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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

The bar of weight w is pinned at its center O and connected to a torsional spring. The spring has a stiffness k, so that the torque developed is M = kθ. If the bar is released from rest when it is
The roll of paper of mass M has radius of gyration kA about an axis passing through point A. It is pin-supported at both ends by two brackets AB. If the roll rests against a wall for which the
The cylinder has a radius r and mass m and rests in the trough for which the coefficient of kinetic friction at A and B is μk. If a horizontal force P is applied to the cylinder, determine the
The bar has a mass m and length l. If it is released from rest from the position shown, determine its angular acceleration and the horizontal and vertical components of reaction at the pin O.
Disk D of weight W is subjected to counterclockwise moment M = bt. Determine the angular velocity of the disk at time t after the moment is applied. Due to the spring the plate P exerts constant
Determine the position of the center of percussion P of the slender bar of weight W. What is the horizontal force at the pin when the bar is struck at P with force F?Data from problem 65The kinetic
The disk has mass M and is originally spinning at the end of the strut with angular velocity ω. If it is then placed against the wall, for which the coefficient of kinetic friction is μk, determine
The variable-resistance motor is often used for appliances, pumps, and blowers. By applying a current through the stator S, an electromagnetic field is created that “pulls in” the nearest rotor
The relay switch consists of an electromagnet E and an armature AB (slender bar) of mass M which is pinned at A and lies in the vertical plane. When the current is turned off, the armature is held
A boy of mass mb sits on top of the large wheel which has mass mw and a radius of gyration kG. If the boy essentially starts from rest at θ = 0°, and the wheel begins to rotate freely, determine
The two-bar assembly is released from rest in the position shown. Determine the initial bending moment at the fixed joint B. Each bar has mass m and length l. A 1 в 1 C
The cord is wrapped around the inner core of the spool. If block B of weight WB is suspended from the cord and released from rest, determine the spool’s angular velocity when t = t1. Neglect the
The two blocks A and B have a mass mA and mB, respectively, where mB > mA. If the pulley can be treated as a disk of mass M, determine the acceleration of block A. Neglect the mass of the cord and
The wheel has mass M and radius of gyration kB. It is originally spinning with angular velocity ω1. If it is placed on the ground, for which the coefficient of kinetic friction is μc, determine the
A force F is applied perpendicular to the axis of the rod of weight W and moves from O to A at a constant rate v. If the rod is at rest when θ = 0° and F is at O when t = 0, determine the rod’s
Block A has a mass m and rests on a surface having a coefficient of kinetic friction μk. The cord attached to A passes over a pulley at C and is attached to a block B having a mass 2m. If B is
The slender rod of mass m is released from rest when θ = θ0. At the same instant ball B having the same mass m is released. Will B or the end A of the rod have the greatest speed when they pass the
The punching bag of mass M has a radius of gyration about its center of mass G of kG. If it is subjected to a horizontal force F, determine the initial angular acceleration of the bag and the tension
The trailer has mass M1 and a mass center at G, whereas the spool has mass M2, mass center at O, and radius of gyration about an axis passing through O kO. If a force F is applied to the cable,
The rocket has weight W, mass center at G, and radius of gyration about the mass center kG when it is fired. Each of its two engines provides a thrust T. At a given instant, engine A suddenly fails
The uniform board of weight W is suspended from cords at C and D. If these cords are subjected to constant forces FA and FB respectively, determine the acceleration of the board’s center and the
The wheel has a weight W and a radius of gyration kG. If the coefficients of static and kinetic friction between the wheel and the plane are μs and μk, determine the maximum angle θ of the
The spool has mass M and radius of gyration kG. It rests on the surface of a conveyor belt for which the coefficient of static friction is μs and the coefficient of kinetic friction is μk. If the
The wheel has weight W and radius of gyration kG. If the coefficients of static and kinetic friction between the wheel and the plane are μs and μk, determine the wheel’s angular acceleration as
The spool has mass M and radius of gyration kG. It rests on the surface of a conveyor belt for which the coefficient of static friction is μs. Determine the greatest acceleration of the conveyor so
A uniform rod having weight W is pin-supported at A from a roller which rides on horizontal track. If the rod is originally at rest, and horizontal force F is applied to the roller, determine the
The slender bar of weight W is supported by two cords AB and AC. If cord AC suddenly breaks, determine the initial angular acceleration of the bar and the tension in cord AB. Given: W = 150
