B x. B cos B. B sin B 0 N 64 N 64 N (47 N) 79 N

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1 85. What is the net force acting on the ring in Figure 5-18? Figure 5-18 R 2 A 2 B 2 R A 2 B 2 (5. N) 2 (4. N) N tan A B tan 1 A B tan from B The net force is 64.3 N at What is the net force acting on the ring in Figure 5-19? 128 N Figure 5-19 A 128 N 64 N 64 N A A cos A (64 N)(cos 18 ) 64 N A y A sin A (64 N)(sin 18 ) N y 5. N 4. N 4. y N 128 N B B cos B (128 N)(cos 3. ) 111 N B y B sin B (128 N)(sin 3. ) 64 N R A B 64 N 111 N 47 N R y A y B y N 64 N 64 N R R 2 R 2 y (47 N) 2 4 (6N) 2 79 N tan 1 R y R tan A Ship at Sea A ship at sea is due into a port 5. km due south in two days. However, a severe storm comes in and blows it 1. km due east from its original position. How far is the ship from its destination? In what direction must it travel to reach its destination? R 2 A 2 B 2 R (1. km) 2. (5) km km tan 1 R y R tan R 59.9 km, south of west 12 Solutions Manual Physics: Principles and Problems

2 Chapter 5 continued 88. Space Eploration A descent vehicle landing on Mars has a vertical velocity toward the surface of Mars of 5.5 m/s. At the same time, it has a horizontal velocity of 3.5 m/s. a. At what speed does the vehicle move along its descent path? R 2 A 2 B 2 R (5.5 /s) m 2 /s) (3.5 m 2 v R 6.5 m/s b. At what angle with the vertical is this path? tan 1 R y R tan from horizontal, which is 32 from vertical 89. Navigation Alfredo leaves camp and, using a compass, walks 4 km E, then 6 km S, 3 km E, 5 km N, 1 km W, 8 km N, and, finally, 3 km S. At the end of three days, he is lost. By drawing a diagram, compute how far Alfredo is from camp and which direction he should take to get back to camp. Take north and east to be positive directions. North: 6 km 5 km 8 km 3 km 4 km. East: 4 km 3 km 1 km 3 km. The hiker is 4 km north and 3 km west of camp. To return to camp, the hiker must go 3 km east and 4 km south. R 2 A 2 B 2 R (3 ) km 2 (4km) 2 5 km tan 1 R y R tan 1 4 km 3 km 53 R 5 km, 53 south of east 5.2 Friction page 142 Level 1 9. If you use a horizontal force of 3. N to slide a 12.-kg wooden crate across a floor at a constant velocity, what is the coefficient of kinetic friction between the crate and the floor? k k F horizontal k F horizontal A 225-kg crate is pushed horizontally with a force of 71 N. If the coefficient of friction is.2, calculate the acceleration of the crate. ma F net F appl where k k Therefore a F appl k m 3. N (12. kg)(9.8 m/s 2 ) 71 N (.2)(225 kg)(9.8 m/s 2 ) 225 kg 1.2 m/s 2 Level A force of 4. N accelerates a 5.-kg block at 6. m/s 2 along a horizontal surface. a. How large is the frictional force? ma F net F appl so F appl ma 4. N (5. kg)(6. m/s 2 ) N b. What is the coefficient of friction? k k so k N (5. kg)(9.8 m/s 2 ).2 Physics: Principles and Problems Solutions Manual 13

