Chapter 6: Work and Energy
Section: 6-1 Topic: Work Work and Kinetic Energy Type: Conceptual 1. A body body of ma ma m lide a ditance d along along a !ori"ontal !ori"ontal urface. #o$ muc! $ork i done by gra%ity& A' mgd (' "ero C' –mgd )' *ne cannot tell from t!e gi%en information. E' +one of t!ee i correct. An: ( Section: 6-1 Topic: Work Work and Kinetic Energy Type: Conceptual ,. A body body mo%e $it! $it! decreain decreaing g peed. W!ic! of t!e t!e follo$ing follo$ing tateme tatement nt i true& true& A' T!e T!e net net $or $ork don donee on on t!e t!e body body i po poiti iti%e %e and and t!e kine kineti ticc ene enerrgy i inc incrreai eaing ng.. (' T!e T!e net net $or $ork don donee on on t!e t!e body body i po poiti iti%e %e and and t!e kine kineti ticc ene enerrgy i dec decre rea aiing. ng. C' T!e T!e net net $or $ork don donee on on t!e t!e body body i "er "ero and and t!e t!e kine kinettic ener energy gy i decr decrea eai ing ng.. )' T!e T!e net net $or $ork don donee on on t!e t!e body body i nega negati ti%e %e and and t!e kine kineti ticc ene enerrgy i incr increa eai ing ng.. E' T!e T!e net net $or $ork don donee on on t!e t!e body body i nega negati ti%e %e and and t!e kine kineti ticc ene enerrgy i decr decrea eai ing ng.. An: E Section: 6-1 Topic: Work Work and Kinetic Energy Type: Conceptual . A block block lide lide a certain certain ditance ditance do$n do$n an incline. incline. T!e $ork done done by gra%ity gra%ity iW i W. W!at i t!e $ork done by gra%ity if t!i block lide t!e ame ditance up t!e incline& A' W (' "ero C' –W )' /ra%ity ca cannot do do $o $ork0 o ome ot ot!er fo force do doe t!e $o $ork. E' T!e $o $ork ca cannot not be be det deteermin mined un unle t! t!e di ditance nce tr tra%el %eled i i gi gi%en. An: C Section: 6-1 Topic: Work Work and Kinetic Energy Type: Conceptual . 2nitially 2nitially a body mo%e mo%e in one direction direction and !a kinetic kinetic energy energy K. K. T!en it mo%e in t!e oppoite direction $it! t!ree time it initial initial peed. W!at i t!e kinetic energy no$& A' K (' K C' 3 K )' 4 K E' 34 K An: ) Section: 6-1 Topic: Work Work and Kinetic Energy Type: 5actual . T!e S2 unit of of energy energy can be be e7preed e7preed a A' kg 8 m9 )' kg 8 m 8 , (' kg 8 m9, E' +one +one of of t!e t!ee e i corre correct ct.. C' m9kg 8 ' An: E Section: 6-1 Topic: Work Work and Kinetic Energy Type: +umerical 6. T!e a%erage a%erage marat!on marat!on runner can complete complete t!e ,.,-km ,.,-km ditance ditance of t!e marat!on marat!on in ! and ; min. 2f t!e runner< ma ma i = kg $!at i i t!e runner< a%erage kinetic energy during t!e run&
Page 1
Chapter 6: Work and Energy
An:
A' >, ? E
(' . ´ 1; ?
Section: 6-1
C' ,1 ?
)' 1,6 ?
Topic: Work Work and Kinetic Energy
E' ,1 ?
Type: +umerical
=.
