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engineering
mechanical engineering

Questions and Answers of Mechanical Engineering

Disk A, of mass 2 kg and radius r = 60 mm, is at rest when it is placed in contact with a belt which moves at a constant speed v = 15 m/s. Knowing that μk = 0.20 between the disk and the belt,
A sphere of radius r and weight W with an initial clockwise angular velocity ω0 is placed in the corner formed by the floor and a vertical wall. Denoting by μk the coefficient of kinetic friction
Two identical uniform cylinders of mass m and radius r are at rest at time t = 0 when a couple M of constant magnitude M
Two identical 16-lb uniform cylinders of radius r = 4 in. are at rest when a couple M of constant magnitude 4 lb ??ft is applied to cylinder A. Slipping occurs between the two cylinders and between
Each of the double pulleys shown has a centroidal mass moment of inertia of 0.25 kg ?? m2, an inner radius of 100 mm, and an outer radius of 150 mm. Neglecting bearing friction, determine (a) The
Each of the gears A and B has a mass of 675 g and has a radius of gyration of 40 mm, while gear C has a mass of 3.6 kg and has a radius of gyration of 100 mm. Assume that kinetic friction in the
A computer tape moves over the two drums shown. Drum A weighs 1.4 lb and has a radius of gyration of 0.75 in., while drum B weighs 3.5 lb and has a radius of gyration of 1.25 in. In the lower portion
Show that the system of moment a for a rigid slab in plane motion reduces to a single vector, and express the distance from the mass center G to the line of action of this vector in terms of the
Show that, when a rigid slab rotates about a fixed axis through O perpendicular to the slab, the system of the moment a of its particles is equivalent to a single vector of magnitude mrω,
Show that the sum HA of the moments about a point A of the moment of the particles of a rigid slab in plane motion is equal to IA ω, where ω is the angular velocity of the slab at the instant
Consider a rigid slab initially at rest and subjected to an impulsive force F contained in the plane of the slab. We define the center of percussion P as the point of intersection of the line of
A flywheel is rigidly attached to a 38-mm-radius shaft that rolls without sliding along parallel rails. Knowing that after being released from rest the system attains a speed of 152mm/s in 30s,
A drum of 100-mm radius is attached to a disk of 200-mm radius. The disk and drum have a combined mass of 5 kg and a combined radius of gyration of 150 mm. A cord is attached to the drum at A and
Cords are wrapped around a thin-walled pipe and a solid cylinder as shown. Knowing that the pipe and the cylinder are each released from rest at time t = 0, determine at time t the velocity of the
A 12-in.-radius cylinder of weight 16 lb rests on a 6-lb carriage. The system is at rest when a force P of magnitude 2.5 lb is applied as shown for 1.2 s. Knowing that the cylinder rolls without
The bar AB of negligible mass is attached by pins to two disks and the system is released from rest in the position shown. Disk A has a weight of 12 lb and a radius of gyration of 3.6 in. Disk B has
The 10-lb uniform bar AB is attached by pins to two uniform disks and the system is released from rest in the position shown. The weight of disk A is 12 lb and that of disk B is 6 lb. Assuming that
A 15-kg double pulley has a radius of gyration of 125 mm and is attached to a 10-kg slider block by a pin at point G. The system is at rest when constant forces PA and PB are applied to the cords as
A 160-mm-diameter pipe of mass 6 kg rests on a 1.5-kg plate. The pipe and plate are initially at rest when a force P of magnitude 25 N is applied for 0.75 s. Knowing that μs = 0.25 and μk = 0.20
A sphere of radius r and mass m is placed on a horizontal floor with no linear velocity but with a clockwise angular velocity ω0. Denoting by k μ the coefficient of kinetic friction between the
A sphere of radius r and mass m is projected along a rough horizontal surface with the initial velocities shown. If the final velocity of the sphere is to be zero, express (a) The required magnitude
A semicircular panel of radius r is attached with hinges to a circular plate of radius r and initially held in the vertical position as shown. The plate and the panel are made of the same material
A 1.6-kg tube AB can slide freely on rod DE which in turn can rotate freely in a horizontal plane. Initially the assembly is rotating with an angular velocity ω = 5 rad/s and the tube is held in
Two 10-lb disks and a small motor are mounted on a 15-lb rectangular platform which is free to rotate about a central vertical spindle. The normal operating speed of the motor is 180 rpm. If the
A 10-lb disk is attached to the shaft of a motor mounted on arm AB which is free to rotate about the vertical axle CD. The arm-and-motor unit has a moment of inertia of 0.032 lb ?? ft ?? s2 with
Two 0.36-kg balls are put successively into the center C of the slender 1.8-kg tube AB. Knowing that when the first ball is put into the tube the initial angular velocity of the tube is 8 rad/s and
The 30-kg uniform disk A and the bar BC are at rest and the 5-kg uniform disk D has an initial angular velocity ω1 of magnitude 440 rpm when the compressed spring is released and disk D contacts
The 8-lb disk B is attached to the shaft of a motor mounted on plate A, which can rotate freely about the vertical shaft C. The motor-plate-shaft unit has a moment of inertia of 0.14 lb ?? ft ?? s2
A 1.2-lb slender bar B fits inside a slot cut in a horizontal triangular plate which is free to rotate about a vertical axis through point O. Initially the angular velocity of the plate is 10 rad/s
The 4-kg rod AB can slide freely inside the 6-kg tube CD. The rod was entirely within the tube (x = 0) and released with no initial velocity relative to the tube when the angular velocity of the
A small 3-kg collar C can slide freely on a thin ring of mass 4.5 kg and radius 325 mm. The ring is welded to a short vertical shaft, which can rotate freely in a fixed bearing. Initially the ring
A 3.6-lb collar A and a 1.4-lb collar B can slide without friction on a frame consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about its vertical axis of symmetry.
