximated by a cosine curve having an amplitude of 50 mm and wave length of 4 m. If the two
The motor of mass M is supported by a simply supported beam of negligible mass. If block A of mass m is clipped onto the rotor, which is turning at constant angular velocity of , determine the
Determine the angular velocity of the flywheel in Prob. 22–57 which will produce an amplitude of vibration of 0.25 in.Prob. 22–57The electric motor turns an eccentric flywheel which is equivalent
The block, having a weight of 15 lb, is immersed in a liquid such that the damping force acting on the block has a magnitude of F = (0.8 | v | ) lb, where is the velocity of the block in ft/s. If the
Determine the amplitude of vibration of the trailer in Prob. 22-60 if the speed v = 15 km/h.Prob. 22-60The 450-kg trailer is pulled with a constant speed over the surface of a bumpy road, which may
If the 12-kg rod is subjected to a periodic force of F = (30 sin 6t) N, where t is in seconds, determine the steady-state vibration amplitude θmax of the rod about the pin B. Assume θ is small.
A block having a mass of 0.8 kg is suspended from a spring having a stiffness of 120 N/m. If a dashpot provides a damping force of 2.5 N when the speed of the block is 0.2 m s, determine the period
The 200-lb electric motor is fastened to the midpoint of the simply supported beam. It is found that the beam deflects 2 in. when the motor is not running. The motor turns an eccentric flywheel which
The block, having a weight of 12 lb, is immersed in a liquid such that the damping force acting on the block has a magnitude of F = (0.7 | v |) lb, where v is in ft/s. If the block is pulled down
A 7-lb block is suspended from a spring having a stiffness of k = 75 lb/ft. The support to which the spring is attached is given simple harmonic motion which may be expressed as δ = (0.15 sin 2t)
The damping factor, c/cc, may be determined experimentally by measuring the successive amplitudes of vibrating motion of a system. If two of these maximum displacements can be approximated by x₁
Determine the magnification factor of the block, spring, and dashpot combination in Prob. 22–65.Prob. 22–65..A 7-lb block is suspended from a spring having a stiffness of k = 75 lb/ft. The
The bar has a weight of 6 lb. If the stiffness of the spring is k = 8 lb/ft and the dashpot has a damping coefficient c = 60 lb · s/ft, determine the differential equation which describes the motion
The 10-kg block-spring-damper system is continually damped. If the block is displaced to x = 50 mm and released from rest, determine the time required for it to return to the position x = 2 mm. x k =
A block having a mass of 7 kg is suspended from a spring that has a stiffness k = 600 N/m. If the block is given an upward velocity of 0.6 m/s from its equilibrium position at t = 0, determine its
A bullet of mass m has a velocity of Vo just before it strikes the target of mass M. If the bullet embeds in the target, and the vibration is to be critically damped, determine the dashpot's damping
A bullet of mass m has a velocity v0 just before it strikes the target of mass M. If the bullet embeds in the target, and the dashpot’s damping coefficient is 0 < c << cc,determine the
Determine the differential equation of motion for the damped vibratory system shown. What type of motion occurs? Take k = 100 N/m, c = 200 N · s/m,m = 25 kg. C et C www.c
Draw the electrical circuit that is equivalent to the mechanical system shown. Determine the differential equation which describes the charge q in the circuit. m k C
The 20-kg block is subjected to the action of the harmonic force F = (90 cos 6t) N, where t is in seconds. Write the equation which describes the steady-state motion. k = 400 N/m 50000 W k = 400
Determine the differential equation of motion for the damped vibratory system shown. What type of motion occurs? c = 200 N-s/m k = 100 N/m 25 kg = 200 N - s/m
At the given instant, the rod is spinning about the z axis with an angular velocity ω1 = 8rad/s and angular acceleration ω̇1 = 2 rad/s2. At this same instant, the disk is spinning at a constant
At the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity ω₁ = 6 rad/s, while at the same instant the arm is rotating upward at a constant
At the instant shown, the frame of the brush cutter is traveling forward in the x direction with a constant velocity of 1 m/s, and the cab is rotating about the vertical axis with a constant angular
Determine the moment of inertia of the cone with respect to a vertical ȳ axis passing through the cone’s center of mass. What is the moment of inertia about a parallel axis y′ that passes
At the instant shown, the frame of the brush cutter is traveling forward in the x direction with a constant velocity of 1 m/s, and the cab is rotating about the vertical axis with an angular velocity
Determine by direct integration the product of inertia Iyz for the homogeneous prism. The density of the material is ρ. Express the result in terms of the total mass m of the prism. X h a Z a y
Determine by direct integration the product of inertia Ixy for the homogeneous prism. The density of the material is ρ. Express the result in terms of the total mass m of the prism. X h a N D
Determine the product of inertia Ixy for the homogeneous tetrahedron. The density of the material is ρ. Express the result in terms of the total mass m of the soild. Use a triangular element of
Determine the product of inertia Ixy for the bent rod. The rod has a mass per unit length of 2 kg/m. X 500 mm Z 400 mm 600 mm y
Determine the moments of inertia for the homogeneous cylinder of mass m about the x′, y′, z′ axes. y. X -r. r Z
Show that the sum of the moments of inertia of a body, Ixx + Iyy + Izz, is independent of the orientation of the x, y, z axes and thus depends only on the location of the origin.