A 6.;-kg block lide from point A do$n a frictionle cur%e to point (. After t!e block pae point ( a friction force oppoe t!e motion of t!e block o t!at it come to a top ,. m from (. Calculate t!e coefficient of kinetic friction bet$een t!e block and t!e urface after poition (. A' ,. (' ;.; C' @;.; )' ;.; + E' ,. + An: ( Section: 6-1 Topic: Work Work and Kinetic Energy Type: +umerical >. T!e $ork $ork e7pended e7pended to accelerat acceleratee a car from from ; to ; m9 A' i mo more t! t!an t!a t!att re reui uired to to ac accelerate it it fr from ; ; m9 m9 to to 6; 6; m9 m9. (' i eual ual to t!at !at reuired red to ac accel celerate it it from ; m9 to 6; 6; m9. C' i le le t! t!an t! t!at re reuired to to ac accelerate ate it it fr from ; ; m9 m9 to to 6; 6; m9 m9. )' can be be an any of of t!e pr preceding de depending on on t! t!e ti time ta taken. E' i decribed by none of t!ee tatement. An: C Section: 6-1 Topic: Work Work and Kinetic Energy Type: +umerical 4. T!e kinetic energy of a car i 1.;; ´ 1; ?. 2f t!e car< peed i increaed increaed by ,; percent t!e kinetic energy of t!e car become A' .;; ´ 1; ? (' 1.,; ´ 1; ? C' 1. ´ 1; ? )' 1.; ´ 1; ? E' unkn unkno$ o$n0 n0 t!e an an$er $er depe depend nd on t!e ma ma of t!e t!e car car $!ic! !ic! i not not gi%e gi%en. n. An: C Section: 6-1 Topic: Work Work and Kinetic Energy Type: +umerical 1;. A bullet $it! a ma of 1, g mo%ing !ori"ontally !ori"ontally trike a fi7ed block of $ood and penetrate a ditance of ., cm. T!e peed of t!e bullet But before t!e colliion i 6; m9. T!e a%erage force t!at t!e $ood e7erted on t!e bullet $a A' .= ´ 1; + (' = +
Page 2
Chapter 6: Work and Energy
C' )' E' An:
.= ´ 1;6 + unkno$n0 t!e ma of t!e $ood i reuired. +one of t!ee i correct. A
Section: 6-1 Topic: Work and Kinetic Energy Type: +umerical 11. A bullet $it! a ma of 1;.; g and an initial peed of >;; m9 penetrate .;; cm into a fi7ed block of $ood before topping. T!e a%erage force e7erted by t!e block on t!e bullet $a A' 16; + )' 6. ´ 1; + (' E' 6. ´ 1; + 1. ´ 1; + C' 1. ´ 1; + An: ) Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 1,. A -kg obBect lide do$n a frictionle urface inclined at an angle of ; from t!e !ori"ontal. T!e total ditance mo%ed by t!e obBect along t!e plane i 1; meter. T!e $ork done on t!e obBect by t!e normal force of t!e urface i A' "ero (' ;.; k? C' ;. k? )' ;.> k? E' ;., k? An: A Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 1. 2f you double t!e peed of an obBect it kinetic energy i A' t!e ame. (' doubled. C' tripled. )' uadrupled. E' !al%ed. An: ) Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 1. T!e $eig!t of an obBect on t!e moon i one-i7t! it $eig!t on t!e eart!. A body mo%ing $it! a gi%en peed on t!e moon !a kinetic energy eual to DDDDDDDDDDDDDD it $ould !a%e if it $ere mo%ing at t!e ame peed on t!e eart!. A' t!e kinetic energy )' 6 time t!e kinetic energy (' 196 t!e kinetic energy E' 6 time t!e kinetic energy C' 196 t!e kinetic energy An: A Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 1. A force F pu!e a block along a !ori"ontal urface againt a force of friction F . 2f f t!e block undergoe a diplacement s at contant %elocity t!e $ork done by t!e reultant force on t!e block A' i eual to t!e $ork done by t!e force of friction F f . (' i gi%en by W F 8 s . C' )' E' An:
increae t!e kinetic energy of t!e block. increae t!e potential energy of t!e block. i "ero. E
Page 3
Chapter 6: Work and Energy
Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 16. +egati%e $ork mean A' t!e kinetic energy of t!e obBect increae. (' t!e applied force i %ariable. C' t!e applied force i perpendicular to t!e diplacement. )' t!e applied force i oppoite to t!e diplacement. E' not!ing0 t!ere i no uc! t!ing a negati%e $ork. An: ) Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 1=. A particle mo%e !alf$ay around a circle of radiu R. 2t i acted on by a radial force of magnitude F. T!e $ork done by t!e radial force i A' "ero (' FR C' F p R )' , FR E' ,p R An: A Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 1>. 2f mec!anical $ork i done on a body t!e body mut A' accelerate. )' !a%e no friction force e7erted on it. (' be in euilibrium. E' mo%e. C' not e7ert any force. An: E Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual 14. A %ariable force i repreented on an F -%eru- x grap!. W!ic! of t!e follo$ing i t!e $ork done by t!i force& A' t!e lope of t!e cur%e (' t!e area bounded by t!e cur%e and t!e x a7i C' t!e area bounded by t!e cur%e and t!e F a7i )' t!e F %alue multiplied by t!e x %alue E' t!e F %alue di%ided by t!e x %alue An: ( Section: 6-1 Topic: Work and Kinetic Energy Type: Conceptual ,;. T$o kier tart at t!e ame place and fini! at t!e ame place. Skier A take a traig!t moot! route to t!e fini! $!erea Skier ( take a cur%y bumpy route to t!e fini!. 2f you aume t!at friction i negligible $!ic! of t!e follo$ing tatement i true& A' Skier A !a t!e ame peed a kier ( at t!e fini!. (' Skier ( !a t!e greater peed at t!e fini!. C' Skier A !a t!e greater peed at t!e fini! becaue t!e route i traig!t. )' Skier A !a t!e greater peed at t!e fini! becaue t!e route i moot!. E' Skier A !a t!e greater peed at t!e fini! becaue t!e route i bot! traig!t and moot!. An: A Section: 6-1
Topic: Work and Kinetic Energy
Page 4
Type: +umerical
Chapter 6: Work and Energy
,1. A particle t!at i ubBected to a %ariable force tra%el a ditance of ,; m in a traig!t line in t!e ame direction a t!e force. T!e force %arie a follo$: 5irt .; m and F ;. +e7t .; m and F .; +. +e7t .; m and F 6.; +. Fat .; m and F decreae uniformly from 6.; + to "ero.