Collar C has a weight of 18 lb and can slide freely on rod AB, which in turn can rotate freely in a horizontal plane. The assembly is rotating with an angular velocity ω of 1.5 rad/s when a spring
In Prob. 17.71 determine the velocity of the tube relative to the rod as the tube strikes end E of the assembly. Problem 17.71: A 1.6-kg tube AB can slide freely on rod DE which in turn can rotate
In Prob. 17.74, determine the velocity of each ball relative to the tube as it leaves the tube. Problem 17.74: Two 0.36-kg balls are put successively into the center C of the slender 1.8-kg tube AB.
A 6-lb uniform cylinder A can roll without sliding on a 10-lb cart C and is attached to a spring AB of constant k = 7 lb/ft as shown. The system is released from rest when the spring is stretched 0.8
Rod AB has a weight of 6 lb and is attached to a 10-lb cart C. Knowing that the system is released from rest in the position shown and neglecting friction, determines (a) The velocity of point B as
Two identical 10-lb slender rods AB and BC are welded together to form an L-shaped assembly which is suspended from a hinge at B and is at rest in a vertical plane. A 0.03-lb bullet strikes the
Two identical 10-lb slender rods AB and BC are welded together to form an L-shaped assembly which is suspended from a hinge at B and is at rest in a vertical plane. A 0.03-lb bullet strikes the
A 15-g magnet D is released from rest in the position shown, falls a distance of 320 mm, and becomes attached at A to the 200-g steel bar AB. Assuming that the impact is perfectly plastic, determine
A 30-kg uniform circular plate of radius r is supported by a ball-and socket joint at point A and is at rest in the vertical xy plane when a bullet with a mass of 15 g is fired with the velocity v0 =
In Prob. 17.89, determine (a) The required distance h if the impulsive reaction at point A is to be zero, (b) The corresponding velocity of the mass center G of the plate immediately after the bullet
A uniform slender rod AB of mass m is at rest on a frictionless horizontal surface when hook C engages a small pin at A. Knowing that the hook is pulled upward with a constant velocity v0, determine
A uniform slender rod AB of mass m and length L has a vertical velocity of magnitude v1 and no angular velocity when it strikes a rigid frictionless support at point C. Knowing that h = L/4 and
The uniform slender rod AB of mass 3 kg and length 750 mm forms an angle β = 30?with the vertical as it strikes the smooth corner shown with a vertical velocity v1 of magnitude 2.4 m/s and no
A uniform slender rod AB of mass m and length L has a vertical velocity of magnitude v1 and no angular velocity when it strikes a rigid frictionless support at point C. Knowing that h = L/4 and
A slender rod of mass m and length L is released from rest in the position shown and hits edge D. Assuming perfectly elastic impact (e = 1) at D, determine the distance b for which the rod will
A uniform sphere of radius r rolls down the incline shown without slipping. It hits a horizontal surface and, after slipping for a while, it starts rolling again. Assuming that the sphere does not
A uniform slender rod AB is at rest on a frictionless horizontal table when end A of the rod is struck by a hammer which delivers an impulse that is perpendicular to the rod. In the subsequent
A uniform slender rod of length L is dropped onto rigid supports at A and B. Immediately before striking A the velocity of the rod is v1. Since support B is slightly lower than support A, the rod
The slender rod AB of length L forms an angle β with the vertical axis as it strikes the frictionless surface shown with a vertical velocity v1 and no angular velocity. Assuming that the impact is
