17-1. Determine the moment of inertia /v for the slender

FI7-1. The cart and its load have a total mass of 100 kg. Determine the acceleration of the cart and the normal reactions on the pair of wheels at A and B. Neglect the mass of the wheels.

FI7-2. If the 80-kg cabinet is allowed to roll down the inclined plane, determine the acceleration of the cabinet and the normal reactions on the pair of rollers at A and B that have negligible mass.

The 20-lb link AB is pinned to a moving frame at A and held in a vertical position by means of a string BC which can support a maximum tension of 10 lb. Determine the maximum acceleration of the frame without breaking the string. What are the corresponding components of reaction at the pin A?

FI7-4. Determine the maximum acceleration of the truck without causing the assembly to move relative to the truck. Also what is the corresponding normal reaction on legs A and B? The 100-kg table has a mass center at G and the coefficient of static friction between the legs of the table and the bed of the truck is /xv = 0.2.

F17-5. At the instant shown both rods of negligible mass swing with a counterclockwise angular velocity of (i) = 5 rad/s, while the 50-kg bar is subjected to the 100-N horizontal force. Determine the tension developed in the rods and the angular acceleration of the rods at this instant.

At the instant shown, the link CD rotates with an angular velocity of \(\omega=6\mathrm{\ rad}/\mathrm{s}\). If it is subjected to a couple moments \(M=450\mathrm{\ N}\cdot\mathrm{m}\). determine the force developed in link AB. the horizontal and vertical component of reaction on pin D, and the angular acceleration of link CD at this instant. The block has a mass of 50 kg and center of mass at G. Neglect the mass of links AB and CD.

FI7-7. The 100-kg wheel has a radius of gyration about its center O of kQ = 500 mm. If the wheel starts from rest, determine its angular velocity in / = 3 s.

FI7-8. The 50-kg disk is subjected to the couple moment of M = (9/) N-m, where / is in seconds. Determine the angular velocity of the disk when / = 4 s starting from rest.

F17-9. At the instant shown, the uniform 30-kg slender rod has a counterclockwise angular velocity of id = 6 rad/s. Determine the tangential and normal components of reaction of pin O on the rod and the angular acceleration of the rod at this instant.

At the instant shown, the 30-kg disk has a counterclockwise angular velocity of \(\omega=10 \mathrm{\ rad} / \mathrm{s}\). Determine the tangential and normal components of reaction of the pin O on the disk and the angular acceleration of the disk at this instant.

FI7-11. The uniform slender rod has a mass of 15 kg. Determine the horizontal and vertical components of reaction at the pin O, and the angular acceleration of the rod just after the cord is cut.

FI7-12. The uniform 30-kg slender rod is being pulled by the cord that passes over the small smooth peg at A. If the rod has a counterclockwise angular velocity of to = 6 rad/s at the instant shown, determine the tangential and normal components of reaction at the pin O and the angular acceleration of the rod.

F17-13. The uniform 60-kg slender bar is initially at rest on a smooth horizontal plane when the forces are applied. Determine the acceleration of the bars mass center and the angular acceleration of the bar at this instant.

FI7-14. The 100-kg cylinder rolls without slipping on the horizontal plane. Determine the acceleration of its mass center and its angular acceleration.

F17-15. The 20-kg wheel has a radius of gyration about its center O of k() = 300 mm. When the wheel is subjected to the couple moment, it slips as it rolls. Determine the angular acceleration of the wheel and the acceleration of the wheels center O. The coefficient of kinetic friction between the wheel and the plane is fik = 0.5.

FI7-16. The 20-kg sphere rolls down the inclined plane without slipping. Determine the angular acceleration of the sphere and the acceleration of its mass center.

FI7-17. The 200-kg spool has a radius of gyration about its mass center of kG = 300 mm. If the couple moment is applied to the spool and the coefficient of kinetic friction between the spool and the ground is fik = 0.2, determine the angular acceleration of the spool, the acceleration of G and the tension in the cable.

FI 7-18. The 12-kg slender rod is pinned to a small roller A that slides freely along the slot. If the rod is released from rest at 0 = 0. determine the angular acceleration of the rod and the acceleration of the roller immediately after the release.

17-1. Determine the moment of inertia /v for the slender rod. The rod's density p and cross-sectional area A are constant. Express the result in terms of the rods total mass m.

17-2. The solid cylinder has an outer radius R, height h. and is made from a material having a density that varies from its center as p = k + ar2, where k and a are constants. Determine the mass of the cylinder and its moment of inertia about the z axis.