An:
W!at $a t!e total $ork done by t!i force during t!e full ,;-m trip& A' 1 ? (' ; ? C' ? )' 6; ? E' = ? ) Section: 6-1
Topic: Work and Kinetic Energy
Type: +umerical
,,.
An:
A ma m ,. kg i liding along a frictionle table $it! initial peed v a !o$n in t!e figure. 2t trike a coiled pring t!at !a a force contant k ;; +9m and compree it a ditance x, 3 x1 3.; cm. T!e initial peed v of t!e block $a A' ;.=1 m9 (' 1.; m9 C' 1. m9 )' ;.; m9 E' 1.= m9 A Section: 6-1
Topic: Work and Kinetic Energy
Type: +umerical
,.
An:
A 6.;-kg block lide from ret at poition A do$n a frictionle incline to poition (. T!e peed of t!e block at ( i A' .1 m9 (' . m9 C' 11 m9 )' 1.> m9 E' ,; m9 ( Section: 6-1
Topic: Work and Kinetic Energy
Page 5
Type: Conceptual
Chapter 6: Work and Energy
,.
An:
Gou releae an obBect from ret at a !ig! altitude. 2f air reitance i conidered t!e cur%e t!at bet repreent t!e kinetic energy of t!e body a a function of t!e ditance fallen i A' 1 (' , C' )' E' C Section: 6-1
Topic: Work and Kinetic Energy
Type: +umerical
,.
An:
2n pu!ing a load a $oman e7ert a force a gi%en by t!e grap!. W!at $a t!e t!e total $ork done by t!e $oman& A' ;; ? (' ,;; ? C' ,;;; ? )' 1;;; ? E' ;; ? ) Section: 6-1
Topic: Work and Kinetic Energy
Type: +umerical
,6.
T!e grap! repreent t!e force acting on a body plotted againt t!e diplacement of t!e body in t!e direction of t!e force. T!e total $ork done by t!e force from x ; to x x i A' m (' mx, H b C' I8mx, H b )' mx H b E' I8mx, H bx
Page 6
Chapter 6: Work and Energy
An:
E
Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: +umerical ,=. A contant force of + directed at angle q to t!e !ori"ontal pull a crate of $eig!t 1;; + from one end of a room to anot!er a ditance of m. /i%en t!at t!e %ertical component of t!e pulling force i 1, + calculate t!e $ork done by t!e force in mo%ing t!e crate. A' .1 ´ 1;, ? (' >.; ? C' .4 ´ 1;, +9m )' 1.= ´ 1;, ? E' .4 ´ 1; ? An: ) Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: +umerical ,>. T$o force bot! of magnitude 1, + and directed degree eit!er ide of t!e direction of motion pull a crate 1 m. #o$ muc! $ork i done by t!e force in mo%ing t!e crate& A' 1.> ´ 1;, ? )' ,.4 ´ 1;, +9m (' 1. ´ 1;, ? E' ,.1 ´ 1;, ? C' ,.4 ´ 1;, ? An: C Section: 6-1 Statu: +e$ to t! edition Type: +umerical
Topic: Work and Kinetic Energy
,4.