A uniform rod having weight W is pin-supported at A from a roller which rides on horizontal track. Assume that the roller at A is replaced by a slider block having a negligible mass. If the rod is
The lawn roller has mass M and radius of gyration kG. If it is pushed forward with a force F when the handle is in the position shown, determine its angular acceleration. The coefficients of static
A long strip of paper is wrapped into two rolls, each having mass M. Roll A is pin-supported about its center whereas roll B is not centrally supported. If B is brought into contact with A and
A “lifted” truck can become a road hazard since the bumper is high enough to ride up a standard car in the event the car is rear-ended. As a model of this case consider the truck to have a mass
A woman sits in a rigid position in the middle of the swing. The combined weight of the woman and swing is W and the radius of gyration about the center of mass G is kG. If a man pushes on the swing
A girl sits snugly inside a large tire such that together the girl and tire have a total weight W, a center of mass at G, and a radius of gyration kG about G. If the tire rolls freely down the
The circular plate of weight W is suspended from a pin at A. If the pin is connected to a track which is given acceleration aA, determine the horizontal and vertical components of reaction at A and
The assembly consists of a disk of mass mD and a bar of mass mb which is pin connected to the disk. If the system is released from rest, determine the angular acceleration of the disk. The
The assembly consists of a disk of mass mD and a bar of mass mb which is pin connected to the disk. If the system is released from rest, determine the angular acceleration of the disk. The
The wheel is made from a thin ring of mass mring and two slender rods each of mass mrod. If the torsional spring attached to the wheel’s center has stiffness k, so that the torque on the center of
The uniform rectangular plate has weight W. If the plate is pinned at A and has an angular velocity ω, determine the kinetic energy of the plate. Given: W = 30 lb rad S @=3 a = 2 ft b = 1 ft
At the instant shown, the disk of weight W has counterclockwise angular velocity ω when its center has velocity v. Determine the kinetic energy of the disk at this instant. Given: W = 30 lb @ = 5 V
At the instant shown, link AB has angular velocity ωAB. If each link is considered as a uniform slender bar with weight density γ, determine the total kinetic energy of the system. Given: @AB
Determine the kinetic energy of the system of three links. Links AB and CD each have weight W1, and link BC has weight W2. Given: W₁ = 10 lb W₂ = 20 lb @AB = 5 rad TAB = 1 ft "BC = 2 ft TCD = 1
The bar of weight W is pinned at its center O and connected to a torsional spring. The spring has a stiffness k, so that the torque developed is M = kθ. If the bar is released from rest when it is
The mechanism consists of two rods, AB and BC, which have weights W1 and W2, respectively, and a block at C of weight W3. Determine the kinetic energy of the system at the instant shown, when the
The pulley of mass Mp has a radius of gyration about O of kO. If a motor M supplies a force to the cable of P = a (b − ce−dx), where x is the amount of cable wound up, determine the speed of the
A yo-yo has weight W and radius of gyration kO. If it is released from rest, determine how far it must descend in order to attain angular velocity ω. Neglect the mass of the string and assume that
The uniform pipe has a mass M and radius of gyration about the z axis of kG. If the worker pushes on it with a horizontal force F, applied perpendicular to the pipe, determine the pipe’s angular
The soap-box car has weight Wc including the passenger but excluding its four wheels. Each wheel has weight Ww, radius r, and radius of gyration k, computed about an axis passing through the
The disk of mass md is originally at rest, and the spring holds it in equilibrium. A couple moment M is then applied to the disk as shown. Determine its angular velocity at the instant its mass
The slender rod of mass mrod is subjected to the force and couple moment. When it is in the position shown it has angular velocity ω1. Determine its angular velocity at the instant it has rotated
The slender rod of mass M is subjected to the force and couple moment. When the rod is in the position shown it has angular velocity ω1. Determine its angular velocity at the instant it has rotated
The elevator car E has mass mE and the counterweight C has mass mC. If a motor turns the driving sheave A with constant torque M, determine the speed of the elevator when it has ascended a distance d
The elevator car E has mass mE and the counterweight C has mass mC. If a motor turns the driving sheave A with torque aθ2 + b, determine the speed of the elevator when it has ascended a distance d
The gear has a weight W and a radius of gyration kG. If the spring is unstretched when the torque M is applied, determine the gear’s angular velocity after its mass center G has moved to the left a
The disk of mass md is originally at rest, and the spring holds it in equilibrium. A couple moment M is then applied to the disk as shown. Determine how far the center of mass of the disk travels