Determine the radii of gyration kx and ky for the solid formed by revolving the shaded area about the y axis. The density of the material is ρ. 4 ft y 0.25 ft xy = 1 -4 ft- 0.25 ft X
Determine the moments of inertia Ixx, Iyy, Izz for the bent rod. The rod has a mass per unit length of 2 kg/m. X 500 mm N 400 mm 600 mm y
Determine the moment of inertia of the cone about the z′ axis. The weight of the cone is 15 lb, the height is h = 1.5 ft, and the radius is r = 0.5 ft. h N z'
Determine the products of inertia Ixy, Lyz, and Ixz of the thin plate. The material has a density per unit area of 50 kg/m². X 400 mm 400 mm N 200 mm
Determine the moment of inertia about the z axis of the assembly which consists of the 1.5-kg rod CD and the 7-kg disk. N e B C A 200 mm 100 mm
Determine the moments of inertia about the x, y, z axes of the rod assembly. The rods have a mass of 0.75 kg/m. x 2 m 2 m A N D .30° B 1 m C y
Determine the moment of inertia Ixx of the composite plate assembly. The plates have a specific weight of 6 lb/ft². -0.5 ft X 0.5 ft. Z 0.5 ft 0.25 ft 0.5 ft y
Determine the products of inertia Ixy, Iyz, and Ixz of the thin plate. The material has a mass per unit area of 50 kg/m². x 200 mm 200 mm 400 mm 400 mm 200 mm 200 mm -100 mm y
Determine the moment of inertia of both the 1.5-kg rod and 4-kg disk about the z′ axis. 300 mm -100 mm.
The bent rod has a mass of 4 kg m. Determine the moment of inertia of the rod about the OA axis. N 0.6 m 1.2 m X a A T 0.4 m
The bent rod has a weight of 1.5 lb/ft. Locate the center of gravity G(x̄, ȳ) and determine the principal moments ofinertia Ix', Iy' and Iz' of the rod with respect to the x', y', z' axes. X 1
Determine the moment of inertia of the rod-and-thin-ring assembly about the z axis. The rods and ring have a mass per unit length of 2 kg/m. 500 mm B 120° 120° X N A 0 D C 400 mm 120° y
Determine the products of inertia Ixy, Iyz, and Ixz of the solid. The material is steel, which has a specific weight of 490 lb/ft3. X 0.25 ft 0.5 ft Z 0.5 ft 0.25 ft 0.125 ft 0.125 ft y
If a body contains no planes of symmetry, the principal moments of inertia can be determined mathematically. To show how this is done, consider the rigid body which is spinning with an angular
Show that if the angular momentum of a body is determined with respect to an arbitrary point A, then HA can be expressed by Eq. 21-9. This requires substituting ρA = ρG + ρG/A into Eq. 21-6 and
A thin plate, having a mass of 4 kg, is suspended from one of its corners by a ball-and-socket joint O. If a stone strikes the plate perpendicular to its surface at an adjacent corner A with an
The 10-kg circular disk spins about its axle with a constant angular velocity of ω₁= 15 rad/s. Simultaneously, arm OB and shaft OA rotate about their axes with constant angular velocities of ω2 =
The large gear has a mass of 5 kg and a radius of gyration of kz = 75 mm. Gears B and C each have a mass of 200 g and a radius of gyration about the axis of their connecting shaft of 15 mm. If the
The 10-kg circular disk spins about its axle with a constant angular velocity of ω₁ = 15 rad/s. Simultaneously, arm OB and shaft OA rotate about their axes with constant angular velocities of
The 4-kg rod AB is attached to the 1-kg collar at A and a 2-kg link BC using ball-and-socket joints. If the rod is released from rest in the position shown, determine the angular velocity of the link
The rod assembly is supported at G by a ball-and-socket joint. Each segment has a mass of 0.5 kg/m. If the assembly is originally at rest and an impulse of I = {-8k} N · s is applied at D, determine
The rod weighs 3 lb/ft and is suspended from parallel cords at A and B. If the rod has an angular velocity of 2 rad/s about the z axis at the instant shown, determine how high the center of the rod
The 25-lb thin plate is suspended from a ball-and-socket joint at O. A 0.2-lb projectile is fired with a velocity of v = {-300i - 250j + 300k} ft/s into the plate and becomes embedded in the plate at
The rod assembly has a mass of 2.5 kg/m and is rotating with a constant angular velocity of ω = {2k} rad/s whenthe looped end at C encounters a hook at S, which providesa permanent connection.
