Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. Chapter 4 1. You and your bike have a cobined ass of 80 k. How uch brakin force has to be applied to slow you fro a velocity of 5 /s to a coplete stop in 2 s? a v t f vi f t i 2.5 /s 2 F a 80 k (2.5 /s 2 ) 200 2. Before openin his parachute, a sky diver with a ass of 90.0 k experiences an upward force fro air resistance of 150. a. What net force is actin on the sky diver? F ravity 90.0 k 9.80 /s 2 882 downward F air resistance F ravity 150 (882 ) 732 730 downward b. What is the sky diver s acceleration? a 730 90. 0 k 8.1 /s 2 0.0 /s 5.0 /s 2.0 s 0.0 s 8.1 /s 2 downward 3. A lare helicopter is used to lift a heat pup to the roof of a new buildin. The ass of the helicopter is 5.010 3 k and the ass of the heat pup is 1500 k. a. How uch force ust the air exert on the helicopter to lift the heat pup with an acceleration of 1.5 /s 2? F lift F overcoe ravity a (6.510 3 k)(1.5 /s 2 ) (6.510 3 k )(9.80 /s 2 ) 7.310 4 upward b. Two chains connected to the load each can withstand a tension of 15,000. Can the load be safely lifted at 1.5 /s 2? F load F lift F overcoe ravity a (1.510 3 k)(1.5 /s 2 ) (1.510 3 k)(9.80 /s 2 ) 2.2510 3 1.4710 4 1.710 4 The load can be safely lifted because the total force on the chains is less than their cobined capability of 3.010 4 4. In a lab experient, you attach a 2.0-k weiht to a sprin scale. You lift the scale and weiht with a constant readin of 22.5. a. What is the value and direction of the acceleration on the weiht? F scale F ravity a F 22.5 (2.0 k)(9.80 /s 2 ) 2.9 upward net 2. 0 k 2. 9 0.69 /s 2 6.910 1 /s 2 b. How far do you lift the weiht in the first 2.0-s interval? d f d i v i t 1 2 at 2 0 (0 /s)(2.0 s) 1.4 1 2 (6.9101 /s 2 )(2.0 s) 2 5. As a lare jet flies at a constant altitude, its enines produce a forward thrust of 8.410 5. The ass of the plane is 2.610 5 k. Physics: Principles and Probles Suppleental Probles 75
Chapter 4 continued a. What is the forward acceleration of the plane, inorin air resistance? F a a F 8. 4105 2. 6105 k 3.2 /s 2 b. How uch upward force ust the air exert on the plane when it is flyin horizontally? Because the plane is not chanin altitude, 0, so F lift F ravity F lift F ravity (2.610 5 k)(9.80 /s 2 ) 2.510 6 6. Two asses are tied to a rope on a pulley, as shown below. 2.0 k a. When the syste is released fro this position, what is the acceleration of the 2.00-k ass? F -lare F -sall a F 1.5 lare sall (2.00 k)(9.80 /s 2 ) (0.80 k)(9.80 /s 2 ) 11.8 downward 11.8 2.8 k Frictionless pulley 0.8 k 4.2 /s 2 downward b. How lon does it take for the 2.0-k ass to fall to the floor? Solve d f d i v i t 1 2 at 2 for t while d i 0, v i 0 /s t 2 d a ( 2) (1. 5 ) 4. 2 /s2 0.85 s 7. A an is standin on a scale inside an airplane. When the airplane is travelin horizontally (in other words, the vertical acceleration of the plane is zero) the scale reads 705.6. What is the vertical acceleration of the plane in each of the followin situations? a. When the scale reads 950.0. F a F scale (F ) a F scale F a F 3.39 /s 2 b. When the scale reads 500.0. F F F scale F F scale F F (F scale F ) F (9.80 /s 2 )(950.0 705.6 ) 705.6 a F scale (F ) Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. 76 Suppleental Probles Physics: Principles and Probles
Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. Chapter 4 continued a F scale F a (F scale F ) F 2.86 /s 2 8. An airboat lides across the surface of the water on a cushion of air. Perfor the followin calculations for a boat in which the ass of the boat and passeners is 450 k. a. If there is no friction, how uch force ust the propeller fan exert on the air to accelerate the boat at 5.00 /s 2? F a F scale F F scale F F (9.80 /s 2 )(500.0 705.6 ) 705.6 (450 k)(5.00 /s 2 ) 2.210 3 b. If the actual acceleration with the fan eneratin the force calculated in part a is only 4.95 /s 2, how uch friction does the air cushion exert on the boat? a friction a ideal a actual riction a friction (a ideal a actual )(450 k) (5.00 /s 2 4.95 /s 2 ) 22 c. What is the upward force exerted by the air cushion on the boat? F lift F ravity (450 k)(9.80 /s 2 ) 4.410 3 9. A olf ball with a ass of 45 is struck by a club, leavin the tee with a speed of 1.810 2 k/h. The period of acceleration was 0.50 /s. a. What is the averae acceleration on the ball as it was struck (in /s 2 )? v i a v f, where v t i 0 k/h a 50 /s 5.0 10 4 s 1.010 5 /s 2 b. What is the force exerted on the club? F a (1.810 2 k/h) 1 000 1 k 1 h 36 00 s 1 s (45 ) 1 k 1000 4.510 3 (1.010 5 /s 2 ) c. What is the force exerted on the club by the ball? F ball F club 4.510 3 10. A packae of instruents is attached to a heliu-filled weather balloon that exerts an upward force of 45. a. If the instruent packae weihs 10.0 k, will the balloon be able to lift it? F lift a a F lift 45 10. 0 k 4.5 /s 2 (0.50 s) 100 0 s The balloon cannot lift the packae because the upward acceleration is less than the downward acceleration of ravity, 9.80 /s 2. Alternative calculation: F ravity (10.0 k)(9.80 /s 2 ) 98.0, which exceeds the upward force b. What is the upward acceleration if the instruents weih 2.0 k? F lift F ravity a Physics: Principles and Probles Suppleental Probles 77
Chapter 4 continued a 2 5.4 2.0 k 45 (2.0 k)(9.80 /s 2 ) 25.4 13 /s 2 upward 11. A 12-k block sits on a table. A 10.0-k block sits on top of the 12-k block. If there is nothin on top of the 10.0-k block, what is the force that the table exerts on the 12-k block? F table F block 1 F block 2 (12 k)(9.80 /s 2 ) (10.0 k)(9.80 /s 2 ) 220 12. A box experiences a net force of 41 while it is bein lifted. What is the acceleration of the box? a a 4.2 /s 2 13. A rope can withstand 1.00010 3 of tension. If the rope is bein used to pull a 10.0-k packae across a frictionless surface, what is the reatest acceleration that will not break the rope? F a a F 41 9.7 k 1.0 0010 3 10. 0 k 1.0010 2 /s 2 14. A 0.100-k weiht is attached to a sprin scale. Find the readin on the scale for each of the followin situations. a. When the scale is not ovin. F (0.100 k)(9.80 /s 2 ) 0.980 b. When the scale accelerates at 2.4 /s 2 in the horizontal direction. The vertical coponent of the acceleration is zero, so the readin on the scale is calculated the sae way as when the scale is not ovin. F (0.100 k)(9.80 /s 2 ) 0.980 15. A penny is dropped fro the top of a 30.0--tall tower. The tower, however, is not located on Earth. The penny has a ass of 2.5 and experiences a ravitational force of 0.028. a. What is acceleration due to ravity on this planet? a F 0.028 0.0025 k 11 /s 2 b. After 1.00 s, the penny has a velocity of 10.1 /s. Assuin the force exerted on the penny by air resistance is unifor and independent of speed, what is the anitude of the force of air resistance on the penny? a F (F a ) F a F a, where a a v t F v t Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. 78 Suppleental Probles Physics: Principles and Probles