The linkage consists of two rods AB and CD each of weight W1 and bar AD of weight W2. When θ = 0, rod AB is rotating with angular velocity ωO. If rod CD is subjected to a couple moment M and bar AD
The spool has weight W and radius of gyration kG. A horizontal force P is applied to a cable wrapped around its inner core. If the spool is originally at rest, determine its angular velocity after
The linkage consists of two rods AB and CD each of weight W1 and bar AD of weight W2. When θ = 0, rod AB is rotating with angular velocity ωO. If rod CD is subjected to a couple moment M and bar AD
The cement bucket of weight W1 is hoisted using a motor that supplies a torque M to the axle of the wheel. If the wheel has a weight W2 and a radius of gyration about O of kO, determine the speed of
The assembly consists of two slender rods each of weight Wr and a disk of weight Wd. If the spring is unstretched when θ = θ1 and the assembly is released from rest at this position, determine the
The uniform door has mass M and can be treated as a thin plate having the dimensions shown. If it is connected to a torsional spring at A, which has stiffness k, determine the required initial twist
The uniform slender bar has a mass m and a length L. It is subjected to a uniform distributed load w0 which is always directed perpendicular to the axis of the bar. If it is released from the
The soap-box car has weight Wc including the passenger but excluding its four wheels. Each wheel has weight Ww radius r, and radius of gyration k, computed about an axis passing through the wheel’s
The beam has weight W and is being raised to a vertical position by pulling very slowly on its bottom end A. If the cord fails when θ = θ1 and the beam is essentially at rest, determine the speed
The assembly consists of two slender rods each of weight Wr and a disk of weight Wd. If the spring is unstretched when θ = θ1 and the assembly is released from rest at this position, determine the
A yo-yo has weight W and radius of gyration kO. If it is released from rest, determine how far it must descend in order to attain angular velocity ω. Neglect the mass of the string and assume that
The beam has weight W and is being raised to a vertical position by pulling very slowly on its bottom end A. If the cord fails when θ = θ1 and the beam is essentially at rest, determine the speed
The spool has mass mS and radius of gyration kO. If block A of mass mA is released from rest, determine the distance the block must fall in order for the spool to have angular velocity ω. Also, what
The disk of weight W is rotating about pin A in the vertical plane with an angular velocity ω1 when θ = 0°. Determine its angular velocity at the instant shown, θ = 90 deg. Also, compute the
When slender bar AB of mass M is horizontal it is at rest and the spring is unstretched. Determine the stiffness k of the spring so that the motion of the bar is momentarily stopped when it has
The door is made from one piece, whose ends move along the horizontal and vertical tracks. If the door is in the open position θ = 0°, and then released, determine the speed at which its end A
The overhead door BC is pushed slightly from its open position and then rotates downward about the pin at A. Determine its angular velocity just before its end B strikes the floor. Assume the door is
The cylinder of weight W1 is attached to the slender rod of weight W2 which is pinned at point A. At the instant θ = θ0 the rod has an angular velocity ω0 as shown. Determine the angle θf to
The semicircular segment of mass M is released from rest in the position shown. Determine the velocity of point A when it has rotated counterclockwise 90°. Assume that the segment rolls without
The end A of the garage door AB travels along the horizontal track, and the end of member BC is attached to a spring at C. If the spring is originally unstretched, determine the stiffness k so that
The cord is wrapped around the inner core of the spool. If block B of weight WB is suspended from the cord and released from rest, determine the spool’s angular velocity when t = t1. Neglect the
The fan blade has mass mb and a moment of inertia I0 about an axis passing through its center O. If it is subjected to moment M = A(1 − ebt) determine its angular velocity when t = t1 starting from
Disk D of weight W is subjected to counterclockwise moment M = bt. Determine the angular velocity of the disk at time t2 after the moment is applied. Due to the spring the plate P exerts constant
The disk has mass M and is originally spinning at the end of the strut with angular velocity ω. If it is then placed against the wall, for which the coefficient of kinetic friction is μk determine
The man pulls the rope off the reel with a constant force P in the direction shown. If the reel has weight W and radius of gyration kG about the trunnion (pin) at A, determine the angular velocity of
A flywheel has a mass M and radius of gyration kG about an axis of rotation passing through its mass center. If a motor supplies a clockwise torque having a magnitude M = kt, determine the
The slender rod of mass M rests on a smooth floor. If it is kicked so as to receive a horizontal impulse I at point A as shown, determine its angular velocity and the speed of its mass center.
