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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

The uniform slender bar of mass m and length L is held in the position shown by the stop at A. What acceleration a will cause the normal force acting on the roller at B to become (a) One-half of
The homogeneous crate of mass m is mounted on small wheels as shown. Determine the maximum force P which can be applied without overturning the crate about(a) Its lower front edge with h =
The frame is made from uniform rod which has a mass ρ per unit length. A smooth recessed slot constrains the small rollers at A and B to travel horizontally. Force P is applied to the frame through
A uniform slender rod rests on a car seat as shown. Determine the deceleration a for which the rod will begin to tip forward. Assume that friction at B is sufficient to prevent slipping. Vertical А
Determine the value of P which will cause the homogeneous cylinder to begin to roll up out of its rectangular recess. The mass of the cylinder is m and that of the cart is M. The cart wheels have
The uniform 5-kg bar AB is suspended in a vertical position from an accelerating vehicle and restrained by the wire BC. If the acceleration is a = 0.6g, determine the tension T in the wire and the
If the collar P is given a constant acceleration a = 3g to the right, the pendulum will assume a steady-state deflection θ = 30°. Determine the stiffness kT of the torsional spring which will allow
The uniform 30-kg bar OB is secured to the accelerating frame in the 30° position from the horizontal by the hinge at O and roller at A. If the horizontal acceleration of the frame is a = 20 m/s2,
The bicyclist applies the brakes as he descends the 10° incline. What deceleration a would cause the dangerous condition of tipping about the front wheel A? The combined center of mass of the rider
The right-angle bar acts to control the maximum acceleration of an experimental vehicle by depressing the spring-loaded limit switch A with a vertical force. If a 60-percent reduction in the force
The 1650-kg car has its mass center at G. Calculate the normal forces NA and NB between the road and the front and rear pairs of wheels under conditions of maximum acceleration. The mass of the
The four-wheel-drive all-terrain vehicle has a mass of 300 kg with center of mass G2. The driver has a mass of 85 kg with center of mass G1. If all four wheels are observed to spin momentarily as the
A cleated conveyor belt transports solid homogeneous cylinders up a 15° incline. The diameter of each cylinder is half its height. Determine the maximum acceleration which the belt may have without
The thin hoop of negligible mass and radius r contains a homogeneous semicylinder of mass m which is rigidly attached to the hoop and positioned such that its diametral face is vertical. The assembly
Determine the magnitude P and direction θ of the force required to impart a rearward acceleration a = 5 ft/sec2 to the loaded wheelbarrow with no rotation from the position shown. The combined
The mine skip has a loaded mass of 2000 kg and is attached to the towing vehicle by the light hinged link CD. If the towing vehicle has an acceleration of 3 m/s2, calculate the corresponding
The block A and attached rod have a combined mass of 60 kg and are confined to move along the 60° guide under the action of the 800-N applied force. The uniform horizontal rod has a mass of 20 kg
The homogeneous rectangular plate weighs 40 lb and is supported in the vertical plane by the light parallel links shown. If a couple M = 80 lb-ft is applied to the end of link AB with the system
A jet transport with a landing speed of 200 km/h reduces its speed to 60 km/h with a negative thrust R from its jet thrust reversers in a distance of 425 m along the runway with constant
The 1300-lb homogeneous plate is suspended from the overhead carriage by the two parallel steel cables. What acceleration a will cause the tensions in the two cables to be equal? What is the
The uniform L-shaped bar pivots freely at point P of the slider, which moves along the horizontal rod. Determine the steady-state value of the angle θ if. (a) A = 0 (b) A = g/2. For
The 30,000-lb concrete pipe section is being transported on a flatbed truck. Five inextensible cables are passed across the top of the pipe and tightened securely to the flatbed with an initial
Determine the maximum counterweight W for which the loaded 4000-lb coal car will not overturn about the rear wheels B. Neglect the mass of all pulleys and wheels. 12" 3 B 30° W
The 1800-kg rear-wheel-drive car accelerates forward at a rate of g/2. If the modulus of each of the rear and front springs is 35 kN/m, estimate the resulting momentary nose-up pitch angle θ. (This
Two pulleys are fastened together to form an integral unit. At a certain instant, the indicated belt tensions act on the unit and the unit is turning counterclockwise. Determine the angular
The uniform 20-kg slender bar is pivoted at O and swings freely in the vertical plane. If the bar is released from rest in the horizontal position, calculate the initial value of the force R exerted
The figure shows an overhead view of a hydraulically-operated gate. As fluid enters the piston side of the cylinder near A, the rod at B extends causing the gate to rotate about a vertical axis
The motor M is used to hoist the 12,000-lb stadium panel (centroidal radius of gyration k̅ = 6.5 ft) into position by pivoting the panel about its corner A. If the motor is capable of producing 5000