Chapter 4 continued F v f v i t 0.028 (0.0025 k) 10.1 /s 0.0 /s 1.00 s 0.0028 The air resistance is in the opposite direction fro the force of ravity and the penny s otion, as it should be. 16. The cobined ass of a sled and its rider is 46.4 k. The sled is pulled across a frozen lake so that the force of friction between the sled and the ice is very sall. a. Assuin that friction between the sled and the ice is neliible, what force is required to accelerate the sled at 3.45 /s 2? F a (46.4 k)(3.45 /s 2 ) 1.6010 2 b. A force of 150.0 is applied to the sled and produces an acceleration of 3.00 /s 2. What is the anitude of the force of friction that resists the acceleration? a F applied a F applied F applied a 150.0 (46.4 k)(3.00 s 2 ) 10.8 Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. Physics: Principles and Probles Suppleental Probles 79
Chapter 5 1. A sall plane takes off and flies 12.0 k in a direction southeast of the airport. At this point, followin the instructions of an air traffic controller, the plane turns 20.0 to the east of its oriinal fliht path and flies 21.0 k. What is the anitude of the plane s resultant displaceent fro the airport? E A R B R 2 A 2 B 2 2AB cos R (12.0 k) 2 (21.0 k) 2 2.0 2(1)(21.0 k os k)(c0.0 ) 16 32.5 k 2. A haer slides down a roof that akes a 32.0 anle with the horizontal. What are the anitudes of the coponents of the haer s velocity at the ede of the roof if it is ovin at a speed of 6.25 /s? y 32.0 v y 58.0 Fourth quadrant: v x 0 and v y 0. v x v cos (6.25 /s)(cos 32.0 ) 5.30 /s v y v sin (6.25 /s)(sin 32.0 ) 3.31 /s v x v x Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. 80 Suppleental Probles Physics: Principles and Probles
Chapter 5 continued 3. A worker has to ove a 17.0-k crate alon a flat floor in a warehouse. The coefficient of kinetic friction between the crate and the floor is 0.214. The worker pulls horizontally on a rope attached to the crate, with a 49.0- force. What is the resultant acceleration of the crate? F x-direction:, x F p a x a k k a F p k a F p k 49.0 (0.214)(17.0 k)(9.80 /s 2 ) 17.0 k 0.785 /s 2 4. To et a cart to ove, two farers pull on ropes attached to the cart, as shown below. One farer pulls with a force of 50.0 in a direction 35.0 east of north, while the other exerts a force of 30.0 in a direction 25.0 west of north. What are the anitude and the direction of the cobined force exerted on the cart? Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. R x A x B x A cos 1 B cos 2 R y A y B y A sin 1 B sin 2 R R 2 x R 2 y (A s co 1 B cos 2 ) 2 (A sinb 1 sin 2 ) 2 ((50.0 s )(co ) 55.00.0 (3(cos ) 15.0 ) 1) (50.0 2 ( )(sin ) 55.0 0.0 (3(sin ) 15.0 ) 1) 2 70.0 tan 1 R R y tan 1 x A sin 1 B sin 2 A cos 1 B cos 2 25.0 35.0 E tan 1 76.8 (50.0 )(sin 55.0 ) (30.0 )(sin 115.0 ) (50.0 )(cos 55.0 ) (30.0 )(cos 115.0 ) R 70.0 at 76.8 north of east Physics: Principles and Probles Suppleental Probles 81
Chapter 5 continued 5. Takashi trains for a race by rowin his canoe on a lake. He starts by rowin alon a straiht path. Then he turns and rows 260.0 west. If he then finds he is located 360.0 exactly north of his startin point, what was his displaceent alon the straiht path? R B A E x-direction: F p a a 0 (since v constant) F p 0 F p k k F k F F p 45.0 235 0.191 7. A rod supports a 2.35-k lap, as shown below. R x 0.0, R y 360.0 B x 260.0, B y 0.0 R A B, A R B A x R x B x 0.0 (260.0 ) 260.0 A y R y B y 360.0 0.0 360.0 A A 2 x A 2 y (260.0 ) 2 0 (360. ) 2 444.1 tan 1 A A y x tan 1 3 60. 