The drum has mass M, radius r, and radius of gyration kO. If the coefficients of static and kinetic friction at A are μs and μk respectively, determine the drum's angular velocity at time t after
Disk A of mass mA is mounted on arm BC, which has a negligible mass. If a torque of M = M0eat is applied to the arm at C, determine the angular velocity of BC at time t starting from rest. Solve the
The inner hub of the wheel rests on the horizontal track. If it does not slip at A, determine the speed of the block of weight Wb at time t after the block is released from rest. The wheel has weight
The spool has weight Ws and radius of gyration kO. If the block B has weight Wb and a force P is applied to the cord, determine the speed of the block at time t starting from rest. Neglect the mass
The ball of mass m and radius r rolls along an inclined plane for which the coefficient of static friction is μ. If the ball is released from rest, determine the maximum angle θ for the incline so
The slender rod has a mass m and is suspended at its end A by a cord. If the rod receives a horizontal blow giving it an impulse I at its bottom B, determine the location y of the point P about which
The square plate has a mass M and is suspended at its corner A by a cord. If it receives a horizontal impulse I at corner B, determine the location y' of the point P about which the plate appears to
The crate has a mass Mc. Determine the constant speed v0 it acquires as it moves down the conveyor. The rollers each have radius r, mass M, and are spaced distance d apart. Note that friction causes
The pendulum consists of a slender rod AB of mass M1 and a disk of mass M2. It is released from rest without rotating. When it falls a distance d, the end A strikes the hook S, which provides a
A man has a moment of inertia Iz about the z axis. He is originally at rest and standing on a small platform which can turn freely. If he is handed a wheel which is rotating at angular velocity ω
Rod ACB of mass mr supports the two disks each of mass md at its ends. If both disks are given a clockwise angular velocity ωA1 = ωΒ1 = ω0 while the rod is held stationary and then released,
Two wheels A and B have masses mA and mB and radii of gyration about their central vertical axes of kA and kB respectively. If they are freely rotating in the same direction at ωA and ωΒ about the
A horizontal circular platform has a weight W1 and a radius of gyration kz about the z axis passing through its center O. The platform is free to rotate about the z axis and is initially at rest. A
A bullet of mass mb having velocity v is fired into the edge of the disk of mass md as shown. Determine the angular velocity of the disk of mass md just after the bullet becomes embedded in it. Also,
The square plate has a weight W and is rotating on the smooth surface with a constant angular velocity ω0. Determine the new angular velocity of the plate just after its corner strikes the peg P and
The two disks each have weight W. If they are released from rest when θ = θ1, determine the maximum angle θ2 after they collide and rebound from each other. The coefficient of restitution is e.
The pendulum consists of a solid ball of weight Wb and a rod of weight Wr. If it is released from rest when θ1 = 0°, determine the angle θ2 after the ball strikes the wall, rebounds, and the
The plank has a weight W, center of gravity at G, and it rests on the two sawhorses at A and B. If the end D is raised a distance c above the top of the sawhorses and is released from rest, determine
A solid ball with a mass m is thrown on the ground such that at the instant of contact it has an angular velocity ω1 and velocity components vGx1 and vGy1 as shown. If the ground is rough so no

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