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- A flat cushion of mass m is released from rest at the corner of the roof of a building, at height h. A wind blowing along the side of the building exerts a constant horizontal force of magnitude F on the cushion as it drops as shown in Figure P5.48. The air exerts no vertical force. (a) Show that the path of the cushion is a straight line. (b) Does die cushion fall with constant velocity? Explain. (c) If m = 1.20 kg, h = 8.00 m, and F = 2.40 N, how far from the building will the cushion hit the level ground? What If? (d) If the cushion is thrown downward with a nonzero speed at the top of the building, what will be the shape of its trajectory? Explain. Figure P5.48A small sports car collides head-on with a massive truck. The greater impact force (in magnitude) acts on (a) the car, (b) the truck, (c) neither, the force is the same on both. Which vehicle undergoes the greater magnitude acceleration? (d) the car, (e) the truck, (f) the accelerations are the same.Calculate the normal force on a 15.0 kg block in the following circumstances: (a) The block is resting on a level surface. (b) The block is resting on a surface tilted up at a 30.0 angle with respect to the horizontal. (c) The block is resting on the floor of an elevator that is accelerating upwards at 3.00 m./s2. (d) The block is on a level surface and a force of 125 N is exerted on it at an angle of 30.0 above the horizontal. (Sec Section 1.5.)
- Assume the resistive force acting on a speed skater is proportional to the square of the skaters speed v and is given by f = kmv2, where k is a constant and m is the skaters mass. The skater crosses the finish line of a straight-line race with speed vi and then slows down by coasting on his skates. Show that the skaters speed at any time t after crossing the finish line is v(t) = vi/(1 + ktvi).A 5.00-kg block is placed on top of a 10.0-kg block (Fig. P5.50). A horizontal force of 45.0 N is applied to the 10-kg block, and the 5-kg block is tied to the wall. The coefficient of kinetic friction between all moving surfaces is 0.200. (a) Draw a free-body diagram for each block and identify the action-reaction forces between the blocks. (b) Determine the tension in the string and the magnitude of the acceleration of the 10-kg block. Figure P5.50A potato of mass 0.5 kg moves under Earth’s gravity with an air resistive force of −kmv. (a) Find the terminal velocity if the potato is released from rest and k = 0.01 s−1. (b) Find the maximum height of the potato if it has the same value of k, but it is initially shot directly upward with a student-made potato gun with an initial velocity of 120 m/s.
- A box rests on a surface (Fig. P6.64). A force Fapp is applied to the box in two different ways. In both cases. Fapp has the same magnitude, but in case 1 the force is directed below the horizontal, whereas in case 2 it is directed above the horizontal. a. Draw a free-body diagram for both cases. b. Now Fapp is increased in both cases until the box just barely remains at rest. Compare Fs, max for each free-body diagram. c. Use your answer to part (b) to find a best way to move a heavy desk. Describe and explain your solution.A 9.00-kg hanging object is connected by a light, inextensible cord over a light, frictionless pulley to a 5.00-kg block that is sliding on a flat table (Fig. P5.7). Taking the coefficient of kinetic friction as 0.200, find the tension in the string. Figure P5.7In Example 4.5, we pushed on two blocks on a table. Suppose three blocks are in contact with one another on a frictionless, horizontal surface as shown in Figure P4.49. 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. (a) Draw a separate free-body diagram for each block. (b) Determine the acceleration of the blocks. (c) Find the resultant force on each block. (d) Find the magnitudes of the contact forces between the blocks. (e) 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 hammer blow makes your back sting. The supervisor helps you put a heavy block of wood between the wall and your back. Using the situation analyzed in parts (a) through (d) as a model, explain how this change works to make your job more comfortable. Figure P4.49
- An inventive child 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. P4.88), the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The childs true weight is 320- N, and the chair weighs 160 N. The childs feet are not touching the ground. (a) Show that the acceleration of the system is upward, and find its magnitude. (b) Find the force the child exerts on the chair. Figure P4.88A block of mass m = 5.8 kg is pulled up a = 25 incline as in Figure P4.24 with a force of magnitude F = 32 N. (a) Find the acceleration of the bloc k if the incline is frictionless. (b) Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.10. Figure P4.24As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 61.0 kg. If this fish is moving upward at 3.00 m/s as its head first breaks the surface and has an upward speed of 6.00 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine (a) the salmons acceleration and (b) the magnitude of the force F during this interval.