17-3. Determine the moment of inertia of the thin ring about the z axis. The ring has a mass m.

*17-4. Determine the moment of inertia of the semiellipsoid with respect to the x axis and express the result in terms of the mass m of the semiellipsoid. The material has a constant density p.

17-5. The sphere is formed by revolving the shaded area around the x axis. Determine the moment of inertia /, and express the result in terms of the total mass m of the sphere.

17-6. Determine the mass moment of inertia /, of the cone formed by revolving the shaded area around the z axis.The total density of the material is p. Express the result in terms of the mass m of the cone.

17-7. The solid is formed by revolving the shaded area around the y axis. Determine the radius of gyration kr The specific weight of the material is y = 380 lb/ft3. The material has a constant density p.

*17-8. The concrete shape is formed by rotating the shaded area about the y axis. Determine the moment of inertia /v. The specific weight of concrete is y = 150 lb/ft3.

17-9. Determine the moment of inertia /- of the torus.The mass of the torus is m and the density p is constant.

17-10. Determine the mass moment of inertia of the pendulum about an axis perpendicular to the page and passing through point O. The slender rod has a mass of 10 kg and the sphere has a mass of 15 kg.

17-11. The slender rods have a weight of 3 Ib/ft. Determine the moment of inertia of the assembly about an axis Suggestion: Use a shell element. perpendicular to the page and passing through the pin at A.

Determine the moment of inertia of the solid steel assembly about the x axis. Steel has a specific weight of \(\gamma_{s t}=490 \mathrm{\ lb} / \mathrm{ft}^{3}\).

The wheel consists of a thin ring having a mass of 10 kg and four spokes made from slender rods and each having a mass of 2 kg. Determine the wheel's moment of inertia about an axis perpendicular to the page and passing through point A.

If the large ring, small ring and each of the spokes weigh 100 lb. 15 lb. and 20 lb. respectively, determine the mass moment of inertia of the wheel about an axis perpendicular to the page and passing through point A.

17-15. Determine the moment of inertia about an axis perpendicular to the page and passing through the pin at 0. The thin plate has a hole in its center. Its thickness is 50 mm, and the material has a density p = 50 kg/m3.

*17-16. Determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O. The material has a mass per unit area of 20 kg/m2.

17-17. The assembly consists of a disk having a mass of 6 kg and slender rods AB and DC which have a mass of 2 kg/m. Determine the length L of DC so that the center of mass is at the bearing O. What is the moment of inertia of the assembly about an axis perpendicular to the page and passing through 0?

17-18. The assembly consists of a disk having a mass of 6 kg and slender rods AB and DC which have a mass of 2 kg/m. If L = 0.75 m. determine the moment of inertia of the assembly about an axis perpendicular to the page and passing through O.

17-19. The pendulum consists of two slender rods AB and OC which have a mass of 3 kg/m.The thin circular plate has a mass of 12 kg/nr. Determine the location v of the center of mass G of the pendulum, then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G.

*17-20. The pendulum consists of two slender rods AB and OC which have a mass of 3 kg/m. The thin circular plate has a mass of I2kg/'m2. Determine the moment of inertia of the pendulum about an axis perpendicular to the page and passing through the pin at O.

17-21. The pendulum consists of the 3-kg slender rod and the 5-kg thin plate. Determine the location v of the center of mass G of the pendulum: then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G.

*17-22. Determine the moment of inertia of the overhung crank about the x axis.The material is steel having a destiny of fj 7.85 Mg/m\

17-23. Determine the moment of inertia of the overhung crank about the ,v' axis.The material is steel having a destiny of p = 7.85 Mg/m3.

17-24. The door has a weight of 200 lb and a center of gravity at G. Determine how far the door moves in 2 s. starting from rest, if a man pushes on it at C with a horizontal force F = 30 lb. Also, find the vertical reactions at the rollers A and B.

17-25. The door has a weight of 200 lb and a center of gravity at G. Determine the constant force F that must be applied to the door to push it open 12 ft to the right in 5 s, starting from rest. Also, find the vertical reactions at the rollers A and B.

17-26. The uniform pipe has a weight of 500 lb/ft and diameter of 2 ft. If it is hoisted as shown with an acceleration of 0.5 ft/s2. determine the internal moment at the center A of the pipe due to the lift.

17-27. The drum truck supports the 600-lb drum that has a center of gravity at G. If the operator pushes it forward with a horizontal force of 20 lb. determine the acceleration of the truck and the normal reactions at each of the four wheels. Neglect the mass of the wheels.

