The system shown is released from rest. Determine the acceleration of the blocks? The cable is inextensible. The coefficient of dynamic friction is 0.4 for contact surfaces of A and B.
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- The 60-lb plank rests on a frictionless roller at A, and the 20-lb triangular support BD. Both bodies are homogenous. The coefficients of static friction are 0.4 at B and 0.3 at D. Determine the largest force P that can be applied to the plank without initiating motion.Find the smallest distance d for which the hook will remain at rest when acted on by the force P. Neglect the weight of the hook, and assume that the vertical wall is frictionless.Two identical chairs, each weighing 14 lb, are stacked as shown. The center of gravity of each chair is denoted by G. The coefficient of static friction is 0.2 at B (the contact point between the chairs) and 0.35 at A, C, and D. Determine the smallest force P that would cause sliding.
- A 1.6-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle e is 38, the angular velocity of the arm about a horizontal axis through O is 55 deg/s clockwise and its angular acceleration is 205 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 440 mm/s. Determine the necessary minimum gripping force Pif the coefficient of static friction between the sphere and the gripping surfaces is 0.51. Compare Pwith the minimum gripping force P; required to hold the sphere in static equilibrium in the 38° position. 1.5 m Answers: P = i Ps= iA 1.7-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle e is 24°, the angular velocity of the arm about a horizontal axis through O is 57 deg/s clockwise and its angular acceleration is 222 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 430 mm/s. Determine the necessary minimum gripping force Pif the coefficient of static friction between the sphere and the gripping surfaces is 0.56. Compare P with the minimum gripping force P3 required to hold the sphere in static equilibrium in the 24° position. 2.1 m Answers: P = i N P = iA 1.4-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle e is 37°, the angular velocity of the arm about a horizontal axis through O is 45 deg/s clockwise and its angular acceleration is 166 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 450 mm/s. Determine the necessary minimum gripping force Pif the coefficient of static friction between the sphere and the gripping surfaces is 0.59. Compare P with the minimum gripping force P; required to hold the sphere in static equilibrium in the 37° position. 1.3 m Answers: P = i N P3 = N
- A 2.2-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle is 36°, the angular velocity of the arm about a horizontal axis through O is 45 deg/s clockwise and its angular acceleration is 176 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 550 mm/s. Determine the necessary minimum gripping force P if the coefficient of static friction between the sphere and the gripping surfaces is 0.58. Compare P with the minimum gripping force P, required to hold the sphere in static equilibrium in the 36° position. 1.0 m $ Answers: P= Ps= i i N N1. The system below is released from rest. The ramp and flat services are frictionless and the coefficient of static friction between to the 1kg and the 20kg block is 0.2. Does the 1kg block slip? 20⁰ 100kg friction frictionless 1kg 20kg3. The coefficients of friction between the load A and the bed of the utility vehicle are us 0.4 and uk = 0.36. The angle 0 = 20°. Determine the largest forward and rearward acceleration of the vehicle for which the load will not slide on the bed.
- Problem 2 Determine the magnitude of W so that the 200-lb body will have an acceleration up the plane of 4.025 ft/s² . Coefficient of kinetic friction is 0.20. 200 lb 30° W lbBlocks A and B each have 6.5 kg mass. All contact surfaces have the same coefficient of friction. Determine the force P needed to cause impending motion of block B to the right if the coefficient of static friction is 0.4. (Round the final answer to four decimal places.)5. How far will the 100-kg block move 2 seconds after it is released from the position shown. The pulley is frictionless. Use coefficient of kinetic friction is 0.15. 100 kg e = 30° 30 kg