T$o parent $!en mo%ing into a ne$ !oue attempt to pull a large crate do$n t!e large !all$ay a !o$n in t!e figure abo%e. *ne parent applie a force of magnitude 1; + directed degree to t!e direction of motion $!ile t!e ot!er parent applie a force of 1,; + on t!e ot!er ide of t!e direction of motion. 2f t!ey mo%e t!e crate 1 m and perform $ork ,.6 k? at $!at angle to t!e direction of motion did t!e econd parent pull on t!e crate& A' degree )' degree (' ; degree E' 6 degree C' 6; degree An: E Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: +umerical ;. Car drag racing take place o%er a ditance of a J mile ;, m' from a tanding tart. 2f a car ma 1;; kg' could be propelled for$ard $it! a pulling force eual to t!at of
Page 7
Chapter 6: Work and Energy
A' (' C' An:
gra%ity $!at $ould be t!e c!ange in kinetic energy and t!e terminal peed of t!e car in mp!' at t!e end of t!e race be& 5or comparion a modern !ig!-performance port car may reac! a terminal peed of But o%er 1;; mp! .= m9.' 6; k? and ,>. m9 )' 6>; k? and =;.; m9 .4, k? and >>.4 m9 E' .4, ? and >>.4 m9 .4, ? and =4;; m9 E
Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: +umerical 1. Kid lo%e to cra! t!eir toy car toget!er. *ne uc! colliion in%ol%e a ;. kg car mo%ing at ;. m9 colliding $it! a tationary toy car of ma ;. kg. T!e t$o toy tick toget!er and mo%e a$ay from t!e colliion point at ;.1>> m9. (y $!at factor i t!e initial kinetic energy greater t!an t!e final kinetic energy& A' ;.6 (' 1.6 C' ,. )' ., E' 1.; T!e kinetic energy tay t!e ame. An: ( Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: +umerical ,. W!at i t!e difference in $ork needed to pu! a 1;; kg crate at contant peed' a ditance of , m along an inclined plane t!at i at an angle of ,; degree $it! t!e !ori"ontal if t!e coefficient of kinetic friction $a eual to ;.,; or "ero& A' 6=; + (' 1;; + C' no difference )' =; + E' 1 + An: ) Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: Conceptual . A %ertical lig!t pring tretc!e a ditance h meter $!en a ma m i !ung from it. T!e pring9ma ytem i no$ placed on a !ori"ontal frictionle table and et into ocillation $it! amplitude h and ma7imum %elocity v. W!at i t!e total energy in%ol%ed in t!e pring9ma ocillating ytem. A' I kh, H I mv, )' mgh H I kh, H I mv, (' I kh, H mgh E' I mv, C' I mv, H I mgh, An: E Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: Conceptual . A motorcycle of ma m tarting from ret can attain a peed % after $ork W i performed by it engine. 2f t!e engine could perform $ork W t!en t!e final peed $ould be& A' % (' ,% C' 16% )' ,%'19, E' %'19, An: ( Section: 6-1 Statu: +e$ to t! edition Type: +umerical
Page 8
Topic: Work and Kinetic Energy
Chapter 6: Work and Energy
. 2n a tele%iion tube an electron tarting from ret e7perience a force of .; ´ 1;-1 + o%er a ditance of ; cm. T!e final peed of t!e electron i do not $orry about relati%itic effect' A' )' 1. ´ 1;> m9 . ´ 1;1 m9 (' E' 6.6 ´ 1;> m9 6.6 ´ 1;= m9 C' . ´ 1;= m9 An: C Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: +umerical 6. A donkey i attac!ed by a rope to a $ooden cart at an angle of , degree to t!e !ori"ontal. T!e tenion in t!e rope i ,1; +. 2f t!e cart i dragged !ori"ontally along t!e floor $it! a contant peed of 6 km9! calculate !o$ muc! $ork t!e donkey doe in minute. A' =; k? (' ,4; k? C' 6>; k? )' 11 k? E' ;.=; k? An: C Section: 6-1 Statu: +e$ to t! edition Topic: Work and Kinetic Energy Type: +umerical =. W!at i t!e $ork done by a car< braking ytem $!en it lo$ t!e 1;;-kg car from an initial peed of 46 km9! do$n to 6 km9! in a ditance of m& A' >. k? (' ,; k? C' 1. ? )' ,. ? E' >. ? An: C Section: 6-, >. An:
Topic: Work and Energy in T!ree )imenion
Type: +umerical
2f %ector A 3, i H j and a %ector B i – j t!e inner product A' 3, (' = C' 3= )' , E' 1= A L
L
L
L
A · B i
Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical 4. 2f %ector A = i H j and a %ector B , i H j t!e inner product A 8 B i A' , (' ,6 C' ,4 )' 1 E' 1, An: ( L
L
L
L
Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical ;. T!e angle bet$een t!e %ector A 3, i H j and B i – j i appro7imately L
L
A' An:
(' =
C' 1=
)' 1
L
L
E' ,6
C Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical 1. T!e angle bet$een t!e %ector A = i H j and B , i H j i appro7imately L
An:
A' 1 )
(' 1;6
C' ,
)' ,=
Page 9
L
E' 1
L
L
Chapter 6: Work and Energy
Section: 6-, ,. An:
Topic: Work and Energy in T!ree )imenion
Type: +umerical
T!e angle bet$een t!e %ector A i H , j H k and t!e x a7i i appro7imately A' 1= (' ,6 C' = )' > E' = E L
L
L
Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical . T!e angle bet$een t!e %ector A i H , j H k and t!e y a7i i appro7imately L
L
An:
A' > A
(' =
Section: 6-, . An:
C' 1=
)' ,6
L
E' =
Topic: Work and Energy in T!ree )imenion
Type: +umerical
T!e angle bet$een t!e %ector A i H , j H k and t!e z a7i i appro7imately A' 1= (' = C' = )' > E' ,6 ( L
L
L
Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical . A -kg obBect undergoe a diplacement D s , i H j . )uring t!e diplacement a L
L
contant force F i 3 , j act on t!e obBect. All %alue are gi%en in S2 unit. T!e $ork done by t!e force F on t!i obBect i A' > ? (' 36 ? C' , ? )' 1 ? E' 3, ? C L
An:
L
Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical 6. A -kg obBect undergoe a diplacement D s 3 i H , j . )uring t!e diplacement a L
L
contant force F i H > j act on t!e obBect. All %alue are gi%en in S2 un it. T!e $ork done by t!e force F on t!i obBect i A' 31 ? (' 16 ? C' 3 ? )' 1 ? E' 6 ? ) L
An:
L
Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical =. A 1;-kg obBect undergoe a diplacement D s 6 i 3 j H , k . )uring t!e L
L
diplacement a contant force F 3 i H 6 j 3 4 k act on t!e obBect. All %alue are gi%en in S2 unit. T!e $ork done by t!e force F on t!i obBect i A' 3, ? (' 36 ? C' 3; ? )' 3 ? E' 36; ? E L
An:
L
L
L
Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical >. A 1-kg obBect undergoe a diplacement D s i H , j H k . )uring t!e diplacement a L
L
L
contant force F , i H j H k act on t!e obBect. All %alue are gi%en in S2 unit. L
L
L
Page 10
Chapter 6: Work and Energy
An:
T!e $ork done by t!e force F on t!i obBect i A' ,; ? (' > ? C' 1 ? )' 1> ? E' , ? A Section: 6-,
Topic: Work and Energy in T!ree )imenion Type: +umerical 4. A 1;-kg obBect undergoe a diplacement D s i H j H k . )uring t!e diplacement a contant force F 3 i H j H k act on t!e obBect. All %alue are L
L
An:
L
L
L
L
gi%en in S2 unit. T!e $ork done by t!e force F on t!i obBect i A' 31 ? (' ; ? C' 1 ? )' 1, ? E' ? (
Section: 6- Topic: Mo$er Type: Conceptual ;. Conider t$o engine. T!e larger i rated at , W and t!e maller at 1 W. T!e maller one can do a certain uantity of $ork in , !. T!e larger can do t$ice a muc! $ork in a time of A' ; min (' 1 ! C' , ! )' ! E' 1. ! An: C Section: 6- Topic: Mo$er Type: +umerical 1. A motor i lifting a ma of .; kg at a contant peed of 6.;; m9. 2f friction i neglected t!e po$er de%eloped by t!e motor to do t!i lifting i A' =; W (' 1. ´ 1; W C' ,.1 ´ 1; W )' 4 W E' W An: C Section: 6-4
Topic: Mo$er
Type: +umerical
,.