A uniform slender rod AB of mass m and length L is falling freely with a velocity v0 when end B strikes a smooth inclined surface as shown. Assuming that the impact is perfectly elastic, determine
A uniformly loaded square crate is falling freely with a velocity v0 when cable AB suddenly becomes taut. Assuming that the impact is perfectly plastic, determine the angular velocity of the crate
A uniform slender rod AB of mass m and length L is released from rest in the position shown. Knowing that the impact between knob B and the horizontal surface is perfectly elastic, determine (a) The
A slender 5-kg rod is released from rest in the position shown. It is observed that after the rod strikes the vertical surface it rebounds to a horizontal position. (a) Determine the coefficient of
A 0.06-lb bullet is fired with a horizontal velocity into the lower end of a 45-lb slender bar which is initially at rest in a vertical plane. Knowing that the bullet becomes embedded in the bar and
A 0.05-lb bullet is fired with a horizontal velocity of magnitude 1500ft/s into the lower end of a 40-lb slender bar which is initially at rest in a vertical plane. Knowing that the bullet becomes
A 0.05-lb bullet is fired with a horizontal velocity of magnitude 1500ft/s into the lower end of a 40-lb slender bar which is initially at rest in a vertical plane. Knowing that the bullet becomes
A uniform slender rod AB of length L = 600 mm is placed with its center equidistant from two supports that are located at a distance b = 100 mm from each other. End B of the rod is raised a distance
A uniformly loaded square crate is released from rest with its corner D directly above A; it rotates about A until its corner B strikes the floor, and then rotates about B. The floor is sufficiently
A slender rod AB is released from rest in the position shown. It swings down to a vertical position and strikes a second and identical rod CD which is resting on a friction-less surface. Assuming
Solve Prob. 17.109 assuming that the impact between the rods is perfectly elastic. Problem 17.109: A slender rod AB is released from rest in the position shown. It swings down to a vertical position
The 18-lb rigid body BD consists of two identical 2.4-in.-radius spheres and the rod which connects them and has a centroidal radius of gyration of 10 in. The body is at rest on a horizontal
Solve Prob. 17.111, assuming that the impact is perfectly elastic. Problem 17.111: The 18-lb rigid body BD consists of two identical 2.4-in.-radius spheres and the rod which connects them and has a
Block A of mass m is attached to a cord which is wrapped around a uniform disk of mass M. The block is released from rest and falls through a distance h before the cord becomes taut. Derive
The plank CDE has a weight of 30lb and rests on a small pivot at D. The 110-lb gymnast A is standing on the plank at C when the 140-lb gymnast B jumps from a height of 7.5 ft and strikes the plank at
Solve Prob. 17.114 assuming that the gymnasts change places so that gymnast A jumps onto the plank while gymnast B stands at C. Problem 17.114: The plank CDE has a weight of 30 lb and rests on a
The 2.5-kg slender rod AB is released from rest in the position shown and swings to a vertical position where it strikes the 1.5-kg slender rod CD. Knowing that the coefficient of restitution between
The uniform slender rod AB of mass AB m is attached by a pin to collar C of mass mc and the system is falling freely with a velocity v0 when collar C strikes a horizontal surface as shown. Denoting
(a) The linear and angular velocities of each sphere immediately after the impact, (b) The velocity of each sphere after it has started rolling uniformly.
