- The gear train shown consists of four gears of the same thickness and of the same material; two gears are of radius r, and the other two are of radius nr. The system is at rest when the couple M0 is
- Two disks of the same material are attached to a shaft as shown. Disk A has a radius r and a thickness b, while disk B has a radius nr and a thickness 2b. A couple M with a constant magnitude is
- A small sphere of mass m and radius r is released from rest at A and rolls without sliding on the curved surface to point B where it leaves the surface with a horizontal velocity. Knowing that a =
- The double pulley shown has a mass of 15 kg and a centroidal radius of gyration of 160 mm. Cylinder A and block B are attached to cords that are wrapped on the pulleys as shown. The coefficient of
- An adapted golf device attaches to a wheelchair to help people with mobility impairments play putt-putt. The stationary frame OD is attached to the wheelchair, and a club holder OB is attached to the
- Disk A has a mass of 4 kg and a radius r = 75 mm; it is at rest when it is placed in contact with the belt, which moves at a constant speed v = 18 m/s. Knowing that μk = 0.25 between the disk and
- The 10-in.-radius brake drum is attached to a larger flywheel which is not shown. The total mass moment of inertia of the flywheel and drum is 16 lb·ft·s2 and the coefficient of kinetic friction
- A 10-kg storm window measuring 900 × 1500 mm is held by hinges at A and B. In the position shown, it is held away from the side of the house by a 600-mm stick CD. If the stick is suddenly removed,
- Greek engineers had the unenviable task of moving large columns from the quarries to the city. One engineer, Chersiphron, tried several different techniques to do this. One method was to cut pivot
- The 30-kg turbine disk has a centroidal radius of gyration of 175 mm and is rotating clockwise at a constant rate of 60 rpm when a small blade of weight 0.5 N at point A becomes loose and is thrown
- A slender 9-lb rod can rotate in a vertical plane about a pivot at B. A spring of constant k = 30 lb/ft and of unstretched length 6 in. is attached to the rod as shown. Knowing that the rod is
- A collar with a mass of 1 kg is rigidly attached to a slender rod AB of mass 3 kg and length L = 600 mm. The rod is released from rest in the position shown. Determine the distance d for which the
- Two uniform cylinders, each of weight W = 14 lb and radius r = 5 in., are connected by a belt as shown. Knowing that at the instant shown the angular velocity of cylinder B is 30 rad/s clockwise,
- Each of the two rods shown is of length L = 1 m and has a mass of 5 kg. Point D is connected to a spring of constant k = 20 N/m and is constrained to move along a vertical slot. Knowing that the
- A 100-kg solid cylindrical disk, 800 mm in diameter, is to be raised over a 200-mm obstruction. A cable is wrapped around the disk and pulled with a constant horizontal force T = 260 N as shown.
- Each of the gears A and B has a mass of 10 kg and a radius of gyration of 190 mm, while gear C has a mass of 2.5 kg and a radius of gyration of 80 mm. If a couple M of constant magnitude 6 N·m is
- The 80-mm-radius gear shown has a mass of 5 kg and a centroidal radius of gyration of 60 mm. The 4-kg rod AB is attached to the center of the gear and to a pin at B that slides freely in a vertical
- A 100-kg solid cylindrical disk, 800 mm in diameter, is to be raised over a 200-mm obstruction. A cable is wrapped around the disk and pulled with a constant horizontal force T as shown. Knowing that
- A collar with a mass of 1 kg is rigidly attached at a distance d = 300 mm from the end of a uniform slender rod AB. The rod has a mass of 3 kg and is of length L = 600 mm. Knowing that the rod is
- The 4-kg rod AB is attached to a collar of negligible mass at A and to a flywheel at B. The flywheel has a mass of 16 kg and a radius of gyration of 180 mm. Knowing that in the position shown the
- A sphere of mass m and radius r rolls without slipping inside a curved surface of radius R. Knowing that the sphere is released from rest in the position shown, derive an expression for (a) The
- A 5-m-long ladder has a mass of 15 kg and is placed against a house at an angle θ = 20°. Knowing that the ladder is released from rest, determine the angular velocity of the ladder and the velocity
- The 1.5-kg uniform slender bar AB is connected to the 3-kg gear B that meshes with the stationary outer gear C. The centroidal radius of gyration of gear B is 30 mm. Knowing that the system is
- The ends of a 9-lb rod AB are constrained to move along slots cut in a vertical plate as shown. A spring of constant k = 3 lb/in. is attached to end A in such a way that its tension is zero when θ =
- The flywheel of a punching machine has a weight of 650 lb and a radius of gyration of 30 in. Each punching operation requires 1800 ft·lb of work. (a) Knowing that the speed of the flywheel is