Each of the two drums and connected hubs of 8-in. radius weighs 200 lb and has a radius of gyration about its center of 15 in. Calculate the angular acceleration of each drum. Friction in each
Determine the angular acceleration and the force on the bearing at O for (a) The narrow ring of mass m. (b) The flat circular disk of mass m immediately after each is released from rest in
The uniform 5-kg portion of a circular hoop is released from rest while in the position shown where the torsional spring of stiffness kT = 15 N ∙ m/rad has been twisted 90° clockwise from its
The 30-in. slender bar weighs 20 lb and is mounted on a vertical shaft at O. If a torque M = 100 lb-in. is applied to the bar through its shaft, calculate the horizontal force R on the bearing as the
The half ring of mass m and radius r is welded to a small horizontal shaft mounted in a bearing as shown. Neglect the mass of the shaft and determine the angular acceleration of the ring when a
The uniform plate of mass m is released from rest while in the position shown. Determine the initial angular acceleration a of the plate and the magnitude of the force supported by the pin at O. The
The uniform slender bar AB has a mass of 8 kg and swings in a vertical plane about the pivot at A. If θ˙ = 2 rad/s when θ = 30°, compute the force supported by the pin at A at that instant.
The uniform 16.1-lb slender bar is hinged about a horizontal axis through O and released from rest in the horizontal position. Determine the distance b from the mass center to O which will result in
The 15-kg uniform steel plate is freely hinged about the horizontal z-axis. Calculate the force supported by each of the bearings at A and B an instant after the plate is released from rest while in
The square frame is composed of four equal lengths of uniform slender rod, and the ball attachment at O is suspended in a socket (not shown). Beginning from the position shown, the assembly is
A uniform torus and a cylindrical ring, each solid and of mass m, are released from rest in the positions shown. Determine the magnitude of the pin reaction at O and the angular acceleration of each
A reel of flexible power cable is mounted on the dolly, which is fixed in position. There are 200 ft of cable weighing 0.436 lb per foot of length wound on the reel at a radius of 15 in. The empty
The uniform bar of mass m is supported by the smooth pin at O and is connected to the cylinder of mass m1 by the light cable which passes over the light pulley at C. If the system is released from
A vibration test is run to check the design adequacy of bearings A and B. The unbalanced rotor and attached shaft have a combined mass of 2.8 kg. To locate the mass center, a torque of 0.660 N ∙ m
The solid cylindrical rotor B has a mass of 43 kg and is mounted on its central axis C-C. The frame A rotates about the fixed vertical axis O-O under the applied torque M = 30 N∙m. The rotor may be
The right-angle body is made of uniform slender bar of mass m and length L. It is released from rest while in the position shown. Determine the initial angular acceleration a of the body and the
The uniform slender bar is released from rest in the horizontal position shown. Determine the value of x for which the angular acceleration is a maximum, and determine the corresponding angular
The right-angle plate is formed from a flat plate having a mass p per unit area and is welded to the horizontal shaft mounted in the bearing at O. If the shaft is free to rotate, determine the
The semicircular disk of mass m and radius r is released from rest at θ = 0 and rotates freely in the vertical plane about its fixed bearing at O. Derive expressions for the n- and t-components of
The uniform steel I-beam has a mass of 300 kg and is supported in the vertical plane as shown. Calculate the force R supported by the pin at O for the condition immediately after the support at B is
The gear train shown operates in a horizontal plane and is used to transmit motion to the rack D of mass mD. If an input torque M is applied to gear A, what will be the resulting acceleration a of
The uniform semicircular ring of mass m = 2.5 kg and mean radius r = 200 mm is mounted on spokes of negligible mass and pivoted about a horizontal axis through O. If the ring is released from rest in
The link B weighs 0.80 lb with center of mass 2.20 in. from O-O and has a radius of gyration about O-O of 2.76 in. The link is welded to the steel tube and is free to rotate about the fixed
A flexible cable 60 meters long with a mass of 0.160 kg per meter of length is wound around the reel. With y = 0, the weight of the 4-kg cylinder is required to start turning the reel to overcome
The uniform 72-ft mast weighs 600 lb and is hinged at its lower end to a fixed support at O. If the winch C develops a starting torque of 900 lb-ft, calculate the total force supported by the pin at
The robotic device consists of the stationary pedestal OA, arm AB pivoted at A, and arm BC pivoted at B. The rotation axes are normal to the plane of the figure. Estimate (a) The moment MA
The uniform parabolic plate has a mass per unit area of 225 kg/m2. If the plate is released from rest while in the horizontal position shown, determine the initial angular acceleration a about the
The 64.4-lb solid circular disk is initially at rest on the horizontal surface when a 3-lb force P, constant in magnitude and direction, is applied to the cord wrapped securely around its periphery.