A small rubber ball of radius r is thrown against a rough floor with a velocity vA of magnitude v0 and a backspin ωA of magnitude ω0. It is observed that the ball bounced from A to B, then from B
In a game of pool, ball A is rolling without slipping with a velocity v0 as it hits obliquely ball B, which is at rest. Denoting by r the radius of each ball and by μk the coefficient of kinetic
A slender 6-kg rod can rotate in a vertical plane about a pivot at B. A spring of constant k = 600 N/m and an un-stretched length of 225 mm is attached to the rod as shown. Knowing that the rod is
A slender 6-kg rod can rotate in a vertical plane about a pivot at B. A spring of constant k = 600 N/m and an un-stretched length of 225 mm is attached to the rod as shown. Knowing that the rod is
The 18-lb cradle is supported as shown by two uniform disks that roll without sliding at all surfaces of contact. The weight of each disk is W = 12 lb and the radius of each disk is r = 4 in. Knowing
Two uniform rods, each of mass m and length L, are connected to form the linkage shown. End D of rod BD can slide freely in the horizontal slot, while end A of rod AB is supported by a pin and
The 700-lb flywheel of a small hoisting engine has a radius of gyration of 24 in. If the power is cut off when the angular velocity of the flywheel is 100 rpm clockwise, determine the time required
A wheel of radius r and centroidal radius of gyration k is released from rest on the incline shown at time t = 0. Assuming that the wheel rolls without sliding, determine (a) The velocity of its
A 1.134-kg disk of radius 100 mm is attached to the yoke BCD by means of short shafts fitted in bearings at B and D. The 0.68-kg yoke has a radius of gyration of 75 mm about the x axis. Initially the
In the helicopter shown, a vertical tail rotor is used to prevent rotation of the cab as the speed of the main blades is changed. Assuming that the tail rotor is not operating, determine the final
A 40-g bullet is fired with a horizontal velocity of 600 m/s into the lower end of a slender 7-kg bar of length L = 600 mm. Knowing that h = 240 mm and that the bar is initially at rest,
A uniform slender rod AB of mass m and length L strikes a rigid frictionless support at point C with an angular velocity of magnitude ω1 when the velocity of its mass center G is zero. Knowing that
A 1.25-oz bullet is fired with a horizontal velocity of 950 ft/s into the 18-lb wooden beam AB. The beam is suspended from a collar of negligible weight that can slide along a horizontal rod.
Member ABC has a weight of 5 lb and is attached to a pin support at B. A 1.5-lb sphere D strikes end C of member ABC with a vertical velocity v1 of 9 ft/s. Knowing g that L = 30 in. and that the
A 5.4-kg slender rod is bent to form a rectangular frame which is attached to a shaft and rotates about its diagonal as shown. Knowing that the assembly has an angular velocity of constant magnitude
A thin homogeneous square plate of mass m and side a is welded to a vertical shaft AB with which it forms an angle of 45?. Knowing that the shaft rotates with a constant angular velocity ω,
A uniform 3.6-lb rod AB is welded at its midpoint G to a vertical shaft GD. Knowing that the shaft rotates with an angular velocity of constant magnitude Ï‰ = 1200 rpm, determine the
A thin homogeneous disk of mass m and radius r is mounted on the horizontal axle AB. The plane of the disk forms an angle Î² =20° with the vertical. Knowing that the axle rotates with
A solid rectangular parallelepiped of mass m has a square base of side a and a length 2a. Knowing that it rotates at the constant rate ω about its diagonal AC?? and that its rotation is observed
Solve Prob. 18.5, assuming that the solid rectangular parallelepiped has been replaced by a hollow one consisting of six thin metal plates welded together. Problem 18.5: A solid rectangular
A homogeneous disk of mass m = 8 kg rotates at the constant rate ω1 = 12 rad/s with respect to arm OA, which itself rotates at the constant rate ω2 = 4 rad/s about the y axis. Determine the angular
A homogeneous disk of mass m = 6 kg rotates at the constant rate ω1 = 16 rad/s with respect to arm ABC, which is welded to a shaft DCE rotating at the constant rate ω2 = 8 rad/s. Determine the
The 60-lb projectile shown has a radius of gyration of 2.4 in. about its axis of symmetry Gx and a radius of gyration of 10 in. about the transverse axis Gy. Its angular velocity Ï‰ can be
Determine the angular momentum HA of the projectile of Prob. 18.9 about the center A of its base, knowing that its mass center G has a velocity v of 1950 ft/s. Give your answer in terms of components
Determine the angular momentum HO of the disk of Sample Prob. 18.2 from the expressions obtained for its linear momentum mv and its angular momentum HG, using Eqs. (18.11). Verify that the result
(a) Show that the angular momentum HB of a rigid body about point HB can be obtained by adding to the angular momentum HA of that body about point A the vector product of the vector rA/B drawn from B
Determine the angular momentum HO of the disk of Prob. 18.7 about the fixed point O. Problem 18.7: A homogeneous disk of mass m = 8 kg rotates at the constant rate ω1 = 12 rad/s with respect to arm
Determine the angular momentum HD of the disk of Prob. 18.8 about point D. Problem 8.18: A homogeneous disk of mass m = 6 kg rotates at the constant rate ω1 = 16 rad/s with respect to arm ABC, which
Two L-shaped arms, each of mass 5 kg, are welded at the one-third points of the 600 mm shaft AB to form the assembly shown. Knowing that the assembly rotates at the constant rate of 360 rpm,
For the assembly of Prob. 18.15, determine (a) The angular momentum HB of the assembly about point B, (b) The angle formed by HB and BA. Problem 18.15: Two L-shaped arms, each of mass 5 kg, are

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