- The uniform rods AB and BC weigh 2.4 kg and 4 kg, respectively, and the small wheel at C is of negligible weight. Knowing that in the position shown the velocity of wheel C is 2 m/s to the right,
- The 3-lb carriage C is supported as shown by two uniform 2-lb disks, each having a radius of 3 in. Knowing that the carriage is initially at rest, determine the velocity of the carriage 0.5 s after
- The mechanism shown is one of two identical mechanisms attached to the two sides of a 200-lb uniform rectangular door. Edge ABC of the door is guided by wheels of negligible mass that roll in
- A 15-lb slender rod AB is riveted to a 12-lb uniform disk as shown. A belt is attached to the rim of the disk and to a spring that holds the rod at rest in the position shown. If end A of the rod is
- The 3-lb carriage C is supported as shown by two uniform 2-lb disks, each having a radius of 3 in. Knowing that the carriage is initially at rest, determine the velocity of the carriage 0.5 s after
- Two uniform cylinders, each of mass m = 6 kg and radius r = 125 mm, are connected by a belt as shown. If the system is released from rest when t = 0, determine (a) The velocity of the center of
- The drive belt on a vintage sander transmits ½ hp to a pulley that has a diameter of d = 4 in. Knowing that the pulley rotates at 1450 rpm, determine the tension difference T1 − T2 between the
- If h = 700 mm and d = 500 mm and each spring has a constant k = 600 N/m, determine the mass m for which the period of small oscillations is (a) 0.50 s, (b) Infinite. Neglect the mass of the rod and
- A square plate of mass m is held by eight springs, each of constant k. Knowing that each spring can act in either tension or compression, determine the frequency of the resulting vibration if (a)
- A belt is placed around the rim of a 500-lb flywheel and attached as shown to two springs, each of constant k = 85 lb/in. If end C of the belt is pulled 1.5 in. down and released, the period of
- A uniform disk of radius r = 250 mm is attached at A to a 650-mm rod AB of negligible mass that can rotate freely in a vertical plane about B. Determine the period of small oscillations (a) If the
- A small collar of mass 1 kg is rigidly attached to a 3-kg uniform rod of length L = 750 mm. Determine (a) The distance d to maximize the frequency of oscillation when the rod is given a small
- A three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a
- Disk A, of weight 5 lb and radius r = 3 in., is at rest when it is placed in contact with a belt that moves at a constant speed v = 50 ft/s. Knowing that μk = 0.20 between the disk and the belt,
- A uniform disk of radius r = 250 mm is attached at A to a 650-mm rod AB of negligible mass that can rotate freely in a vertical plane about B. If the rod is displaced 2° from the position shown and
- A 6-lb slender rod is suspended from a steel wire that is known to have a torsional spring constant K = 1.5 ft·lb/rad. If the rod is rotated through 180° about the vertical and released,
- Two uniform rods, each of weight W = 24 lb and length L = 40 in., are welded together to form the assembly shown. Knowing that the constant of each spring is k = 50 lb/ft and that end A is given a
- The 8-kg uniform bar AB is hinged at C and is attached at A to a spring of constant k = 500 N/m. If end A is given a small displacement and released, determine (a) The frequency of small
- The rotor of an electric motor has a mass of 25 kg, and it is observed that 4.2 min is required for the rotor to coast to rest from an angular velocity of 3600 rpm. Knowing that kinetic friction
- A homogeneous rod of mass per unit length equal to 0.4 kg/m is used to form the assembly shown, which rotates freely about pivot A in a vertical plane. Knowing that the assembly is displaced 2°
- Three shafts and four gears are used to form a gear train that will transmit 7.5 kW from the motor at A to a machine tool at F. (Bearings for the shafts are omitted from the sketch.) Knowing that the
- A uniform disk of radius r = 120 mm is welded at its center to two elastic rods of equal length with fixed ends at A and B. Knowing that the disk rotates through an 8° angle when a 500-mN·m couple
- A horizontal platform P is held by several rigid bars that are connected to a vertical wire. The period of oscillation of the platform is found to be 2.2 s when the platform is empty and 3.8 s when
- A 60-kg uniform circular plate is welded to two elastic rods, which have fixed ends at supports A and B as shown. The torsional spring constant of each rod is 200 N·m/rad, and the system is in
- The 2.75-lb bob of a simple pendulum of length l = 24 in. is suspended from a 3-lb collar C. The collar is forced to move according to the relation xC = δm sin ωf t, with an amplitude δm = 0.4
