Problem 3. (a) 125 s, (b) 1562.5 m. Problem 4. (a) 15 1b, (b) 5 1b, (c) 0. Problem 5. (b) 8.49 m/s2, (c) 4.43 m/s. Problem 6. (a) 4.9 m/s2 (b) 2.71 m/s h - 1.57 m/s o, (c) 1.35 m, (d) 1.14 s. Problem 7. (b) 0.58. Problem 8. (b) 6.3 m/s2, 31.5 N. Problem 9. (a) 1.78 m/s2 (b) 0.37 (c) -9.37 N x, (d) 2.67 m/s. Problem 10. Fa cos 02 sin(01+02) . Problem 11. (a) F, + Psin0. Problem 12. (b) 1.79 m/s2.5 kg Problem 8. A 5 kg object placed on a frictionless, horizontal table is con- nected to a string that passes over a pulley and then is fastened to a hanging 9 kg object. (a) Draw free-body diagrams of both objects. (b) Find the acceleration of the two objects and the tension in the string. Problem 9. A 3 kg block starts from rest at the top of a 30 incline and 9kg slides a distance of 2 m down the incline in 1.5 s. Find (a) the magnitude of the acceleration of the block, (b) the coefcient of kinetic friction between the block and incline, (c) the friction force acting on the block, and (d) the speed of the block after it has slid the 2 m. Problem 10. A bag of cement of weight F9 hangs in equilibrium from three wires as shown in the gure on the right. Two of the wires make angles 6'1 and 6'2 with the horizontal. Assuming the system is in equilibrium nd the tension in the left hand wire, T1. Problem 11. A crate of weight F9 is pushed by a force 13 on a _. horizontal oor. The coefficient of static friction is ,u, and P is directed at an angle :9 below the horizontal. (a) Find the normal force exerted on the block. (b) Show that the minimum value of P that will move the crate is given by P: ,ungsec. 1,u5tan9 Problem 12. Consider the two blocks connected by a string running 1 kg '0' 1 kg over the top of a frictionless triangle. When they are released they 2" will accelerate towards one side. (a) Draw free body diagrams for the two blocks. (b) What is the acceleration of the blocks? PROBLEM SET 4, NEWTON'S LAWS Problem 1. A passenger sitting in the rear of a bus claims that he was injured when the driver slammed on the brakes, causing a suitcase to come ying toward him from the front of the bus. If you were the judge in this case, what disposition would you make? Explain your reasoning. Problem 2. Suppose a truck loaded with sand accelerates along a highway. If the driving force exerted on the truck remains constant, what happens to the truck's acceleration if its trailer leaks sand at a constant rate? Problem 3. A long freight train has a mass of 5 x 106 kg and is initially traveling at 25 m/s. The train needs to stop, so the engineer applies the brake which creates a resistive force of 106 N. (a) Find the time it takes the train to stop. (b) Determine the distance the train travels before stopping. (c) Graph 33(t), '06) and (LE). Problem 4. A 15 lb block rests on the oor. (a) What force does the oor exert on the block? (b) A rope is tied to the block and is run vertically over a pulley. The other end of the rope is attached to a free hanging 10 lb object. What is the force exerted by the oor on the 15 lb block? (c) The 10 lb object is replaced by a 20 lb object. What is the force exerted by the oor now? 10 lb Problem 5. A block starts from rest at the top of a 60 frictionless incline 15 lb of height H = 1 m. (a) Draw a free-body diagram of the block. (b) What is the magnitude of the acceleration of the block? (c) What is the speed of the block at the bottom of the incline? Problem 6. A block of mass m = 2 kg is released from @ rest at h = 0.5 In above the surface of a table, at the top of a 6 = 30 incline of mass M. The frictionless incline "C is xed on a table of height H = 2 In. Sec diagram to the right. (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 end of the table will the block hit the oor? ((1) What time interval elapses between the block being released and hitting the oor? (e) Does the mass of the block, m, affect any of the above calculations? If so, which ones? Problem 7. A block remains stationary on an inclined plane of 30. (a) Draw a free body diagram. (b) Find the minimum coefcient of static friction between the block and incline