0 260. 0 54.16 A 444.1 at 54.16 north of east 6. Mira received a 235- sled for her birthday. She takes the sled out to a flat snowy field. When she pushes it with a 45.0- horizontal force, it slides alon at a constant speed. What is the coefficient of kinetic friction between the sled and the snow? F a. What is the anitude of the tension in the rod? T y F T sin T s in (2.35 k)(9.80 /s 2 ) sin 25.0 54.5 b. Calculate the coponents of the force that the bracket exerts on the rod. x-direction: T x F x 0 F x T cos 25.0 (54.5 )(cos 25.0 ) F x 49.4, inward Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. 82 Suppleental Probles Physics: Principles and Probles
Chapter 5 continued F y T y (2.35 k)(9.80 /s 2 ) F y 23.0, upward 8. A 25.0-k crate has an adjustable handle so that it can be pushed or pulled by the handle at various anles. Deterine the acceleration of the crate for each situation shown in the diara, iven that the coefficient of slidin friction between the floor and the botto of the crate is 0.20. For (a) F F 70.0 at 0.0 25.0 k (a) F 70.0 at 330.0 (b) F 70.0 at 30.0 x-direction:, x F p, x a x a (c) Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. a F p k k a F p k a F p k F p k 70. 0 (0.20)(9.80 /s 2 ) 2 5. 0 k 0.84 /s 2 For (b) F F y F sin x-direction:, x F p, x a x a a F p Physics: Principles and Probles Suppleental Probles 83
Chapter 5 continued F p F cos k k ( F sin ), x F cos k ( F sin ) a a k (70.0 )(cos 30.0 ) (0.20)(70.0 )(sin 30.0 ) (0.20)(9.80 /s 2 ) 25.0 k 0.18 /s 2 For (c) F F y F sin x-direction:, x F p, x a x a F cos k ( F sin ) F cos k F sin a F p F p F cos k k ( F sin ), x F cos k ( F sin ) a a F cos k ( F sin ) F cos k F sin k (70.0 )(cos 30.0 ) (0.20)(70.0 )(sin 30.0 ) (0.20)(9.80 /s 2 ) 25.0 k 0.74 /s 2 Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. 84 Suppleental Probles Physics: Principles and Probles
Chapter 5 continued 9. A child shoves a sall toboan weihin 100.0 up a snowy hill, ivin the toboan an initial speed of 6.0 /s. If the hill is inclined at an anle of 32 above the horizontal, how far alon the hill will the toboan slide? Assue that the coefficient of slidin friction between the toboan and the snow is 0.15., y a y 0 F y 0 F y cos x-direction:, x a x a F x sin F x a k k cos sin k cos a a (sin k cos ) v f 2 v i 2 2a(d f d i ) 0 v i 2 2ad Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. 2 i d v 2a 4.6, up the hill v i 2 2(sin k cos ) (6.0 /s 2 ) (2)(9.80 /s 2 )(sin 32 (0.15)cos 32 ) 10. Two objects are connected by a strin passin over a frictionless, assless pulley. As shown below, the block is on an inclined plane and the ball is hanin over the top ede of the plane. The block has a ass of 60.0 k, and the coefficient of kinetic friction between the block and the inclined plane is 0.22. If the block oves at a constant speed down the incline, and the ball rises at a constant speed, what is the ass of the hanin ball? 1 35.0 2 Physics: Principles and Probles Suppleental Probles 85
Chapter 5 continued v is constant, so there is no acceleration. Ball ( 2 ):, y 2 a y 0 F T F 0 F T 2 Block ( 1 ): (parallel to the incline), y 1 a y 0 F y 0 F y 1 cos k k 1 cos x-direction: (perpendicular to the incline), x 1 a x 0 F x F T 0 F x 1 sin 1 sin k 1 cos F T 0 1 sin k 1 cos 2 0 2 1 sin k 1 cos 1 sin k 1 cos (60.0 k)(sin 35.0 ) (0.22)(60.0 k)(cos 35.0 ) 24 k Copyriht Glencoe/McGraw-Hill, a division of The McGraw-Hill Copanies, Inc. 86 Suppleental Probles Physics: Principles and Probles