- An 800-g rod AB is bolted to a 1.2-kg disk. A spring of constant k = 12 N/m is attached to the center of the disk at A and to the wall at C. Knowing that the disk rolls without sliding, determine the
- A uniform rod of length L is supported by a ball-and-socket joint at A and by a vertical wire CD. Derive an expression for the period of oscillation of the rod if end B is given a small horizontal
- The crude-oil pumping rig shown is driven at 20 rpm. The inside diameter of the well pipe is 2 in., and the diameter of the pump rod is 0.75 in. The length of the pump rod and the length of the
- A 15-lb uniform cylinder can roll without sliding on an incline and is attached to a spring AB as shown. If the center of the cylinder is moved 0.4 in. down the incline and released, determine (a)
- Two 12-lb uniform disks are attached to the 20-lb rod AB as shown. Knowing that the constant of the spring is 30 lb/in. and that the disks roll without sliding, determine the frequency of vibration
- A 10-lb uniform rod CD is welded at C to a shaft of negligible mass that is welded to the centers of two 20-lb uniform disks A and B. Knowing that the disks roll without sliding, determine the period
- The motion of the uniform rod AB is guided by the cord BC and by the small roller at A. Determine the frequency of oscillation when the end B of the rod is given a small horizontal displacement and
- A 3-kg slender rod AB is bolted to a 5-kg uniform disk. A spring of constant 280 N/m is attached to the disk and is unstretched in the position shown. If end B of the rod is given a small
- The inner rim of an 85-lb flywheel is placed on a knife edge, and the period of its small oscillations is found to be 1.26 s. Determine the centroidal moment of inertia of the flywheel. Fig.
- A period of 6.00 s is observed for the angular oscillations of a 4-oz gyroscope rotor suspended from a wire as shown. Knowing that a period of 3.80 s is obtained when a 1.25-in.-diameter steel sphere
- A thin uniform plate cut into the shape of a quarter circle can rotate in a vertical plane about a horizontal axis at point O. Determine the period of the small oscillations of the plate. I G! Fig. P
- Determine the period of small oscillations of a small particle that moves without friction inside a cylindrical surface of radius R. R Fig. P19.72
- Blade AB of the experimental wind-turbine generator shown is to be temporarily removed. Motion of the turbine generator about the y axis is prevented, but the remaining three blades may oscillate as
- The unbalance of the rotor of a 400-lb motor is equivalent to a 3-oz weight located 6 in. from the axis of rotation. In order to limit to 0.2 lb the amplitude of the fluctuating force exerted on the
- A motor weighing 400 lb is supported by springs having a total constant of 1200 lb/in. The unbalance of the rotor is equivalent to a 1-oz weight located 8 in. from the axis of rotation. Determine the
- A 180-kg motor is bolted to a light horizontal beam. The unbalance of its rotor is equivalent to a 28-g mass located 150 mm from the axis of rotation, and the static deflection of the beam due to the
- A motor of weight 100 lb is supported by four springs, each of constant 250 lb/in. The motor is constrained to move vertically, and the amplitude of its motion is observed to be 0.04 in. at a speed
- An 18-lb block A slides in a vertical frictionless slot and is connected to a moving support B by means of a spring AB of constant k = 8 lb/ft. Knowing that the acceleration of the support is a = am
- One of the tail rotor blades of a helicopter has an unbalanced weight of 1 lb at a distance of e = 6 in. from the axis of rotation. The fuselage can be considered to be fixed, and the tail rotor and
- A counter-rotating eccentric mass exciter consisting of two rotating 100-g masses describing circles of radius r at the same speed but in opposite senses is placed on a machine element to induce a
- Gear A has a mass of 1 kg and a radius of gyration of 30 mm; gear B has a mass of 4 kg and a radius of gyration of 75 mm; gear C has a mass of 9 kg and a radius of gyration of 100 mm. The system is
- The 15-kg rear hatch of a vehicle opens as shown and can be modeled as a uniform 0.6-m long slender rod. Knowing that the tailgate is released from rest in the position shown, determine the angular
- A force P with a magnitude of 3 N is applied to a tape wrapped around the body indicated. Knowing that the body rests on a frictionless horizontal surface, determine the acceleration of (a) Point
- A 2000-kg truck is being used to lift a 400-kg boulder B that is on a 50-kg pallet A. Knowing the acceleration of the rear-wheel-drive truck is 1 m/s2, determine (a) The reaction at each of the
- The coefficients of friction between the 30-lb block and the 5-lb platform BD are μs = 0.50 and μk = 0.40. Determine the accelerations of the block and of the platform immediately after wire AB has
