Answer Key 4 b. Two chains connected to the load each Chapter can withstand a tension of 15,000 N. 1. You and your bike have a combined mass Can the load be safely lifted at 1.5 m/s 2? ϭ ϩ of 80 kg. How much braking force has to Fload Flift Fovercome gravity be applied to slow you from a velocity of ϭ ma ϩ mg 5 m/s to a complete stop in 2 s? ϭ (1.5 ϫ10 3 kg)(1.5 m/s 2) ϩ v Ϫ v Ϫ 3 2 a ϭ ᎏf ᎏi ϭ ᎏᎏᎏ0.0 m/s 5.0 m/s (1.5 ϫ10 kg)(9.80 m/s ) t Ϫ t 2.0 s Ϫ 0.0 s f i ϭ 2.25 ϫ10 3 N ϩ 1.47 ϫ10 4 N ϭ 2.5 m/s 2 ϭ 1.7 ϫ10 4 N F ϭ ma The load can be safely lifted ϭ ϫ Ϫ 2 80 kg ( 2.5 m/s ) because the total force on the ϭ Ϫ 200 N chains is less than their combined 4 2. Before opening his parachute, a sky diver capability of 3.0 ϫ10 N with a mass of 90.0 kg experiences an 4. In a lab experiment, you attach a 2.0-kg upward force from air resistance of 150 N. weight to a spring scale. You lift the scale a. What net force is acting on the sky diver? and weight with a constant reading of ϭ 22.5 N. Fgravity mg a. What is the value and direction of the ϭ 90.0 kg ϫ 9.80 m/s 2 acceleration on the weight? ϭ 882 N downward ϭ Ϫ Fnet Fscale Fgravity F ϭ F ϩ F net air resistance gravity ϭ 22.5 N Ϫ (2.0 kg)(9.80 m/s 2) F ϭ 150 N ϩ (Ϫ882 N) net ϭ 2.9 N upward ϭ Ϫ 732 N ϭ 730 N downward a ϭ ᎏmᎏ Fnet b. What is the sky diver’s acceleration? 2.0 kg F ϭ ᎏᎏ a ϭ ᎏnetᎏ 2.9 N m ϭ 0.69 m/s 2 Ϫ730 N ϭ ᎏᎏ Ϫ 90 .0 kg ϭ 6.9 ϫ10 1 m/s 2 McGraw-Hill McGraw-Hill Companies, Inc. ϭ Ϫ 8.1 m/s 2 b. How far do you lift the weight in the ϭ 8.1 m/s 2 downward first 2.0-s interval? d ϭ d ϩ v t ϩ ᎏ1ᎏat 2 3. A large helicopter is used to lift a heat f i i 2 pump to the roof of a new building. The ϭ 0 m ϩ (0 m/s)(2.0 s) ϩ mass of the helicopter is 5.0 ϫ10 3 kg and ᎏ1ᎏ(6.9 ϫ10 Ϫ1 m/s 2)(2.0 s) 2 the mass of the heat pump is 1500 kg. 2 a. How much force must the air exert on ϭ 1.4 m the helicopter to lift the heat pump with an acceleration of 1.5 m/s 2? 5. As a large jet flies at a constant altitude, its engines produce a forward thrust of Copyright Copyright © Glencoe/McGraw-Hill, a division of The F ϭ F ϩ F net lift overcome gravity 8.4 ϫ10 5 N. The mass of the plane is ϭ ma ϩ mg 2.6 ϫ10 5 kg. ϭ (6.5 ϫ10 3 kg)(1.5 m/s 2) ϩ (6.5 ϫ10 3 kg )(9.80 m/s 2) ϭ 7.3 ϫ10 4 N upward Physics: Principles and Problems Supplemental Problems Answer Key 75 Answer Key Chapter 4 continued a. What is the forward acceleration of the b. How long does it take for the 2.0-kg plane, ignoring air resistance? mass to fall to the floor? ϭ F ma Solve d ϭ d ϩ v t ϩ ᎏ1ᎏat 2 for t f i i 2 a ϭ ᎏFᎏ ϭ ϭ m while di 0 m, vi 0 m/s ϫ 5 ϭ ᎏ8.4 1ᎏ0 N t ϭ ᎏ2dᎏ 2.6ϫ105 kg Ί๶a ϭ 2 (2)(1 .5 m) 3.2 m/s ϭ ᎏᎏ Ί๶๶2 b. How much upward force must the air 4.2 m/s exert on the plane when it is flying ϭ 0.85 s horizontally? 