An:
T!e obBect in t!e figure !a a ma of . kg and i pulled up a lope A( $!ic! i 6 m long0 t!e !eig!t (C i .;; m. T!ere i no friction and t!e acceleration i contant. T!e peed v1 at A i . m9 $!erea t!e peed v, at ( i . m9. T!e a%erage po$er de%eloped by t!e motor pulling t!e obBect i A' 1= W (' .4 W C' 1 W )' ;.1 kW E' W A
Section: 6- Topic: Mo$er Type: Conceptual . Mo$er P i reuired to lift a body a ditance d at a contant peed v. W!at po$er i reuired to lift t!e body a ditance ,d at contant peed v& A' P (' , P C' P )' 6 P E' P 9, An: C
Page 11
Chapter 6: Work and Energy
Section: 6- Topic: Mo$er Type: Conceptual . Mo$er P i reuired to do $ork W in time inter%al t . W!at po$er i reuired to do $ork W in time inter%al t & A' P (' P C' P )' P 9 E' P 9 An: E Section: 6- Topic: Mo$er Type: +umerical . W!at i t!e po$er output needed from a motor to lift in t!e abence of friction a ma of 1. ´ 1; kg , m in 6.; at contant peed& A' )' >. ´ 1; W ,.; ´ 1;6 W (' E' .1 ´ 1; W 6.1 ´ 1; W C' ,., ´ 1; W An: ( Section: 6- Topic: Mo$er Type: +umerical 6. A body i acted upon by a force of 1; + and undergoe a diplacement in t!e direction of t!e force in accordance $it! t!e relation s t , H ,t, $!ere i t!e diplacement in meter and t i in econd. T!e rate at $!ic! t!e force i doing $ork at t!e intant t , i A' 1 W (' 1, W C' 1,; W )' 1; W E' 16; W An: ) Section: 6- Topic: Mo$er Type: +umerical =. T!e po$er de%eloped by a certain engine i a function of time according to P , H ,t H t ,
An:
$!ere t!e unit are S2. T!e $ork done by t!e engine in t!e inter%al fromt ; to t , i A' 4 ? (' 1; ? C' 1 ? )' 16 ? E' 1> ? ) Section: 6-
Topic: Mo$er
Type: +umerical
>.
A motor de%elop po$er a !o$n in t!e grap!. T!e energy e7pended by t!e motor in t!e time inter%al bet$een t 1; and t ; i
Page 12
Chapter 6: Work and Energy
An:
A' 1.; ? )
(' 1. ?
C' ;.,; k?
)' ;.6; k?
E' ;.=; k?
Section: 6- Topic: Mo$er Type: +umerical 4. To maintain an automobile in appro7imately contant acceleration it engine mut de%elop po$er t!at increae $it! time. Suppoe t!at in one ituation t!e $ork done by an engine i gi%en by W =;;;t , H ;;;;t H 1;;;;;
A' (' C' An:
$!ere t!e unit are S2. T!e po$er de%eloped by t!i engine att , i )' ,.1 ´ 1; W . ´ 1; W E' .; ´ 1; W 6.> ´ 1; W 1.; ´ 1; W (
Section: 6- Topic: Mo$er Type: +umerical 6;. To maintain an automobile in appro7imately contant acceleration t!e engine mut do $ork at an e%er-increaing rate. Suppoe t!at for a gi%en engine t!e $ork in foot pound i gi%en by W ;;;t , H ;;;;t H >;;;;
An:
$!ere t i in econd. 2n t!i cae $!en t , t!e engine $ould be upplying po$er at a rate of A' 41 !p (' 1 !p C' 1, !p )' 1>> !p E' ,41 !p A Section: 6-
Topic: Mo$er
Type: +umerical
61.
An electrical appliance e7pend energy a !o$n in t!e grap!. T!e po$er de%eloped in t!e appliance bet$een t 1 and t , i A' ;. kW (' ;.11 kW C' ,; W )' 1. kW E' 1.; W
Page 13
Chapter 6: Work and Energy
An:
E
Section: 6- Topic: Mo$er Type: +umerical 6,. A body i acted upon by a force of 1; + and undergoe diplacement in t!e direction of t!e force in accordance $it! t!e relation s t , H ,t
An:
$!ere t!e unit are S2. T!e rate at $!ic! t!e force i doing $ork at t!e intant t , i A' 1 W (' 1, W C' 1,; W )' 1; W E' 16; W )
Section: 6- Topic: Mo$er Type: Conceptual 6. A force F act on a body and produce an acceleration a . T!e body undergoe a diplacement s and attain a %elocity v in time t. T!e intantaneou po$er being
An:
de%eloped at time t i gi%en by A' F 8 v (' F 8 ½ at , C' F 8 a A Section: 6-
Topic: Mo$er
)' F 8 2 s ' 9t ,
E' F 8 s
Type: +umerical
6.