The 2-kg thin disk is connected to the slender rod which is fixed to the ball-and-socket joint at A. If it is released from rest in the position shown, determine the spin of the disk about the rod
The 20-kg sphere rotates about the axle with a constant angular velocity of ωs = 60 rad/s. If shaft AB is subjected to a torque of M = 50 N · m, causing it to rotate, determine the value of ωρ
Solve Prob. 21-34 if the projectile emerges from the plate with a velocity of 275 ft/s in the same direction. X 0.5 ft. 0 N 0.5 ft. 0.25 ft A• -y 0.75 ft 0.25 ft
The 15-kg rectangular plate is free to rotate about the y axis because of the bearing supports at A and B. When the plate is balanced in the vertical plane, a 3-g bullet is fired into it,
At the instant shown the collar at A on the 6-lb rod AB has a velocity of vA= 8 ft/s. Determine the kinetic energy of the rod after the collar A has descended 3 ft. Each collar is attached to the rod
The 5-kg thin plate is suspended at O using a ball-andsocket joint. It is rotating with a constant angular velocity ω = {2k} rad/s when the corner A strikes the hook at S, which provides a permanent
Rod AB has a weight of 6 lb and is attached to two smooth collars at its end points by ball-and-socket joints. If collar A is moving downward at a speed of 8 ft/s, determine the kinetic energy of the
Rod CD of mass m and length L is rotating with a constant angular rate of ω1 about axle AB, while shaft EF rotates with a constant angular rate of ω2. Determine the X, Y, and Z components of
The 40-kg flywheel (disk) is mounted 20 mm off its true center at G. If the shaft is rotating at a constant speed ω = 8 rad/s, determine the maximum reactions exerted on the journal bearings at A
The 40-kg fly wheel (disk) is mounted 20 mm off its true center at G. If the shaft is rotating at a constant speed ω = 8 rad/s, determine the minimum reactions exerted on the journal bearings at A
Derive the scalar form of the rotational equation of motion about the x axis if Ω ≠ ω and the moments and products of inertia of the body are not constant with respect to time.
The man sits on a swivel chair which is rotating with a constant angular velocity of 3 rad/s. He holds the uniform 5-lb rod AB horizontal. He suddenly gives it an angular acceleration of 2 rad/s²,
The 4-lb bar rests along the smooth corners of an open box. At the instant shown, the box has a velocity v = {5k} ft/s and an acceleration a = {2k] ft/s². Determine the x, y, z, components of force
The 4-lb bar rests along the smooth corners of an open box. At the instant shown, the box has a velocity v = {3j} ft/s and an acceleration a = {-6j} ft/s². Determine the x, y, z components of force
The shaft is constructed from a rod which has a mass per unit of 2 kg/m. Determine the x, y, z components of reaction at the bearings A and B if at the instant shown the shaft spins freely and has an
The 20-lb plate is mounted on the shaft AB so that the plane of the plate makes an angle θ = 30° with the vertical. If the shaft is turning in the direction shown with an angular velocity of 25
The uniform hatch door, having a mass of 15 kg and a mass center at G, is supported in the horizontal plane by bearings at A and B. If a vertical force F = 300 N is applied to the door as shown,

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