Holt Physics : Problem Workbook with Answers PDF
Preview Holt Physics : Problem Workbook with Answers
PROBLEM WORKBOOK Holt Physics Problem Workbook This workbook contains additional worked-out samples and practice problems for each ofthe problem types from the Holt Physicstext. Contributing Writers Boris M.Korsunsky Physics Instructor Science Department Northfield Mount Hermon School Northfield,MA Angela Berenstein Science Writer Urbana,IL John Stokes Science Writer Socorro,NM Cover Photo:Lawrence Manning/CORBIS Cover Design:Jason Wilson Copyright © by Holt,Rinehart and Winston All rights reserved.No part ofthis publication may be reproduced or transmitted in any form or by any means,electronic or mechanical,including photocopy, recording,or any information storage and retrieval system,without permission in writing from the publisher. Teachers using HOLT PHYSICS may photocopy blackline masters in complete pages in sufficient quantities for classroom use only and not for resale. Printed in the United States ofAmerica ISBN 0-03-057337-8 1 2 3 4 5 6 095 05 04 03 02 01 Contents Section Title Page Sample and Practice 1A Metric Prefixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Sample and Practice 2A Average Velocity and Displacement . . . . . . . . . . . . . . . . . . . . . . . 3 Sample and Practice 2B Average Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Sample and Practice 2C Displacement with Constant Acceleration. . . . . . . . . . . . . . . . 7 Sample and Practice 2D Velocity and Displacement with Constant Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Sample and Practice 2E Final Velocity After Any Displacement . . . . . . . . . . . . . . . . . . 12 Sample and Practice 2F Falling Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Sample and Practice 3A Finding Resultant Magnitude and Direction. . . . . . . . . . . 16 Sample and Practice 3B Resolving Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Sample and Practice 3C Adding Vectors Algebraically. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Sample and Practice 3D Projectiles Launched Horizontally. . . . . . . . . . . . . . . . . . . . . . . 22 Sample and Practice 3E Projectiles Launched at an Angle . . . . . . . . . . . . . . . . . . . . . . . . 24 Sample and Practice 3F Relative Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Sample and Practice 4A Net External Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Sample and Practice 4B Newton’s Second Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Sample and Practice 4C Coefficients ofFriction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Sample and Practice 4D Overcoming Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Sample and Practice 5A Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Sample and Practice 5B Kinetic Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 d. ve Sample and Practice 5C Work-Kinetic Energy Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . 44 er s s re Sample and Practice 5D Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 ht All rig Sample and Practice 5E Conservation ofMechanical Energy. . . . . . . . . . . . . . . . . . . . . 50 n. Sample and Practice 5F Power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 o st n Wi nd Sample and Practice 6A Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 a art Sample and Practice 6B Force and Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 h e n Ri Sample and Practice 6C Stopping Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Holt, Sample and Practice 6D Conservation ofMomentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 y b © Sample and Practice 6E Perfectly Inelastic Collision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 ht g yri Sample and Practice 6F Kinetic Energy in Perfectly p Co Inelastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Sample and Practice 6G Elastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Sample and Practice 7A Angular Displacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Sample and Practice 7B Angular Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Contents iii Section Title Page Sample and Practice 7C Angular Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Sample and Practice 7D Angular Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Sample and Practice 7E Tangential Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Sample and Practice 7F Tangential Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Sample and Practice 7G Centripetal Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Sample and Practice 7H Force That Maintains Circular Motion. . . . . . . . . . . . . . . . . . 