T!e $ork done by a crane lifting a boat i plotted on t!e grap!. T!e po$er de%eloped by t!e crane $!en t 1. i A' ; W (' ,; W C' 1; W )' ,= W E' ; W An: ( Section: 6- Statu: +e$ to t! edition Topic: Mo$er Type: +umerical 6. A ;N efficient !ydroelectric po$er plant generate electricity from $ater falling a !eig!t of 11; m and at a rate of x kg9. 2f t!e ma7imum poible po$er output of t!e plant $a ,=.; W $!at i 7& A' ,;;; kg9 )' 1;; kg9 (' ;;;; kg9 E' 1;;;; kg9 C' 1;;;;; kg9 Page 14
Chapter 6: Work and Energy
An:
(
Section: 6- Statu: +e$ to t! edition Topic: Mo$er Type: +umerical 66. A a puni!ment for being late to a practice eion t!e coac! order !er tar at!lete to run up t!e tadium tep. T!e player< ma i >; kg and it take one minute for !er to run up t!e 1,; tep at a contant rate. 2f eac! tep i of !eig!t ;. m $!at i t!e po$er output of t!e player& A' >;.; W (' 1.; W C' 1=; W )' => W E' 4; W An: ) Section: 6- Statu: +e$ to t! edition Topic: Mo$er Type: +umerical 6=. 2f t!e a%erage po$er output of a car engine i t!e ame a a 1;;-W lig!t bulb !o$ long $ould it take a 1,;;-kg car to go from "ero to 46 km9! 6; mp!'& A' >. ´ 1; (' . ´ 1; C' 6 )' 16; E' . ´ 1; An: E Section: 6- Statu: +e$ to t! edition Topic: Mo$er Type: +umerical 6>. A !ydroelectric po$er plant generate electricity from $ater falling a !eig!t of h m and at a rate of ,;;;; kg9. 2f t!e t!eoretical ma7imum po$er output of t!e plant i 1.; W $!at i t!e !eig!t h& A' =; m (' 1 m C' 1;, m )' =6. m E' >. m An: ) Section: 6- Statu: +e$ to t! edition Topic: Mo$er Type: +umerical 64. Egyptian pyramid $orker pu! a 1,;;-kg block up an incline t!at !a an angle of 64 degree to t!e %ertical at a contant peed of ;. m9. T!e coefficient of kinetic friction bet$een t!e block and t!e incline urface i ;.. #o$ muc! po$er mut t!e $orker upply& A' .1 ´ 1;, W (' 4. kW C' . kW )' =.4 kW E' ,. kW An: C Section: 6- Statu: +e$ to t! edition Topic: Mo$er Type: +umerical =;. A (lack!a$k !elicopter i $inc!ing up an inBured oldier from a danger "one. T!e oldier and !i kit !a%e a ma of 1; kg and are pulled up ; m in t!e air at a teady rate. 2f it take ; to pull t!e oldier up !o$ muc! po$er !a been ued by t!e !elicopter< 6N efficient $inc! engine& A' ,. kW (' .> kW C' 1.6 kW )' .1 kW E' ., kW An: ( Section: 6- Statu: +e$ to t! edition Topic: Mo$er Type: +umerical =1. W!at minimum po$er rating mut a $ater pump !a%e if need to raie $ater at ,; kg per minute from a dept! of 4 m& A' 1.=6 kW (' ,4. W C' 1;6 kW )' .; W E' 1>; W An: ( Section: 6-
Statu: +e$ to t! edition
Page 15
Topic: Mo$er
Type: +umerical
Chapter 6: Work and Energy
=,. T!e !uman !eart i eentially a pump for mo%ing blood around t!e body. 2f it a%erage po$er output o%er many beat' i about ,.; W and it pump blood at an o%erall a%erage peed of ;. m9 into t!e output aorta c!annel calculate t!e a%erage force $it! $!ic! t!e !eart mo%e t!e blood into t!e aorta. A' ;.6; + (' 6.= + C' ,, + )' 66 + E' ;.1> + An: ( Section: 6- Topic: Motential Energy Type: Conceptual =. A $oman run up a flig!t of tair. T!e gain in !er gra%itational potential energy i U. 2f !e run up t!e ame tair $it! t$ice t!e peed $!at i !er gain in potential energy& A' U (' ,U C' IU )' U E' JU An: A Section: 6- Topic: Motential Energy Type: Conceptual =. Suana acend a mountain %ia a !ort teep trail. Sean acend t!e ame mountain %ia a long gentle trail. W!ic! of t!e follo$ing tatement i true& A' Suana gain more gra%itational potential energy t!an Sean. (' Suana gain le gra%itational potential energy t!an Sean. C' Suana gain t!e ame gra%itational potential energy a Sean. )' To compare energie $e mut kno$ t!e !eig!t of t!e mountain. E' To compare energie $e mut kno$ t!e lengt! of t!e t$o trail. An: C Section: 6- Topic: Motential Energy Type: Conceptual =. T!e reference point for gra%itational potential energy A' mut be at t!e initial poition of t!e obBect. (' mut be at t!e final poition of t!e obBect. C' mut be at ground le%el. )' mut be at t!e lo$et poition e%er reac!ed by t!e obBect. E' can be c!oen arbitrarily. An: E Section: 6- Topic: Motential Energy Type: Conceptual =6. W!ic! of t!e follo$ing tatement i true& A' T!e kinetic and potential energie of an obBect mut al$ay be poiti%e uantitie. (' T!e kinetic and potential energie of an obBect mut al$ay be negati%e uantitie. C' Kinetic energy can be negati%e but potential energy cannot. )' Motential energy can be negati%e but kinetic energy cannot. E' +one of t!ee tatement i true. An: ) Section: 6- Topic: Motential Energy Type: +umerical ==. A =-kg man climb t!e tair to t!e fift! floor of a building a total !eig!t of 16 m. #i potential energy !a increaed by A' )' .> ´ 1; ? 1., ´ 1; ? (' E' .4 ´ 1; ? .4 ´ 1; ?