*17-28. If the cart is given a constant acceleration of a = 6 ft/s2 up the inclined plane, determine the force developed in rod AC and the horizontal and vertical components of force at pin B.The crate has a weight of 150 lb with center of gravity at G. and it is secured on the platform, so that it does not slide. Neglect the platforms weight.

If the strut AC can withstand a maximum compression force of 150 lb before it fails, determine the cart's maximum permissible acceleration. The crate has a weight of 150 lb with center of gravity at G, and it is secured on the platform, so that it does not slide. Neglect the platform's weight.

The drop gate at the end of the trailer has a mass of \(1.25 \mathrm{Mg}\) and mass center at G. If it is supported by the cable AB and hinge at C, determine the tension in the cable when the truck begins to accelerate at \(5 \mathrm{~m} / \mathrm{s}^2\). Also, what are the horizontal and vertical components of reaction at the hinge C?

17-31. The pipe has a length of 3 m and a mass of 500 kg. It is attached to the back of the truck using a 0.6-m-long chain AB. If the coefficient of kinetic friction at C is ixk 0.4, determine the acceleration of the truck if the angle 0 = 10 with the road as shown.

*17-32. The mountain bike has a mass of 40 kg with center of mass at point G\, while the rider has a mass of 60 kg with center of mass at point G2. Determine the maximum deceleration when the brake is applied to the front wheel, without causing the rear wheel B to leave the road. Assume that the front wheel does not slip. Neglect the mass of all the wheels.

17-33. The mountain bike has a mass of 40 kg with center of mass at point Gj, while the rider has a mass of 60 kg with center of mass at point G2. When the brake is applied to the front wheel, it causes the bike to decelerate at a constant rate of 3 m/s2. Determine the normal reaction the road exerts on the front and rear wheels. Assume that the rear wheel is free to roll. Neglect the mass of all the wheels.

17-34. The trailer with its load has a mass of 150 kg and a center of mass at G. If it is subjected to a horizontal force of P = 600 N. determine the trailers acceleration and the normal force on the pair of wheels at A and at /TThe wheels are free to roll and have negligible mass.

17-35. At the start of a race, the rear drive wheels B of the 1550-lb car slip on the track. Determine the car's acceleration and the normal reaction the track exerts on the front pair of wheels A and rear pair of wheels B. The coefficient of kinetic friction is = 0.7. and the mass center of the car is at G. The front wheels are free to roll. Neglect the mass of all the wheels.

*17-36. Determine the maximum acceleration that can be achieved by the car without having the front wheels A leave the track or the rear drive wheels B slip on the track. The coefficient of static friction is /ll, = 0.9. The car's mass center is at G. and the front wheels are free to roll. Neglect the mass of all the wheels.

17-37. If the 4500-lb van has front-wheel drive, and the coefficient of static friction between the front wheels A and the road is /xv = 0.8, determine the normal reactions on the pairs of front and rear wheels when the van has maximum acceleration. Also, find this maximum acceleration.The rear wheels arc free to roll. Neglect the mass of the wheels.

17-38. If the 4500-lb van has rear-wheel drive, and the coefficient of static friction between the front wheels B and the road is ^ = 0.8. determine the normal reactions on the pairs of front and rear wheels when the van has maximum acceleration. The front wheels are free to roll. Neglect the mass of the wheels.

17-39. The uniform bar of mass m is pin connected to the collar, which slides along the smooth horizontal rod. If the collar is given a constant acceleration of a. determine the bar's inclination angle 0. Neglect the collar's mass.

*17-40. The lift truck has a mass of 70 kg and mass center at G. If it lifts the 120-kg spool with an acceleration of 3 m/s2. determine the reactions of each of the four wheels on the ground. The loading is symmetric. Neglect the mass of the movable arm CD.

17-41. The lift truck has a mass of 70 kg and mass center at G. Determine the largest upward acceleration of the 120-kg spool so that no reaction of the wheels on the ground exceeds 600 N.

17-42. The uniform crate has a mass of 50 kg and rests on the cart having an inclined surface. Determine the smallest acceleration that will cause the crate either to tip or slip relative to the cart. What is the magnitude of this acceleration? The coefficient of static friction between the crate and the cart is fis = 0.5.

17-43. Determine the acceleration of the 150-lb cabinet and the normal reaction under the legs A and B if B = 35 lb. The coefficients of static and kinetic friction between the cabinet and the plane are ^ = 0.2 and = 0.15. respectively. The cabinets center of gravity is located at G.