A long cable of length L and mass ρ per unit length is wrapped around the periphery of a spool of negligible mass. One end of the cable is fixed, and the spool is released from rest in the position
The uniform semicircular rod of mass m is lying motionless on the smooth horizontal surface when the force F is applied at B as shown. Determine the resulting initial acceleration of point A. m F В A
The spacecraft is spinning with a constant angular velocity w about the z-axis at the same time that its mass center O is traveling with a velocity vO in the y-direction. If a tangential
The body consists of a uniform slender bar and a uniform disk, each of mass m/2. It rests on a smooth surface. Determine the angular acceleration a and the acceleration of the mass center of the body
Determine the angular acceleration of each of the two wheels as they roll without slipping down the inclines. For wheel A investigate the case where the mass of the rim and spokes is negligible and
The solid homogeneous cylinder is released from rest on the ramp. If θ = 40°, μs = 0.30, and μk = 0.20, determine the acceleration of the mass center G and the friction force exerted by the ramp
The 30-kg spool of outer radius ro = 450 mm has a centroidal radius of gyration k̅ = 275 mm and a central shaft of radius ri = 200 mm. The spool is at rest on the incline when a tension T = 300 N is
The fairing which covers the spacecraft package in the nose of the booster rocket is jettisoned when the rocket is in space where gravitational attraction is negligible. A mechanical actuator moves
The uniform heavy bar AB of mass m is moving on its light end rollers along the horizontal with a velocity v when end A passes point C and begins to move on the curved portion of the path with radius
The uniform slender bar of mass m and total length L is released from rest in the position shown. Determine the force supported by the small roller at A and the acceleration of roller A along the
During a test, the car travels in a horizontal circle of radius R and has a forward tangential acceleration a. Determine the lateral reactions at the front and rear wheel pairs if (a) The car
The 9-ft steel beam weighs 280 lb and is hoisted from rest where the tension in each of the cables is 140 lb. If the hoisting drums are given initial angular accelerations a1 = 4 rad/sec2 and a2 = 6
The mass center G of the 20-lb wheel is off center by 0.50 in. If G is in the position shown as the wheel rolls without slipping through the bottom of the circular path of 6-ft radius with an angular
End A of the uniform 5-kg bar is pinned freely to the collar, which has an acceleration a = 4 m/s2 along the fixed horizontal shaft. If the bar has a clockwise angular velocity w = 2 rad/s as it
The uniform rectangular panel of mass m is moving to the right when wheel B drops off the horizontal support rail. Determine the resulting angular acceleration and the force TA in the strap at A
The truck, initially at rest with a solid cylindrical roll of paper in the position shown, moves forward with a constant acceleration a. Find the distances which the truck goes before the paper rolls
The uniform rectangular 300-lb plate is held in the horizontal position by two cables each of length L = 3 ft. If the cable at A suddenly breaks, calculate the tension TB in the cable at B an instant
Small ball-bearing rollers mounted on the ends of the slender bar of mass m and length l constrain the motion of the bar in the horizontal x-y slots. If a couple M is applied to the bar initially at
The assembly consisting of a uniform slender bar (mass m/5) and a rigidly attached uniform disk (mass 4m/5) is freely pinned to point O on the collar that in turn slides on the fixed horizontal
The yo-yo has a mass m and a radius of gyration k about its center O. The cord has a maximum length y = L and is wound around the small inner hub of radius r with its end secured to a point on the
The uniform bar of mass m is constrained by the light rollers which move in the smooth guide, which lies in a vertical plane. If the bar is released from rest, what is the force at each roller an
A bowling ball with a circumference of 27 in. weighs 14 lb and has a centroidal radius of gyration of 3.28 in. If the ball is released with a velocity of 20 ft/sec but with no angular velocity as it
The figure shows the edge view of a uniform concrete slab with a mass of 12 Mg. The slab is being hoisted slowly by the winch D with cable attached to the dolly. At the position θ = 60°, the
In a study of head injury against the instrument panel of a car during sudden or crash stops where lap belts without shoulder straps or airbags are used, the segmented human model shown in the figure
The 25-mm-thick uniform steel plate is being pulled very slowly into position by the cable connected to a winch. If the cable breaks at the instant represented, what are the force under each roller
The connecting rod AB of a certain internal-combustion engine weighs 1.2 lb with mass center at G and has a radius of gyration about G of 1.12 in. The piston and piston pin A together weigh 1.80 lb.
