5.37. a Car Is Traveling at 50 Mi/Hr on a Horizontal Highway. (A) If the Coefficient Of

6E/S&J

5.37. A car is traveling at 50 mi/hr on a horizontal highway. (a) If the coefficient of static friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and s = 0.600? 6E/S&J

5.41. A 3.00-kg block starts from rest at the top of a 30.0 incline and slides a distance of 2.00 m down the incline in 1.50 s. Find (a) the magnitude of the acceleration of the block, (b) the coefficient of kinetic friction between the block and the plane, (c) the friction force acting on the block, and (d) the speed of the block after it has slid 2.00 m. 6E/S&J

5.44. Three objects are connected on the table as shown in Figure P5.44. The table is rough and has a coefficient of kinetic friction of 0.350. The objects have masses of 4.00 kg, 1.00 kg, and 2.00 kg as shown, and the two pulleys are frictionless. (a) Draw free-body diagrams of each object. (b) Determine the magnitude and direction of the acceleration of the system. (c) Determine the tensions in the two cords. 6E/S&J

5.45. Two blocks connected by a rope of negligible mass are being dragged by a horizontal force F (see Fig. P5.45). Suppose that F = 68.0 N, m1 = 12.0 kg, m2 = 18.0 kg, and the coefficient of kinetic friction between each block and the surface is 0.100. (a) Draw a free-body diagram for each block. (b) Determine the tension T and the magnitude of the acceleration of the system. 6E/S&J

5.48. The board sandwiched between two other boards in Figure P5.48 weighs 95.5 N. If the coefficient of friction between the boards is 0.663, what must be the magnitude of the compression forces (assume horizontal) acting on both sides of the center boards to keep it from slipping? 6E/S&J

5.51. An inventive child named Pat wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P5.51), Pat pulls on the loose end of the rope with such a force that the spring scale reads 250 N. Pat’s true weight is 320 N, and the chair weighs 160 N. (a) Draw free-body diagrams for Pat and the chair considered as separate systems, and another diagram for Pat and the chair considered as one system. (b) Show that the acceleration of the system is upward and find its magnitude. (c) Find the force Pat exerts on the chair. 6E/S&J

5.52. A time-dependent force F = (8.00i – 4.00tj) N, where t is in seconds, is exerted on a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s? (b) How far is the object from its initial position when its speed is 15.0 m/s? (c) Through what total displacement has the object traveled at this time? 6E/S&J

5.54. Three blocks are in contact with each other on a frictionless, horizontal surface, as in Figure P5.54. A horizontal force F is applied to m1. Take m1 = 2.00 kg, m2 = 3.00 kg, m3 = 4.00 kg, and F = 18.0 N. Draw a separate free-body diagram for each block and find (a) the acceleration of the blocks, (b) the resultant force on each block, and (c) the magnitudes of the contact forces between the blocks. (d) You are working on a construction project. A coworker is nailing up plasterboard on one side of a light partition, and you are on the opposite side, providing "backing" by leaning against the wall with your back pushing on it. Every blow makes your back sting. The supervisor helps you to put a heavy block of wood between the wall and your back. Using the situation analyzed in parts (a), (b), and (c) as a model, explain how this works to make your job more comfortable. 6E/S&J

5.55. An object of mass M is held in place by an applied force F and a pulley system as shown in Figure P5.55. The pulleys are massless and frictionless. Find (a) the tension in each section of the rope, T1, T2, T3, T4, and T5, and (b) the magnitude of F. Suggestion: Draw a free-body diagram for each pulley. 6E/S&J

5.56. A high diver of mass 70.0-kg jumps off a board 10.0 m above the water. If his downward motion is stopped 2.00 s after he enters the water, what average upward force did the water exert on him? 6E/S&J

5.57. A crate of weight Fg is pushed by a force P on a horizontal floor. (a) If the coefficient of static friction is s and P is directed at an angle  below the horizontal, show that the minimum value of P that will move the crate is given by: mF sec q P = s g 1- ms tan q 6E/S&J

5.58. A block of mass m = 2.00 kg is released from rest h = 0.500 m from the surface of a table, at the top of a  = 30.0 incline as shown in Figure P5.58. The frictionless incline is fixed on a table of height H = 2.00 m. (a) Determine the acceleration of the block as it slides down the incline. (b) What is the velocity of the block as it leaves the incline? (c) How far from the table will the block hit the floor? (d) How much time has elapsed between when the block is released and when it hits the floor? (e) Does the mass of the block affect any of the above calculations? 6E/S&J

5.61. What horizontal force must be applied to the cart shown in Figure P5.61 in order that the blocks remain stationary relative to the cart? Assume all surfaces, wheels, and pulley are frictionless. (Hint: Note that the force exerted by the string accelerates m1.) 6E/S&J

6.5. A coin placed 30.0 cm from the center of a rotating, horizontal turntable slips when its speed is 50.0 cm/s. (a) What force causes the centripetal acceleration when the coin is stationary relative to the turntable? (b) What is the coefficient of static friction between coin and turntable? 6E/S&J

6.9. Consider a conical pendulum with an 80.0-kg bob on a 10.0-m wire making an angle of 5.00 with the vertical (Fig. P6.9). Determine (a) the horizontal and vertical components of the force exerted by the wire on the pendulum and (b) the radial acceleration of the bob.