*17-44. The assembly has a mass of 8 Mg and is hoisted using the boom and pulley system. If the winch at B draws in the cable with an acceleration of 2 m/s2. determine the compressive force in the hydraulic cylinder needed to support the boom. The boom has a mass of 2 Mg and mass center at G.

17-45. The 2-Mg truck achieves a speed of 15 m/s with a constant acceleration after it has traveled a distance of 100 m. starting from rest. Determine the normal force exerted on each pair of front wheels B and rear driving wheels A. Also, find the traction force on the pair of wheels at ,4.The front wheels are free to roll. Neglect the mass of the wheels.

17-46. Determine the shortest time possible for the rear-wheel drive. 2-Mg truck to achieve a speed of 16 m/s with a constant acceleration starting from rest. The coefficient of static friction between the wheels and the road surface is fis = 0.8.The front wheels arc free to roll. Neglect the mass of the wheels.

17-47. Tlie snowmobile has a weight of 250 lb. centered at G|, while the rider has a weight of 150 lb. centered at G2. If the acceleration is a = 20 ft/s2, determine the maximum height h of G2 of the rider so that the snowmobiles front skid does not lift off the ground. Also, what are the traction (horizontal) force and normal reaction under the rear tracks at A?

*17-48. The snowmobile has a weight of 250 lb, centered at G|. while the rider has a weight of 150 lb. centered at G2. If h = 3 ft, determine the snowmobiles maximum permissible acceleration a so that its front skid does not lift off the ground. Also, find the traction (horizontal) force and the normal reaction under the rear tracks at A.

17-49. If the carts mass is 30 kg and it is subjected to a horizontal force of P = 90 N. determine the tension in cord A B and the horizontal and vertical components of reaction on end C of the uniform 15-kg rod BC.

If the cart's mass is \(30 \mathrm{~kg}\), determine the horizontal force P that should be applied to the cart so that the cord AB just becomes slack. The uniform rod BC has a mass of \(15 \mathrm{~kg}\).

17-51. The pipe has a mass of 800 kg and is being towed behind the truck. If the acceleration of the truck is cij = 0.5 m/s2. determine the angle 0 and the tension in the cable. The coefficient of kinetic friction between the pipe and the ground is fik = 0.1.

*17-52. The pipe has a mass of 800 kg and is being towed behind a truck. If the angle 0 = 30, determine the acceleration of the truck and the tension in the cable. The coefficient of kinetic friction between the pipe and the ground is fxk = 0.1.

17-53. The arched pipe has a mass of 80 kg and rests on the surface of the platform. As it is hoisted from one level to the next, a = 0.25 rad/s2 and to = 0.5 rad/s at the instant 0 = 30. If it does not slip, determine the normal reactions of the arch on the platform at this instant.

17-54. The arched pipe has a mass of 80 kg and rests on the surface of the platform for which the coefficient of static friction is /x% = 0.3. Determine the greatest angular acceleration o- of the platform, starting from rest when 0 = 45, without causing the pipe to slip on the platform.

17-55. At the instant shown, link CD rotates with an angular velocity of (oCD = 8 rad/s. If link CD is subjected to a couple moment of M = 650 lb-ft, determine the force developed in link AB and the angular acceleration of the links at this instant. Neglect the weight of the links and the platform. The crate weighs 150 lb and is fully secured on the platform.

*17-56. Determine the force developed in the links and the acceleration of the bar's mass center immediately after the cord fails. Neglect the mass of links AB and CD. The uniform bar has a mass of 20 kg.

The \(10-\mathrm{kg}\) wheel has a radius of gyration \(k_A=200 \mathrm{~mm}\). If the wheel is subjected to a moment \)M=(5 t) \mathrm{N} \cdot \mathrm{m}\), where t is in seconds, determine its angular velocity when \(t=3 \mathrm{~s}\) starting from rest. Also, compute the reactions which the fixed pin A exerts on the wheel during the motion.

The 80-kg disk is supported by a pin at A. If it is released from rest from the position shown, determine the initial horizontal and vertical components of reaction at the pin.

17-59. The uniform slender rod has a mass m. If it is released from rest when 0 = 0. determine the magnitude of the reactive force exerted on it by pin B when 0 = 90.

The drum has a weight of \(80 \mathrm{lb}\) and a radius of gyration \(k_O=0.4 \mathrm{ft}\). If the cable, which is wrapped around the drum, is subjected to a vertical force \(P=15 \mathrm{lb}\), determine the time needed to increase the drum's angular velocity from \(\omega_1=5 \mathrm{rad} / \mathrm{s}\) to \(\omega_2=25 \mathrm{rad} / \mathrm{s}\). Neglect the mass of the cable.

