1 Problem 1 A horse drags a sledge across a snow-covered path with a rope that is at an angle of 29.1o above the horizontal. The coefficient of kinetic friction between the sledge and the snow is 0.091. The sledge is dragged at a constant acceleration of 0.825 m/s2. The sledge and load on it taken together have a total mass of 165 kg. (a) (16) Find the normal force on the sledge and load. (b) (4) Find the tension in the rope. horse pulling sledge.jpg Problem 2 A 0.75-kg block sits on top of a 1.8-kg block. The 1.8-kg block is attached to a 1.3-m-long rope, which is tethered to an axle. Both blocks move at constant speed in a circle centered on the axle, as shown in the figure below and the 1.8-kg block slides on a smooth flat surface. The coefficient of static friction between the 0.75-kg block and the 1.8-kg block is 0.64. (a) (15) What is the maximum speed the blocks can have such that the 0.75-kg block does not slip? (b) (5) At the maximum speed you found in part (a), what would be the required tension in the rope to keep the blocks moving in a circle? Two Blocks Revolving around Axle.jpg Problem 3 An elevator is ascending from the ground with a steady velocity of (+0.750 m/s) . A squirrel jumps off the elevator with a velocity of (0.780 m/s) + (0.500 m/s) relative to the elevator. At the moment the squirrel jumps, the elevator is 2.35 m above the ground. (a) (4) What is the initial speed of the squirrel and its initial direction of motion relative to the horizontal, according to an observer on the ground? (b) (6) What is the horizontal displacement of the squirrel's flight? (c) (6) What maximum height does the squirrel attain? (d) (4) For what amount of time does the squirrel remain in the air? Problem 4 The blocks shown in the figure below are at rest and the ropes are massless. The mass of Block A is 2.75 kg, the mass of Block B is 0.870 kg, and the coefficient of static friction between Block A and the surface of the table is 0.480. (a) (14) Find the tensions in ropes 1, 2 and 3, which we let be T1, T2, and T3, respectively. (b) (3) Find the normal force, N. (c) (3) Find the frictional force, fs, exerted on Block A. Show that fs < fs,max. Hint: Draw free body diagrams for Block A, Block B, and for the knot. Then apply Newton's second law to each free body diagram. Two Blocks Connected by String at Rest.jpg Problem 5 Two blocks are connected by a massless string that runs over a massless pulley, as shown in the figure below. The rough inclined surface makes an angle of = 27.2o with the horizontal. The block on the incline has a mass of m1 = 3.1-kg. The mass of the hanging block is m2 = 0.58-kg. The coefficient of kinetic friction acting between the 3.1-kg block and the inclined surface is 0.092. (a) (16) Find the magnitude of the acceleration of the blocks. (b) (4) What is the tension in the string connecting the blocks? You may assume that block m1 accelerates down the incline and block m2 accelerates up. Two Blocks Connected by Rope and Pulley.jpg