81 Sample and Practice 7I Gravitational Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Sample and Practice 8A Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Sample and Practice 8B Rotational Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Sample and Practice 8C Newton's Second Law for Rotation. . . . . . . . . . . . . . . . . . . . . . . 91 Sample and Practice 8D Conservation ofAngular Momentum. . . . . . . . . . . . . . . . . . . 94 Sample and Practice 8E Conservation ofMechanical Energy. . . . . . . . . . . . . . . . . . . . . 96 Sample and Practice 9A Buoyant Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Sample and Practice 9B Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Sample and Practice 9C Pressure as a Function ofDepth. . . . . . . . . . . . . . . . . . . . . . . . 102 Sample and Practice 9D Bernoulli’s Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Sample and Practice 9E Gas Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Sample and Practice 10A Temperature Conversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Sample and Practice 10B Conservation ofEnergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Sample and Practice 10C Calorimetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Sample and Practice 10D Heat ofPhase Change. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Sample and Practice 11A Work Done on or by a Gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 d. Sample and Practice 11B The First Law ofThermodynamics. . . . . . . . . . . . . . . . . . . . . 116 ve er s Sample and Practice 11C Heat-Engine Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 s re ht g Sample and Practice 12A Hooke’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 All ri n. o Sample and Practice 12B Simple Harmonic Motion ofa Simple Pendulum . . . . 121 nst Wi Sample and Practice 12C Simple Harmonic Motion ofa Mass-Spring System. . 122 nd a Sample and Practice 12D Wave Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 art h e n Ri Sample and Practice 13A Intensity ofSound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 olt, H y Sample and Practice 13B Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 b © ht g yri Sample and Practice 14A Electromagnetic Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 op C Sample and Practice 14B Concave Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Sample and Practice 14C Convex Mirrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 iv Contents Section Title Page Sample and Practice 15A Snell’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Sample and Practice 15B Lenses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Sample and Practice 15C Critical Angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Sample and Practice 16A Interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Sample and Practice 16B Diffraction Gratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Sample and Practice 17A Coulomb’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Sample and Practice 17B The Superposition Principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Sample and Practice 17C Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Sample and Practice 17D Electric Field Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Sample and Practice 18A Electrical Potential Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Sample and Practice 18B Potential Difference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Sample and Practice 18C Capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Sample and Practice 19A Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Sample and Practice 19B Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Sample and Practice 19C Electric Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Sample and Practice 19D Cost ofElectrical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Sample and Practice 20A Resistors in Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Sample and Practice 20B Resistors in Parallel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Sample and Practice 20C Equivalent Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Sample and Practice 20D Current in and Potential Difference Across a Resistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 d. e erv Sample and Practice 21A Particle in a Magnetic Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 s e s r Sample and Practice 21B Force on a Current-Carrying Conductor . . . . . . . . . . . . . . 176 ht g All ri n. Sample and Practice 22A Induced emfand Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 o Winst Sample and Practice 22B Induction in Generators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 nd Sample and Practice 22C rms Currents and Potential Differences. . . . . . . . . . . . . . . 