17-61. Cable is unwound from a spool supported on small rollers at A and B by exerting a force of T = 300 N on the cable in the direction shown. Compute the time needed to unravel 5 m of cable from the spool if the spool and cable have a total mass of 600 kg and a centroidal radius of gyration of k() = 1.2 m. For the calculation, neglect the mass of the cable being unwound and the mass of the rollers at A and B. The rollers turn with no friction.

17-62. The 10-lb bar is pinned at its center O and connected to a torsional spring. The spring has a stiffness k = 5 lb ft/rad, so that the torque developed is M = (50) lb ft. where 0 is in radians. If the bar is released from rest when it is vertical at 0 = 90, determine its angular velocity at the instant 0 = 0.

The 10-lb bar is pinned at its center O and connected to a torsional spring. The spring has a stiffness \(k=5 \mathrm{lb} \cdot \mathrm{ft} / \mathrm{rad}\), so that the torque developed is \(M=(5 \theta) \mathrm{lb} \cdot \mathrm{ft}\), where \(\theta\) is in radians. If the bar is released from rest when it is vertical at \(\theta=90^{\circ}\), determine its angular velocity at the instant \(\theta=45^{\circ}\).

17-64. If shaft BC is subjected to a torque of M=(0A5t\/2) N m. where t is in seconds, determine the angular velocity of the 3-kg rod AB when / = 4 s, starting from rest. Neglect the mass of shaft BC.

17-65. Determine the vertical and horizontal components of reaction at the pin support A and the angular acceleration of the 12-kg rod at the instant shown, when the rod has an angular velocity of w = 5 rad/s.

17-66. The kinetic diagram representing the general rotational motion of a rigid body about a fixed axis passing through O is shown in the figure. Show that lGa may be eliminated by moving the vectors m(aG), and nt(aG)n to point P. located a distance rGP = \cGjrOG from the center of mass G of the body. Here kG represents the radius of gyration of the body about an axis passing through G. The point P is called the center of percussion of the body.

17-67. Determine the position rP of the center of percussion P of the 10-lb slender bar. (See Prob. 17-66.) What is the horizontal component of force that the pin at A exerts on the bar when it is struck at P with a force of F = 20 lb?

*17-68. The disk has a mass M and a radius R. If a block of mass m is attached to the cord, determine the angular acceleration of the disk when the block is released from rest. Also, what is the velocity of the block after it falls a distance 2R starting from rest?

17-69. The door will close automatically using torsional springs mounted on the hinges. Each spring has a stiffness A: = 50 N-m/rad so that the torque on each hinge is M = (500) N m, where 0 is measured in radians. If the door is released from rest when it is open at 0 = 90, determine its angular velocity at the instant 0 = 0. For the calculation, treat the door as a thin plate having a mass of 70 kg.

17-70. The door will close automatically using torsional springs mounted on the hinges. If the torque on each hinge is M = kO. where 0 is measured in radians, determine the required torsional stiffness k so that the door will close (0 = 0) with an angular velocity oj = 2 rad/s when it is released from rest at 0 = 90. For the calculation, treat the door as a thin plate having a mass of 70 kg.

The pendulum consists of a \(10-\mathrm{kg}\) uniform slender rod and a \(15-\mathrm{kg}\) sphere. If the pendulum is subjected to a torque of \(M=50 \mathrm{~N} \cdot \mathrm{m}\), and has an angular velocity of \(3 \mathrm{rad} / \mathrm{s}\) when \(\theta=45^{\circ}\), determine the magnitude of the reactive force pin O exerts on the pendulum at this instant.

The disk has a mass of 20 kg and is originally spinning at the end of the strut with an angular velocity of \(\omega=60 \mathrm{\ rad} / \mathrm{s}\). If it is then placed against the wall, for which the coefficient of kinetic friction is \(\mu_{k}=0.3\) determine the time required for the motion to stop. What is the force in strut BC during this time?

17-73. The slender rod of length L and mass m is released from rest when f) = 0. Determine as a function of 0 the normal and the frictional forces which are exerted by the ledge on the rod at A as it falls downward. At what angle 0 does the rod begin to slip if the coefficient of static friction at A is /i?