- A 40-kg vase has a 200-mm-diameter base and is being moved using a 100-kg utility cart as shown. The cart moves freely (μ = 0) on the ground. Knowing the coefficient of static friction between the
- The 10-in.-radius brake drum is attached to a larger flywheel that is not shown. The total mass moment of inertia of the drum and the flywheel about point C is 15 lb·ft·s2, and the coefficient of
- A belt of negligible mass passes between cylinders A and B and is pulled to the right with a force P. Cylinders A and B weigh, respectively, 5 and 20 lb. The shaft of cylinder A is free to slide in a
- Members ACE and DCB are each 600 mm long and are connected by a pin at C. The mass center of the 10-kg member AB is located at G. Determine(a) The acceleration of AB immediately after the system has
- A uniform rod BC of mass 4 kg is connected to a collar A by a 250-mm cord AB. Neglecting the mass of the collar and cord, determine (a) The smallest constant acceleration aA for which the cord and
- Disk A has a mass of 6 kg and an initial angular velocity of 360 rpm clockwise; disk B has a mass of 3 kg and is initially at rest. The disks are brought together by applying a horizontal force of
- A completely filled barrel and its contents have a combined mass of 90 kg and a center of mass at G. A cylinder C with a mass of 200 kg is connected to the barrel as shown. Knowing μs = 0.40 and μk
- A 60-lb uniform thin panel is placed in a truck with end A resting on a rough horizontal surface and end B supported by a smooth vertical surface. Knowing that the deceleration of the truck is 12
- The retractable shelf shown is supported by two identical linkage-andspring systems; only one of the systems is shown. A 20-kg machine is placed on the shelf so that half of its weight is supported
- A 60-lb uniform thin panel is placed in a truck with end A resting on a rough horizontal surface and end B supported by a smooth vertical surface. Knowing that the panel remains in the position
- Gear A weighs 1 lb and has a radius of gyration of 1.3 in.; gear B weighs 6 lb and has a radius of gyration of 3 in.; gear C weighs 9 lb and has a radius of gyration of 4.3 in. Knowing a couple M of
- The support bracket shown is used to transport a cylindrical can from one elevation to another. Knowing that μs = 0.25 between the can and the bracket, determine (a) The magnitude of the upward
- Three bars, each of mass 3 kg, are welded together and pin-connected to two links BE and CF. Neglecting the weight of the links, determine the force in each link immediately after the system is
- Bars AB and BE, each with a mass of 4 kg, are welded together and are pin-connected to two links AC and BD. Knowing that the assembly is released from rest in the position shown and neglecting the
- A prototype rotating bicycle rack is designed to save space at a train station. The combined weight of platform BD and the bicycle is 40 lb and is centered at 1 ft above the midpoint of the platform.
- The control rod AC is guided by two pins that slide freely in parallel curved slots of radius 200 mm. The rod has a mass of 10 kg, and its mass center is located at point G. Knowing that for the
- Each of the double pulleys shown has a mass moment of inertia of 15 lb·ft·s2 and is initially at rest. The outside radius is 18 in., and the inner radius is 9 in. Determine (a) The angular
- In order to determine the mass moment of inertia of a flywheel of radius 600 mm, a 12-kg block is attached to a wire that is wrapped around the flywheel. The block is released and is observed to fall
- The 180-mm-radius disk is at rest when it is placed in contact with a belt moving at a constant speed. Neglecting the weight of the link AB and knowing that the coefficient of kinetic friction
- The 25-lb double pulley shown is at rest and in equilibrium when a constant 3.5-lb·ft couple M is applied. Neglecting the effect of friction and knowing that the radius of gyration of the double
- Two uniform cylinders, each of weight W = 14 lb and radius r = 5 in., are connected by a belt as shown. If the system is released from rest, determine (a) The angular acceleration of each
- The 10-in.-radius brake drum is attached to a larger flywheel that is not shown. The coefficient of kinetic friction between the drum and the brake shoe is 0.35 and the angular velocity of the
- Disk A has a mass mA = 4 kg, a radius rA = 300 mm, and an initial angular velocity ω0 = 300 rpm clockwise. Disk B has a mass mB = 1.6 kg, a radius rB = 180 mm, and is at rest when it is brought into
- The flywheel shown has a radius of 20 in., a weight of 250 lb, and a radius of gyration of 15 in. A 30-lb block A is attached to a wire that is wrapped around the flywheel, and the system is released
- A rectangular plate of mass 5 kg is suspended from four vertical wires, and a force P of magnitude 6 N is applied to corner C as shown. Immediately after P is applied, determine the acceleration