Chapter 17, Problem 111P

The 24-kg wheel has a radius of gyration about its center O of ko = 260 mm, and radius r= 0.4 m. When the wheel is subjected to the couple moment M = 90 N•m, it slips as it rolls. Determine the linear acceleration of the wheel's center O (in m/s?). The coefficient of kinetic friction between the wheel and the plane is Uk = 0.45. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s?. M

The uniform 24-m robotic arm OB weighs 300 kg and is hinged at its lower end to a fixed support at O. If the actuator C develops a starting torque of 1300 N· m, calculate the total force supported by the pin at O as the arm begins to lift off its support at B. Also find the corresponding angular acceleration a of the robotic link. The cable at A is horizontal, and the mass of the pulleys and the actuator is negligible. (see Figure 2) 1200 mm 30° 16 m Figure 2. 8 m B

The uniform slender bar of mass m and total length L is released from rest in the position shown. De- termine the force supported by the small roller at A and the acceleration of roller A along the smooth guide. Evaluate your results for 0 = 15°.

The concrete block weighing 644 lb is elevated by the hoisting mech- anism shown, where the cables are securely wrapped around the re- spective drums. The drums, which are fastened together and turn as a single unit about their mass center at 0, have a combined weight of 322 lb and a radius of gyration about O of 18 in. If a constant tension P = 400 lb is maintained by the power unit at A, determine the vertical acceleration of the block and the resultant force on the bearing at O. Solve using; 24" 12" P = 400 lb (a) Two free body diagrams for concrete block and drum. W = 322 lb ko = 18" (b) One system block diagram ( concrete block and drum as one system). 45° A 644 lb

The 29-kg spool of outer radius ro​=530 mm has a centroidal radius of gyration k=355 mm and a central shaft of radius ri​=215 mm. The spool is at rest on the incline when a tension T=204 N is applied to the end of a cable which is wrapped securely around the central shaft as shown. Determine the acceleration aaa of the spool center GGG and the friction force FFF acting at the interface of the spool and incline. The friction coefficients there are μs=0.28 and μk​=0.17. The tension T is applied parallel to the incline and the angle θ=16. The acceleration aaa and the force F are both positive if up the incline, negative if down.

The uniform 30-kg bar AB hangs from a pin attached to the 50-kg homogeneous disk C. The system is at rest when the horizontal force P =200N is applied. Find the angular accelerations of the disk and the bar immediately after P is applied.

The 29-kg spool of outer radius ro​=530 mm has a centroidal radius of gyration k=355 mm and a central shaft of radius ri​=215 mm. The spool is at rest on the incline when a tension T=204 N is applied to the end of a cable which is wrapped securely around the central shaft as shown. Determine the acceleration aaa of the spool center GGG and the friction force F acting at the interface of the spool and incline. The friction coefficients there are μs=0.28 and μk​=0.17. The tension T is applied parallel to the incline and the angle θ=16. The acceleration aaa and the force F are both positive if up the incline, negative if down. a is not 2.112 or -2.112

The uniform rectangular slab is released from rest in the position shown. Determine the value of x for which the angular acceleration is maximum, and determine the corresponding angular acceleration.

The 32-kg spool of outer radius ro 420 mm has a centroidal radius of gyration k 265 mm and a central shaft of 243 N is applied to the end of a cable radius ri 155 mm. The spool is at rest on the incline when a tension T which is wrapped securely around the central shaft as shown. Determine the acceleration a of the spool center G and the friction force Facting at the interface of the spool and incline. The friction coefficients there are H 0.28 and Hk 0.19. The tension T is applied parallel to the incline and the angle 0 19 The acceleration a and the force F are both positive if up the incline, negative if down. m, E T T A Answers: m/s2 a = i F Z