17-74. Tie 5-kg cylinder is initially at rest when it is placed in contact with the wall B and the rotor at A. If the rotor always maintains a constant clockwise angular velocity oj = 6 rad/s. determine the initial angular acceleration of the cylinder. The coefficient of kinetic friction at the contacting surfaces B and C is fxk = 0.2.

The wheel has a mass of 25 kg and a radius of gyration \(k_{B}=0.15 \mathrm{\ m}\). It is originally spinning at \(\omega_{1}=40 \ \mathrm{rad} / \mathrm{s}\). If it is placed on the ground, for which the coefficient of kinetic friction is \(\mu_{C}=0.5\), determine the time required for the motion to stop. What are the horizontal and vertical components of reaction which the pin at A exerts on AB during this time? Neglect the mass of AB.

17-76. A 40-kg boy sits on top of the large wheel which has a mass of 400 kg and a radius of gyration kG = 5.5 in. If the boy essentially starts from rest at 0 = 0, and the wheel begins to rotate freely, determine the angle at which the boy begins to slip. The coefficient of static friction between the wheel and the boy is /x = 0.5. Neglect the size of the boy in the calculation.

17-77. Gears A and B have a mass of 50 kg and 15 kg, respectively. Their radii of gyration about their respective centers of mass are kc = 250 mm and kD = 150 mm. If a torque of M = 200( 1 - e~lUl) N m. where / is in seconds, is applied to gear A. determine the angular velocity of both gears when / = 3 s. starting from rest.

17-78. Block A has a mass m and rests on a surface having a coefficient of kinetic friction //*. 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 released, determine the acceleration of A. Assume that the cord docs not slip over the pulley. The pulley can be approximated as a thin disk of radius r and mass^m. Neglect the mass of the cord.

17-79. The two blocks A and B have a mass of 5 kg and 10 kg. respectively. If the pulley can be treated as a disk of mass 3 kg and radius 0.15 m. determine the acceleration of block A. Neglect the mass of the cord and any slipping on the pulley.

*17-80. The two blocks A and B have a mass mA and m#. 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 any slipping on the pulley.

Determine the angular acceleration of the 25-kg diving board and the horizontal and vertical components of reaction at the pin A the instant the man jumps off. Assume that the board is uniform and rigid, and that at the instant he jumps off the spring is compressed a maximum amount of 200 mm. \(\omega=0\), and the board is horizontal. Take k = 7 kN/m.

17-82. The lightweight turbine consists of a rotor which is powered from a torque applied at its center. At the instant the rotor is horizontal it has an angular velocity of 15 rad/s and a clockwise angular acceleration of 8 rad/s2. Determine the internal normal force, shear force, and moment at a section through A. Assume the rotor is a 50-m-long slender rod. having a mass of 3 kg/rn.

17-83. 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 a mass m and length /.

*17-84. The armature (slender rod) AB has a mass of 0.2 kg and can pivot about the pin at A. Movement is controlled by the electromagnet E. which exerts a horizontal attractive force on the armature at B of FB = (0.2( 10N, where / in meters is the gap between the armature and the magnet at any instant. If the armature lies in the horizontal plane, and is originally at rest, determine the speed of the contact at B the instant / = 0.01 m. Originally / = 0.02 m.

17-85. The bar has a weight per length of w. If it is rotating in the vertical plane at a constant rate to about point O, determine the internal normal force, shear force, and moment as a function of .v and 0.

1786. A force F = 2 lb is applied perpendicular to the axis of the 5-lb rod and moves from O to A at a constant rate of 4 ft/s. If the rod is at rest when 0 = 0 and F is at O when / = 0, determine the rod's angular velocity at the instant the force is at A.Through what angle has the rod rotated when this occurs? The rod rotates in the horizontal plane.

17-87. The 15-kg block A and 20-kg cylinder B are connected by a light cord that passes over a 5-kg pulley (disk). If the system is released from rest, determine the cylinders velocity after its has traveled downwards 2 m. Neglect friction between the plane and the block, and assume the cord does not slip over the pulley.

*17-88. The 15-kg block A and 20-kg cylinder B are connected by a light cord that passes over a 5-kg pulley (disk). If the system is released from rest, determine the cylinders velocity after its has traveled downwards 2 m.The coefficient of kinetic friction between the block and the horizontal plane is pk = 0.3. Assume the cord does not slip over the pulley.

17-89. The Catherine wheel" is a firework that consists of a coiled tube of powder which is pinned at its center. If the powder burns at a constant rate of 20 g/s such as that the exhaust gases always exert a force having a constant magnitude of 0.3 N,directed tangent to the wheel, determine the angular velocity of the wheel when 75% of the mass is burned off. Initially, the wheel is at rest and has a mass of lOOgand a radius of r=75 mm. For the calculation, consider the wheel to always be a thin disk.

