3 * A block of mass m rests on a plane that is inclined at an angle 6 with the horizontal. It follows that the coefficient of static friction between the block and plane is (2) u, = g, (b) p, = tan, (c) u, = tan, (d) u, = tan. 4 . A block of mass m is at rest on a plane that is inclined at an angle of 30 with the horizontal, as shown in Figure 5-56. Which of the following statements about the magnitude of the static fric- tional force f is necessarily true? (a) f > mg, (b) f, > mg cos30, (c) f = mg cos 30, (d) f = mg sin 30, (e) None of these statements is true. m 30 FIGURE 5-56 Problem 46 . . If it is started properly on the frictionless inside surface of a cone (Figure 5-57), a block is capable of maintaining uniform circular motion. Draw the free-body diagram of the block and iden- tify clearly which force (or forces, or force components) is responsi- ble for the centripetal acceleration of the block. FIGURE 5-57 Problem 6by Earth, (b) is much greater than the gravitational force exerted on the moon by Earth, (c) actually is the gravita- tional force exerted on the moon by Earth, (d) cannot be answered yet, because we have not yet studied Newton's law of gravity. SSM 16 . . A block is sliding on a frictionless sur- face along a loop-the-loop, as in Figure 5-59a. The block is moving fast enough so that it never loses contact with the track. Match the points along the track to the appropriate free-body dia- 2. grams in Figure 5.59b. 3. D A C 4. B (a) 5. FIGURE 5-59 Problem 16 (b)32 Ablock of wood is pulled at constant velocity by a hori- zontal string across a horizontal surface with a force of 20 N. The coefficient of kinetic friction between the surfaces is 0.3. The force of friction is (a) impossible to determine without knowing the mass of the block, (b) impossible to determine without knowing the speed of the block, (c) 0.30 N, (d) 6.0 N, (e) 20 N. 36 * A box weighing 600 N is pushed along a horizontal floor at constant velocity with a force of 250 N parallel to the floor. What is the coefficient of kinetic friction between the box and the floor? 43 ** Ablock of mass m, = 250 g is at rest on a plane that makes an angle of 6 = 30 with the horizontal. The coefficient of kinetic friction between the block and the plane is 0.100. The block is attached to a second block of mass m, = 200 g that hangs freely by a string that passes over a frictionless, massless pulley (Figure 5-62). When the second block has fallen 30.0 cm, what will be its speed? "ssm* FIGURE 5-62 Problems 43,44, 45 50 * You and your best pal make a friendly bet that you can place a 2.0-kg box against the side of a cart, as in Figure 5-63, and that the box will not fall to the ground, even though you guarantee to use no hooks, ropes, fasteners, magnets, glue, or adhesives of any kind. When your friend accepts the bet, you begin pushing the cart in the direction shown in the figure. The coefficient of static friction between the box and the cart is 0.60. (a) Find the minimum acceler- ation for which you will win the bet. (b) What is the magnitude of the frictional force in this case? () Find the force of friction on the box if the acceleration is twice the minimum needed for the box not to fall. (d) Show that, for a box of any mass, the box will not fall if the magnitude of the forward acceleration is a = g/u_, where u_is the coefficient of static friction. FIGURE 5-63 Problem 50 56 . . A 100-kg mass is pulled along a frictionless surface by a horizontal force F such that its acceleration is a, = 6.00m/s2 (Figure 5-66). A 20.0-kg mass slides along the top of the 100-kg mass and has an acceleration of a, = 4.00 m/s2. (It thus slides backward relative to the 100-kg mass.) (a) What is the frictional force exerted by the 100-kg mass on the 20.0-kg mass? (b) What is the net force acting on the 100-kg mass? What is the force F? (c) After the 20.0-kg mass falls off the 100-kg mass, what is the acceleration of the 100-kg mass? (Assume that the force F does not change.) 20kg 42 = 4.00 m/s2 100kg a1 = 6.00 m/s2 FIGURE 5-66 Problem 56