7. A man is standing on a scale inside an Because the plane is not changing airplane. When the airplane is traveling altitude, horizontally (in other words, the vertical ϭ ϭ Ϫ Fnet 0, so Flift Fgravity acceleration of the plane is zero) the ϭ Ϫ scale reads 705.6 N. What is the vertical Flift Fgravity acceleration of the plane in each of the ϭ Ϫ ϫ 5 Ϫ 2 (2.6 10 kg)( 9.80 m/s ) following situations? ϭ 2.5 ϫ10 6 N a. When the scale reads 950.0 N. ϭ 6. Two masses are tied to a rope on a pulley, Fg mg as shown below. F m ϭ ᎏg g F ϭ ma Frictionless pulley net ϭ ϩ Ϫ Fnet Fscale ( Fg) Copyright Copyright © Glencoe/McGraw-Hill, a division of The ma ϭ F Ϫ F 2.0 kg 0.8 kg scale g F Ϫ F a ϭ ᎏᎏscale g m 1.5 m F Ϫ F ϭ ᎏᎏscale g F ΂ᎏᎏg ΃ a. When the system is released from this g position, what is the acceleration of the g(F Ϫ F ) ϭ ᎏᎏscale g 2.00-kg mass? Fg F ϭ F Ϫ F ϩ (9.80 m/s 2)(950.0 N Ϫ 705.6 N) McGraw-Hill Companies, Inc. net g-large g-small ϭ ᎏᎏᎏᎏ Ϫ mlarge g msmall g 705.6 N ϭ (2.00 kg)(9.80 m/s 2) Ϫ ϭ 3.39 m/s 2 (0.80 kg)(9.80 m/s 2) b. When the scale reads 500.0 N. ϭ ϭ 11.8 N downward Fg mg F F a ϭ ᎏᎏ m ϭ ᎏᎏg m g ϭ ᎏ11.8 N F ϭ ma 2.8 kg net F ϭ F ϩ (ϪF ) ϭ 4.2 m/s 2 downward net scale g 76 Supplemental Problems Answer Key Physics: Principles and Problems Answer Key Chapter 4 continued ϭ Ϫ ma Fscale Fg a. What is the average acceleration on the 2 Ϫ ball as it was struck (in m/s )? Fscale Fg a ϭ ᎏᎏ v Ϫ v m ϭ ᎏf ᎏi ϭ a , where vi 0 km/h Ϫ t Fscale Fg ϭ ᎏᎏ 100 0 m 1 h F (1.8 ϫ10 2 km/h) ᎏᎏ ᎏᎏ ᎏᎏg ΂ 1 km ΃΂ 36 00 s΃ ΂ g ΃ a ϭ ᎏᎏᎏ (0.50 ms) ᎏ1 ᎏs g(F Ϫ F ) ΂100 0 ms ΃ ϭ ᎏsca leᎏg Fg ϭ ᎏ50 mᎏ/s 5.0 ϫ10Ϫ4 s (9.80 m/s 2)(500.0 N Ϫ 705.6 N) ϭ ᎏᎏᎏᎏ ϭ 1.0 ϫ10 5 m/s 2 705.6 N b. What is the force exerted on the club? ϭ Ϫ 2.86 m/s 2 F ϭ ma 8. An airboat glides across the surface of the 1 kg ϭ (45 g) ᎏᎏ ϫ (1.0 ϫ10 5 m/s 2) water on a cushion of air. Perform the ΂100 0 g΃ following calculations for a boat in which ϭ 4.5 ϫ10 3 N the mass of the boat and passengers is 450 kg. c. What is the force exerted on the club by a. If there is no friction, how much force the ball? ϭ Ϫ must the propeller fan exert on the air Fball Fclub to accelerate the boat at 5.00 m/s 2? ϭ Ϫ 4.5 ϫ10 3 N F ϭ ma 10. A package of instruments is attached to a 2 ϭ (450 kg)(5.00 m/s ) helium-filled weather balloon that exerts an ϭ 2.2 ϫ10 3 N upward force of 45 N. b. If the actual acceleration with the fan a. If the instrument package weighs 10.0 kg, generating the force calculated in part a will the balloon be able to lift it? 2 ϭ is only 4.95 m/s , how much friction Flift ma does the air cushion exert on the boat? F a ϭ ᎏliftᎏ ϭ Ϫ m afriction aideal aactual McGraw-Hill McGraw-Hill Companies, Inc. ϭ 45 N Ffriction ma friction ϭ ᎏᎏ Ϫ 10 .0 kg m(aideal aactual )(450 kg) ϭ 4.5 m/s 2 ϭ (5.00 m/s 2 Ϫ 4.95 m/s 2) The balloon cannot lift the package ϭ 22 N because the upward acceleration is c. What is the upward force exerted by the less than the downward acceleration air cushion on the boat? of gravity, 9.80 m/s 2. ϭ Ϫ ϭ Ϫ Flift Fgravity mg Alternative calculation: ϭ Ϫ Ϫ 2 ϭ 2 (450 kg)( 9.80 m/s ) Fgravity (10.0 kg)(9.80 m/s ) 3 ϭ Copyright Copyright © Glencoe/McGraw-Hill, a division of The ϭ 4.4 ϫ10 N 98.0 N, which exceeds the upward force 9. A golf ball with a mass of 45 g is struck by a club, leaving the tee with a speed of b. What is the upward acceleration if the 1.8 ϫ10 2 km/h. The period of acceleration instruments weigh 2.0 kg? ϭ Ϫ was 0.50 m/s. Fnet Flift Fgravity ϭ Ϫ Fnet ma mg Physics: Principles and Problems Supplemental Problems Answer Key 77 Answer Key Chapter 4 continued ϭ 45 N Ϫ (2.0 kg)(9.80 m/s 2) 14.