17-90. If the disk in Fig. 17-20 rolls w ithout slipping, show that when moments are summed about the instantaneous center of zero velocity, fC. it is possible to use the moment equation = I/C a. where IIC represents the moment of inertia of the disk calculated about the instantaneous axis of zero velocity.

The 20-kg punching bag has a radius of gyration about its center of mass G of \(k_{G}=0.4 \mathrm{\ m}\). If it is initially at rest and is subjected to a horizontal force F = 30 N, determine the initial angular acceleration of the bag and the tension in the supporting cable AB.

17-92. The uniform 150-lb beam is initially at rest when the forces are applied to the cables. Determine the magnitude of the acceleration of the mass center and the angular acceleration of the beam at this instant.

17-93. The rocket has a weight of 20 000 lb. mass center at G. and radius of gyration about the mass center of kG = 21 ft when it is fired. Each of its two engines provides a thrust T = 50 000 lb. At a given instant engine A suddenly fails to operate. Determine the angular acceleration of the rocket and the acceleration of its nose B.

17-94. The tire has a weight of 30 lb and a radius of gyration of kCl = 0.6 ft. Tf the coefficients of static and kinetic friction between the tire and the plane are ps = 0.2 and pk = 0.15. determine the tires angular acceleration as it rolls down the incline. Set 0 = 12.

17-95. The tire has a weight of 30 lb and a radius of gyration of kG = 0.6 ft. If the coefficients of static and kinetic friction between the tire and the plane are p, 0.2 and pk = 0.15, determine the maximum angle 0 of the inclined plane so that the tire rolls without slipping.

The spool has a mass of 100 kg and a radius of gyration of \(k_{G}=0.3 \mathrm{\ m}\). If the coefficients of static and kinetic friction at A are \(\mu_{s}=0.2 \text { and } \mu_{k}=0.15 \text {, }\) respectively, determine the angular acceleration of the spool if P = 50 N.

17-97. Solve Prob. 17-96 if the cord and force P = 50 N are directed vertically upwards.

17-98. The spool has a mass of 100 kg and a radius of gyration kG = 0.3 m. If the coefficients of static and kinetic friction at A are /i< = 0.2 and /x1 = 0.15, respectively, determine the angular acceleration of the spool if P = 600 N.

17-99. The upper body of the crash dummy has a mass of 75 lb. a center of gravity at G. and a radius of gyration about G of kG = 0.7 ft. By means of the seat belt this body segment is assumed to be pin-connected to the seat of the car at A. If a crash causes the car to decelerate at 50 ft/s2, determine the angular velocity of the body when it has rotated to 0 = 30.

A uniform rod having a weight of 10 lb is pin supported at A from a roller which rides on a horizontal track. If the rod is originally at rest, and a horizontal force of F = 15 lb is applied to the roller, determine the acceleration of the roller. Neglect the mass of the roller and its size d in the computations.

17-101. Solve Prob. 17-100 assuming that the roller at A is replaced by a slider block having a negligible mass. The coefficient of kinetic friction between the block and the track is fxk = 0.2. Neglect the dimension d and the size of the block in the computations.

The 2-kg slender bar is supported by cord BC and then released from rest at A. Determine the initial angular acceleration of the bar and the tension in the cord.

17-103. If the truck accelerates at a constant rate of 6 m/s2. starting from rest, determine the initial angular acceleration of the 20-kg ladder. The ladder can be considered as a uniform slender rod. The support at B is smooth.

If P = 30 lb, determine the angular acceleration of the 50-lb roller. Assume the roller to be a uniform cylinder and that no slipping occurs.

17-105. If the coefficient of static friction between the 50-lb roller and the ground is fis = 0.25, determine the maximum force P that can be applied to the handle, so that roller rolls on the ground without slipping. Also, find the angular acceleration of the roller. Assume the roller to be a uniform cylinder.

17-106. The spool has a mass of 500 kg and a radius of gyration kG = 1.30 m. It rests on the surface of a conveyor bell for which the coefficient of static friction is /xy = 0.5 and the coefficient of kinetic friction is /x* = 0.4. If the conveyor accelerates at ac = I m/s2, determine the initial tension in the wire and the angular acceleration of the spool. The spool is originally at rest.