182 a hart Sample and Practice 22D Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 e n Ri Holt, Sample and Practice 23A Quantum Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 y b © Sample and Practice 23B The Photoelectric Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 ht yrig Sample and Practice 23C De Broglie Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 p o C Sample and Practice 25A Binding Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Sample and Practice 25B Nuclear Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Sample and Practice 25C Measuring Nuclear Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Contents v NAME ______________________________________ DATE _______________ CLASS ____________________ Holt Physics Problem 1A METRIC PREFIXES PROBLEM In Hindu chronology,the longest time measure is apara.One paraequals 311 040 000 000 000 years.Calculate this value in megahours and in nanoseconds.Write your answers in scientific notation. SOLUTION Given: 1 para =311 040 000 000 000 years Unknown: 1 para =? Mh 1 para =? ns Express the time in years in terms ofscientific notation.Then build conversion factors from the relationships given in Table 1-3. 1 para =3.1104 ×1014 years 365.25days 24h 1Mh × × 1year 1day 1×106h 365.25days 24h 3600s 1ns × × × 1year 1day 1h 1×10−9s Convert from years to megahours by multiplying the time by the first conversion expression. 365.25days 24h 1Mh 1 para =3.1104 ×1014 years × × × 1year 1day 1×106h = 2.7266 ×1012Mh k. o o b s Convert from years to nanoseconds by multiplying the time by the second con- hi n t version expression. er i g earli 1 para =3.1104 ×1014 years × 3651.2y5eadrays × 124dahy × 3610h0s × 1×11n0s−9s n peari = 9.8157 ×1030ns p a e c oti n er d n d u ADDITIONAL PRACTICE e ht g yri p 1. One light-year is the distance light travels in one year.This distance is o c al equal to 9.461 ×1015m.After the sun,the star nearest to Earth is Alpha eri at Centauri,which is about 4.35 light-years from Earth.Express this dis- m W tance in R H a. megameters. b. picometers. Problem 1A 1 NAME ______________________________________ DATE _______________ CLASS ____________________ 2. It is estimated that the sun will exhaust all ofits energy in about ten billion years.By that time,it will have radiated about 1.2 ×1044J (joules) ofenergy.Express this amount ofenergy in a. kilojoules. b. nanojoules. 3. The smallest living organism discovered so far is called a mycoplasm.Its mass is estimated as 1.0 ×10–16g.Express this mass in a. petagrams. b. femtograms. c. attograms. 4. The “extreme”prefixes that are officially recognized are yocto,which in- –24 dicates a fraction equal to 10 ,and yotta,which indicates a factor equal 24 to 10 .The maximum distance from Earth to the sun is 152 100 000 km. Using scientific notation,express this distance in a. yoctometers (ym). b. yottameters (Ym). 5. In 1993,the total production ofnuclear energy in the world was 2.1 ×1015watt-hours,where a watt is equal to one joule (J) per second. Express this number in a. joules. b. gigajoules. 6. In Einstein’s special theory ofrelativity,mass and energy are equivalent. An expression ofthis equivalence can be made in terms ofelectron volts (units ofenergy) and kilograms,with one electron volt (eV) being equal to 1.78 ×10–36kg.Using this ratio,express the mass ofthe heaviest mammal on earth,the blue whale,which has an average mass of 1.90 ×105 kg,in ok. o b a. mega electron volts. his b. tera electron volts. er in t 7. The most massive star yet discovered in our galaxy is one ofthe stars earli g n in the Carina Nebula,which can be seen from Earth’s Southern ari e Hemisphere and from the tropical latitudes ofthe Northern Hemisphere. pp a The star,designated as Eta Carinae,is believed to be 200 times as massive ce as the sun,which has a mass ofnearly 2 ×1030kg.Find the mass ofEta er noti d Carinae in n u d a. milligrams. hte g b. exagrams. yri p o c 8. The Pacific Ocean has a surface area ofabout 166 241 700 km2and an al eri average depth of3940 m.Estimate the volume ofthe Pacific Ocean in at m W a. cubic centimeters. R H b. cubic millimeters. 