3 93. Moving Appliances Your family just had a new refrigerator delivered. The delivery man has left and you realize that the refrigerator is not quite in the right position, so you plan to move it several centimeters. If the refrigerator has a mass of 18 kg, the coefficient of kinetic friction between the bottom of the refrigerator and the floor is.13, and the static coefficient of friction between these same surfaces is.21, how hard do you have to push horizontally to get the refrigerator to start moving? F on fridge riction s s (.21)(18 kg)(9.8 m/s 2 ) 37 N 94. Stopping at a Red Light You are driving a 25.-kg car at a constant speed of 14. m/s along a wet, but straight, level road. As you approach an intersection, the traffic light turns red. You slam on the brakes. The car s wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 25. m. What is the coefficient of kinetic friction between your tires and the wet road? k ma m(v 2 k f v 2 i ) where v f 2d (The minus sign indicates the force is acting opposite to the direction of motion.) vi k 2 2 d g (14. m/s) 2 2(25. m)(9.8 m/s 2 ) Force and Motion in Two Dimensions pages Level An object in equilibrium has three forces eerted on it. A 33.-N force acts at 9. from the -ais and a 44.-N force acts at 6. from the -ais. What are the magnitude and direction of the third force? First, find the magnitude of the sum of these two forces. The equilibrant will have the same magnitude but opposite direction. F N, 9. F N, 6.? F 1 F 1 cos 1 (33. N)(cos 9. ). N F 1y F 1 sin 1 (33. N)(sin 9. ) 33. N F 2 F 2 cos 2 (44. N)(cos 6. ) 22. N F 2y F 2 sin 2 (44. N)(sin 6. ) 38.1 N F 1 F 2. N 22. N 22. N y F 1 y F 2 y 33. N 38.1 N 71.1 N F 2 3 F 2 3y (22. N) 2 (71.1N) N 14 Solutions Manual Physics: Principles and Problems

4 For equilibrium, the sum of the components must equal zero, so tan 1 F 3y F3 18. tan N N N, 253 Level Five forces act on an object: (1) 6. N at 9., (2) 4. N at., (3) 8. N at 27., (4) 4. N at 18., and (5) 5. N at 6.. What are the magnitude and direction of a sith force that would produce equilibrium? Solutions by components F 1 6. N, 9. F 2 4. N,. 8. N, 27. F 4 4. N, 18. F 5 5. N, 6.? F 5 F 5 cos 5 (5. N)(cos 6. ) 25. N F 5y F 5 sin 5 (5. N)(sin 6. ) 43.3 N F 1 F 2 F 4 F 5. N 4. N. N 25. N (4. N) 25. N y F 1y F 2y y F 4y F 5y 6. N. N (8. N) 23.3 N. N 43.3 N F 2 6 F 2 6y (25. N) 2 (23.3N) N 6 tan 1 F 6y F6 18. tan N N N, 223 F 1 F 1 cos 1 (6. N)(cos 9. ). N F 1y F 1 sin 1 (6. N)(sin 9. ) 6. N F 2 F 2 cos 2 (4. N)(cos. ) 4. N F 2y F 2 sin 2 (4. N)(sin. ). N cos 3 (8. N)(cos 27. ). N y sin 3 (8. N)(sin 27. ) 8. N F 4 F 4 cos 4 (4. N)(cos 18. ) 97. Advertising Joe wishes to hang a sign weighing N so that cable A, attached to the store, makes a 3. angle, as shown in Figure 5-2. Cable B is horizontal and attached to an adjoining building. What is the tension in cable B? 3. A B Figure N F 4y F 4 sin 4 (4. N)(sin 18. ). N Physics: Principles and Problems Solutions Manual 15

5 Solution by components. The sum of the components must equal zero, so F g so F g N F A sin 6. so F A 866 N Also, F B F A, so F B F A sin N sin 6. F A cos 6. (866 N)(cos 6. ) 433 N, right 98. A street lamp weighs 15 N. It is supported by two wires that form an angle of 12. with each other. The tensions in the wires are equal. a. What is the tension in each wire supporting the street lamp? F g 2T sin Fg so T 2s in 15 N (2)(s in 3. ) N b. If the angle between the wires supporting the street lamp is reduced to 9., what is the tension in each wire? Fg T 2s in 15 N (2)( sin 45 ) N 99. A 215-N bo is placed on an inclined plane that makes a 35. angle with the horizontal. Find the component of the weight force parallel to the plane s surface. F parallel F g sin (215 N)(sin 35. ) 123 N 1. Emergency Room You are shadowing a nurse in the emergency room of a local hospital. An orderly wheels in a patient who has been in a very serious accident and has had severe bleeding. The nurse quickly eplains to you that in a case like this, the patient s bed will be tilted with the head downward to make sure the brain gets enough blood. She tells you that, for most patients, the largest angle that the bed can be tilted without the patient beginning to slide off is 32. from the horizontal. a. On what factor or factors does this angle of tilting depend? The coefficient of static friction between the patient and the bed s sheets. b. Find the coefficient of static friction between a typical patient and the bed s sheets. F g parallel to bed sin so s tan sin cos sin cos tan s s cos 16 Solutions Manual Physics: Principles and Problems