The truck carries a 1500-mm-diameter spool of cable with a mass of 0.75 kg per meter of length. There are 150 turns on the full spool. The empty spool has a mass of 140 kg with radius of gyration of
The four-bar mechanism lies in a vertical plane and is controlled by crank OA which rotates counterclockwise at a steady rate of 60 rev /min. Determine the torque M which must be applied to the crank
The Ferris wheel at an amusement park has an even number n of gondolas, each freely pivoted at its point of support on the wheel periphery. Each gondola has a loaded mass m, a radius of gyration k
The slender rod of mass m and length l has a particle (negligible radius, mass 2m) attached to its end. If the body is released from rest when in the position shown, determine its angular velocity as
The log is suspended by the two parallel 5-m cables and used as a battering ram. At what angle θ should the log be released from rest in order to strike the object to be smashed with a velocity of 4
The assembly is constructed of homogeneous slender rod which has a mass ρ per unit length, and it rotates freely about a horizontal axis through the pivot at O. If the assembly is nudged from the
The velocity of the 8-kg cylinder is 0.3 m/s at a certain instant. What is its speed v after dropping an additional 1.5 m? The mass of the grooved drum is 12 kg, its centroidal radius of gyration is
The 32.2-lb wheel is released from rest and rolls on its hubs without slipping. Calculate the speed v of the center O of the wheel after it has moved a distance x = 10 ft down the incline. The radius
The uniform semicircular bar of radius r = 75 mm and mass m = 3 kg rotates freely about a horizontal axis through the pivot O. The bar is initially held in position 1 against the action of the
The homogeneous rectangular crate weighs 250 lb and is supported in the horizontal position by the cable at A and the corner hinge at O. If the cable at A is suddenly released, calculate the angular
The 24-lb disk is rigidly attached to the 7-lb bar OA, which is pivoted freely about a horizontal axis through point O. If the system is released from rest in the position shown, determine the
The two wheels of Prob. 6 /78, shown again here, represent two extreme conditions of distribution of mass. For case A all of the mass m is assumed to be concentrated in the center of the hoop in the
The 15-kg slender bar OA is released from rest in the vertical position and compresses the spring of stiffness k = 20 kN/m as the horizontal position is passed. Determine the proper setting of the
The light circular hoop of radius r contains a quarter-circular sector of mass m and is initially at rest on the horizontal surface. A couple M is applied to the hoop, which rolls without slipping
A steady 5-lb force is applied normal to the handle of the hand-operated grinder. The gear inside the housing with its shaft and attached handle together weigh 3.94 lb and have a radius of gyration
The figure shows an impact tester used in studying material response to shock loads. The 60-lb pendulum is released from rest and swings through the vertical with negligible resistance. At the
The uniform rectangular plate is released from rest in the position shown. Determine the maximum angular velocity w during the ensuing motion. Friction at the pivot is negligible. 26
The 50-kg flywheel has a radius of gyration k̅ = 0.4 m about its shaft axis and is subjected to the torque M = 2(1 − e−0.1θ) N∙m, where θ is in radians. If the flywheel is at rest when θ =

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