2 Holt Physics Problem Workbook NAME ______________________________________ DATE _______________ CLASS ____________________ Holt Physics Problem 2A AVERAGE VELOCITY AND DISPLACEMENT PROBLEM The fastest fish,the sailfish,can swim 1.2 ×102km/h.Suppose you have a friend who lives on an island 16 km away from the shore.Ifyou send a message using a sailfish as a messenger,how long will it take for the message to reach your friend? SOLUTION Given: v =1.2 ×102km/h avg ∆x =16 km Unknown: ∆t=? Use the definition ofaverage speed to find ∆t. ∆x v = avg ∆t Rearrange the equation to calculate ∆t. ∆x ∆t = v avg 16 km 16km ∆t= = (cid:2) km(cid:3)(cid:2) 1h (cid:3) 2.0km/min 1.2 ×102 h 60min = 8.0 min k. o o b s hi n t ADDITIONAL PRACTICE er i arli g e 1. The Sears Tower in Chicago is 443 m tall.Joe wants to set the world’s n ari stair climbing record and runs all the way to the roofofthe tower.IfJoe’s e p ap average upward speed is 0.60 m/s,how long will it take Joe to climb from e otic street level to the roofofthe Sears Tower? n der 2. An ostrich can run at speeds ofup to 72 km/h.How long will it take an n u d ostrich to run 1.5 km at this top speed? e ht g yri 3. A cheetah is known to be the fastest mammal on Earth,at least for short p al co runs.Cheetahs have been observed running a distance of5.50 ×102m eri with an average speed of1.00 ×102km/h. at m W a. How long would it take a cheetah to cover this distance at this speed? R H b. Suppose the average speed ofthe cheetah were just 85.0 km/h. What distance would the cheetah cover during the same time inter- val calculated in (a)? Problem 2A 3 NAME ______________________________________ DATE _______________ CLASS ____________________ 4. A pronghorn antelope has been observed to run with a top speed of 97 km/h.Suppose an antelope runs 1.5 km with an average speed of 85 km/h,and then runs 0.80 km with an average speed of67 km/h. a. How long will it take the antelope to run the entire 2.3 km? b. What is the antelope’s average speed during this time? 5. Jupiter,the largest planet in the solar system,has an equatorial radius of about 7.1 ×104km (more than 10 times that ofEarth).Its period ofro- tation,however,is only 9 h,50 min.That means that every point on Jupiter’s equator “goes around the planet”in that interval oftime.Calcu- late the average speed (in m/s) ofan equatorial point during one period ofJupiter’s rotation.Is the average velocity different from the average speed in this case? 6. The peregrine falcon is the fastest offlying birds (and,as a matter offact, is the fastest living creature).A falcon can fly 1.73 km downward in 25 s. What is the average velocity ofa peregrine falcon? 7. The black mamba is one ofthe world’s most poisonous snakes,and with a maximum speed of18.0 km/h,it is also the fastest.Suppose a mamba waiting in a hide-out sees prey and begins slithering toward it with a velocity of+18.0 km/h.After 2.50 s,the mamba realizes that its prey can move faster than it can.The snake then turns around and slowly returns to its hide-out in 12.0 s.Calculate a. the mamba’s average velocity during its return to the hideout. b. the mamba’s average velocity for the complete trip. c. the mamba’s average speed for the complete trip. 8. In the Netherlands,there is an annual ice-skating race called the “Tour of the Eleven Towns.”The total distance ofthe course is 2.00 ×102km,and the record time for covering it is 5 h,40 min,37 s. k. o o a. Calculate the average speed ofthe record race. b s hi b. Ifthe first halfofthe distance is covered by a skater moving with n t a speed of1.05v,where v is the average speed found in (a),how er i arli long will it take to skate the first half? Express your answer in hours g e n and minutes. ari e p p a e c oti n er d n u d e ht g yri p o c al eri at m W R H 4 Holt Physics Problem Workbook NAME ______________________________________ DATE _______________ CLASS ____________________ Holt Physics Problem 2B AVERAGE ACCELERATION PROBLEM In 1977 offthe coast ofAustralia,the fastest speed by a vessel on the water was achieved.Ifthis vessel were to undergo an average acceleration of 2 1.80 m/s ,it would go from rest to its top speed in 85.6 s.What was the speed ofthe vessel? SOLUTION Given: a =1.80 m/s2 avg ∆t =85.6 s v =0 m/s i Unknown: v =? f Use the definition ofaverage acceleration to find v. f ∆v v –v a = = f i avg ∆t ∆t Rearrange the equation to calculate v. f v = a ∆t +v f avg i (cid:2) (cid:3)(cid:2) (cid:3) m m v = 1.80 85.6 s +0 f 2 s s m = 154 s (cid:2) m(cid:3)(cid:2)3.60×103s(cid:3)(cid:2)1km(cid:3) ook. = 154 s 1h 103m b s hi n t km er i = 554 arli h e g n ari e p p a e c ADDITIONAL PRACTICE oti n er d un 1. Ifthe vessel in the sample problem accelerates for 1.00 min,what will d hte its speed be after that minute? Calculate the answer in both meters per g yri second and kilometers per hour. p o c al 2. In 1935,a French destroyer,La Terrible,attained one ofthe fastest eri at speeds for any standard warship.Suppose it took 2.0 min at a constant m W 2 acceleration of0.19 m/s for the ship to reach its top speed after start- R H ing from rest.Calculate the ship’s final speed. 3. In 1934,the wind speed on Mt.Washington in New Hampshire reached a record high.Suppose a very sturdy glider is launched in this wind,so that in 45.0 s the glider reaches the speed ofthe wind.Ifthe Problem 2B 5
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