The spool has a mass of 500 kg and a radius of gyration \(k_{G}=1.30 \mathrm{\ m}\). It rests on the surface of a conveyor belt for which the coefficient of static friction is \(\mu_{s}=0.5\). Determine the greatest acceleration \(a_{C}\) of the conveyor so that the spool will not slip. Also, what are the initial tension in the wire and the angular acceleration of the spool? The spool is originally at rest.

*17-108. The semicircular disk having a mass of 10 kg is rotating at w = 4 rad/s at the instant f) = 60. If the coefficient of static friction at A is jjlx = 0.5, determine if the disk slips at this instant.

17-109. The 500-kg concrete culvert has a mean radius of 0.5 m. If the truck has an acceleration of 3 m/s2. determine the culvert's angular acceleration. Assume that the culvert does not slip on the truck bed. and neglect its thickness.

17-110. The 10-lb hoop or thin ring is given an initial angular velocity of 6 rad/s when it is placed on the surface. If the coefficient of kinetic friction between the hoop and the surface is /i2 = 0.3, determine the distance the hoop moves before it stops slipping.

17-111. A long strip of paper is wrapped into two rolls, each having a mass of 8 kg. Roll A is pin supported about its center whereas roll B is not centrally supported. If B is brought into contact with A and released from rest, determine the initial tension in the paper between the rolls and the angular acceleration of each roll. For the calculation, assume the rolls to be approximated by cylinders.

17-112. The circular concrete culvert rolls with an angular velocity of co = 0.5 rad/s when the man is at the position shown. At this instant the center of gravity of the culvert and the man is located at point G. and the radius of gyration about G is kG = 3.5 ft. Determine the angular acceleration of the culvert. The combined weight of the culvert and the man is 500 lb. Assume that the culvert rolls without slipping, and the man does not move within the culvert.

17-113. The uniform disk of mass m is rotating with an angular velocity of when it is placed on the floor. Determine the initial angular acceleration of the disk and the acceleration of its mass center.The coefficient of kinetic friction between the disk and the floor is fjk.

17-114. The uniform disk of mass m is rotating with an angular velocity of when it is placed on the floor. Determine the time before it starts to roll without slipping. What is the angular velocity of the disk at this instant? The coefficient of kinetic friction between the disk and the floor is jAk.

The 16-lb bowling ball is cast horizontally onto a lane such that initially \(\omega=0\) and its mass center has a velocity v = 8 ft/s. If the coefficient of kinetic friction between the lane and the ball is \(\mu_{k}=0.12\). determine the distance the ball travels before it rolls without slipping. For the calculation, neglect the finger holes in the ball and assume the ball has a uniform density.

The uniform beam has a weight W. If it is originally at rest while being supported at A and B by cables, determine the tension in cable A if cable B suddenly fails. Assume the beam is a slender rod.

17-117. A cord C is wrapped around each of the two 10-kg disks. If they are released from rest, determine the tension in the fixed cord D. Neglect the mass of the cord.

The \(500-\mathrm{lb}\) beam is supported at A and B when it is subjected to a force of \(1000 \mathrm{lb}\) as shown. If the pin support at A suddenly fails, determine the beam's initial angular acceleration and the force of the roller support on the beam. For the calculation, assume that the beam is a slender rod so that its thickness can be neglected.

17-119. The 30-kg uniform slender rod AB rests in the position shown when the couple moment of M = 150 N-m is applied. Determine the initial angular acceleration of the rod. Neglect the mass of the rollers.

*17-120. The 30-kg slender rod AB rests in the position shown when the horizontal force P = 50 N is applied. Determine the initial angular acceleration of the rod. Neglect the mass of the rollers.

PI7-1. The truck is used to pull the heavy container.To be most effective at providing traction to the rear wheels at A, is it best to keep the container where it is or place it at the front of the trailer? Use appropriate numerical values to explain your answer.

The solid cylinder has an outer radius R, height h, and is made of a material having a density that varies from its center as \(\rho=k+a r^{2}\), where k and a are constants. Determine the mass of the cylinder and its moment of inertia about z axis

P17-3. How can you tell the driver is accelerating this SUV? To explain your answer, draw the free-body and kinetic diagrams. Here power is supplied to the rear wheels. Would the photo look the same if power were supplied to the front wheels? Will the accelerations be the same? Use appropriate numerical values to explain your answers.

PI7-4. Here is something you should not try at home, at least not without wearing a helmet! Draw the free-body and kinetic diagrams and show what the rider must do to maintain this position. Use appropriate numerical values to explain your answer.