1. A motor supplies a constant torque or twist of M = 120 lb • ft to the drum. If the drum has a weight of 30 lb and a radius of gyration of k0 = 0.8ft, determine the speed of the 15-lb carte A after it rises s = 4 ft starting from rest. Neglect the weight of the cord.
2. The small bridge consists of an 1,800-lb uniform deck EF (thin plate), two overhead beams AB (slender rods), each having a weight of 200 lb, and a 2,400-lb counterweight BC, which can be considered as a thin plate having the dimensions shown. The weight of the tie rods AE can be neglected. If the operator lets go of the rope when the bridge is at an at-rest position, = 45°, determine the speed at which the end of the deck E hits the roadway step at H, = 0°. The bridge is pin-connected at A, D, E, and F.
3. If the 3-lb solid sphere is released from rest when = 30°, determine its angular velocity when = 0°, which is the lowest point of the curved path having a radius of 11.5 in. The sphere does not slip as it rolls.
4. An 800-lb tree falls from the vertical position such that it pivots about its cut section at A. If the tree can be considered as a uniform rod, pin-supported at A, determine the speed of its top branch just before it strikes the ground.
5. THe 500-g rod AB rests along the smooth inner surface of a hemispherical bowl. If the rod is released from the position shown, determine its angular velocity at the instant it swings downward and becomes horizontal.
6. A man having a weight of 180 lb sits in a chair of the Ferris wheel, which has a weight of 15,000 lb and a radius of gyration of ko = 37 ft. If a torque of M = 80(103) lb • ft is applied about O, determine the angular velocity of the wheel after it has rotated 180°. Neglect the weight of the chairs and note that the man remains in an upright position as the wheel rotates. The wheel starts from rest in the position shown.
7. The uniform slender rod has a mass of 5 kg. Determine the magnitude of the reaction at the pin O when the cord at A is cut and = 90°
8. The spool of cable, originally at rest, has a mass of 200 kg and a radius of gyration of kG = 325 mm. If the spool rests on two small rollers A and B and a constant horizontal force of P = 400 N is applied to the end of the cable, compute the angular velocity of the spool when 8 m of cable has been unraveled. Neglect friction and the mass of the rollers and unraveled cable.
9. A chain that has a negligible mass is draped over a sprocket which has a mass of 2 kg and a radius of gyration of kO = 50 mm. If the 4-kg block A is released from rest in the position shown, s = 1 m, determine the angular velocity which the chain imparts th the sprocket when s = 2 m.
10. The beam having a weight of 150 lb is supported by two cables. If the cable at end B is cut so that the beam is released from rest when = 30°, determine the speed at which end A strikes the wall. Neglect friction at B. Consider the beam to be a thin rod.