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47. (II) In Fig. 456 the coefficient of static friction between mass m A and the table is 0.40, whereas the coefficient of kinetic friction is 0.20. (a) What minimum value of mA will keep the system from starting to move? (b) What value(s) of m A will keep the system moving at constant speed? [Ignore masses of the cord and the (frictionless) pulley.] FIGURE 4-56 Problem 47. 49. (11) Two crates, of mass 65 kg and 125 kg, are in contact and at rest on a horizontal surface (Fig. 457). A 650-N force is exerted on the 6S-kg crate. If the coefficient of kinetic friction is 0.18, calculate (a) the acceleration of the sys- tem, and (b) the force that each crate exerts on the other. (c) Repeat with the crates reversed. 65 kg 125 kg FIGURE 4-57 Problem 49. 57. (II) The block shown in Fig. 4-59 has mass m = 7.0kg and lies on a fixed smooth frictionless plane tilted at an angle 0 = 22.0 to the hori- zontal. (a) Determine the acceleration m of the block as it slides down the plane. X (b) If the block starts from rest 12.0 m up the plane from its base, what will be the block's speed when D it reaches the bottom of the incline? FIGURE 4-59 Block on inclined plane. Problems 57 and 58.59. (II) The crate shown in Fig. 460 lies on a plane tilted at an y angle 9 = 25.0 to the horizontal, with pk = 0.19. (a) Determine the acceleration of the crate as it slides down the plane. (b) If the crate starts from rest 8.15 m up along the plane from its base, what will be the crate's speed when it reaches the bottom of the incline? FIGURE 4-60 Crate on inclined plane. Problems 59 and 60. 4-8 Newton's laws with Friction, Inclines 37. (I) A force of 35.0 N is required to start a 6.0-kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 35.0-N force continues, the box accelerates at 0.60 m/sz. What is the coefficient of kinetic friction? 39. (II) The coefficient of static friction between hard rubber and normal street pavement is about 0.90. Oh how steep a hill (maximum angle} can you leave a car parked? 41. (II) A 2.0-kg silverware drawer does not slide readily. The owner gradually pulls with more and more force, and when the applied force reaches 9.0 N, the drawer suddenly opens, throwing all the utensils to the floor. What is the coefficient of static friction between the drawer and the cabinet? 43. (II) A 1280-kg car pulls a 350-kg trailer. The car exerts a horizontal force of 3.6 x 103 N against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer. 45. (ll) Drag-race tires in contact with an asphalt surface have a very high coefficient of static friction. Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 5, starting from rest. 47. (II) In Fig. 456 the coefficient of static friction between mass mA and the table is 0.40, whereas the coefficient of kinetic friction is 0.20. (a) What minimum value of mi will keep the system from starting to move? (b) What value(s} of mg will keep the system moving at constant speed? [Ignore masses of the cord and the (frictionless) pulley.] 49. (ll) Two crates, of mass 65 kg and 125 kg, are in contact and at rest on a horizontal surface (Fig. 4 57). A 650-N force is exerted on the 65-kg crate. If the coefficient of kinetic friction is 0.18, calculate (a) the acceleration of the system, and (b) the force that each crate exerts on the other. (c) Repeat with the crates reversed. 51. (II) A child on a sled reaches the bottom ofa hill with a velocity of 10.0 m/s and travels 25.0 m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60.0 kg, what is the average retarding force on the sled on the horizontal straightaway? 53. (II) A wet bar of soap slides down a ramp 9.0 m long inclined at 8.0". How long does it take to reach the bottom? Assume pk = 0.060. 55. (ll) Uphill escape ramps are sometimes provided to the side of steep downhill highways for trucks with overheated brakes. For a simple 11 upward ramp, what minimum length would be needed for a runaway truck traveling 140 km/h? Note the large size of your calculated length. (If sand is used for the bed of the ramp, its length can be reduced by a factor of about 2.) 57. (II) The block shown in Fig. 459 has mass m = 7.0 kg and lies on a fixed smooth frictionless plane tilted at an angle :9 = 22.0\" to the horizontal. (:7) Determine the acceleration of the block as it slides down the plane. (b) If the block starts from rest 12.0 m up the plane from its base, what will be the block's speed when it reaches the bottom of the incline? 59. (II) The crate shown in Fig. 460 lies on a plane tilted at an angle 1?: 25.0\" to the horizontal, with pk = 0.19. (0) Determine the acceleration of the crate as it slides down the plane. (b) If the crate starts from rest 8.15 m up along the plane from its base, what will be the crate's speed when it reaches the bottom of the incline