Page 16
Chapter 6: Work and Energy
C' An:
.= ´ 1; ? A
Section: 6- Topic: Motential Energy Type: +umerical =>. A ,;;-kg cable car in #ong Kong i pulled a ditance of 6; m up a !ill inclined at 1, from t!e !ori"ontal. T!e c!ange in t!e potential energy of t!e car i A' )' 6.; ´ 1;= ? 1.> ´ 1;= ? (' E' 1.> ´ 1;6 ? 1., ´ 1;= ? C' .> ´ 1;6 ? An: C Section: 6- Topic: Motential Energy Type: +umerical =4. A block $it! a ma M .> kg i reting on a lide t!at !a a cur%ed urface. T!ere i no friction. T!e peed of t!e block after it !a lid along t!e lide ufficiently far for it %ertical drop to be 14.6 m i A' 14.6 m9 (' > m9 C' = m9 )' ., m9 E' T!e problem cannot be ol%ed becaue t!e !ape of t!e cur%ed lide i not gi%en. An: A Section: 6- Topic: Motential Energy Type: +umerical >;. A pring $it! force contant k ;; +9m i compreed 4.; cm. W!at i t!e potential energy in t!e pring& A' 1., ´ 1; ? (' ,. ? C' ,.= ´ 1; ? )' ,= ? E' 1., ? An: E Section: 6- Topic: Motential Energy Type: Conceptual >1. W!ic! of t!e follo$ing tatement i true& A' 5riction i a coner%ati%e force and doe negati%e $ork. (' Motential energy may be defined by t!e euation U x' –d 5 x'9dx C' T!e $ork done by a coner%ati%e force bet$een t$o point depend on t!e pat! taken bet$een t!oe point. )' A coner%ati%e force cannot c!ange a body< total energy. E' T!e $ork done by a coner%ati%e force $!ile a body mo%e at contant %elocity mut be "ero. An: ) Section: 6-
Topic: Motential Energy
>,.
Page 17
Type: Conceptual
Chapter 6: Work and Energy
An:
W!en t!e potential energy U(r) i gi%en a in 5igure A t!en t!e force i gi%en in 5igure ( by cur%e A' 1 (' , C' )' E' ( Section: 6-
Topic: Motential Energy
Type: +umerical
>.
A block of ma m tart from poition 1 and mo%e up a frictionle inclined plane $it! an initial peed v. At ome later time t!e block !a mo%ed do$n t!e plane and at poition , !a a peed . 2f a and b are t!e !eig!t abo%e t!e bottom of t!e plane t!e magnitude of can be determined from A' , v, 3 , g a – b' )' , v, H , g b 3 a' (' , v, H , g a H b' E' , v, H g a 3 b' C' , v, H , g a 3 b' An: C Section: 6-
Topic: Motential Energy
>.
Page 18
Type: +umerical
Chapter 6: Work and Energy
An:
T!e grap! !o$ a plot of t!e gra%itational potential energy U of a 1-kg body a a function of it !eig!t h abo%e t!e urface of a planet. T!e acceleration due to gra%ity at t!e urface of t!e planet i A' ; m9, (' 4.> m9, C' 6.; m9, )' .; m9, E' +one of t!ee i correct. )
Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: Conceptual >. According to Ouantum C!romodynamic t!e force t!at keep uark confined $it!in a proton or neutron' increae a t!e eparation bet$een t!e indi%idual uark increae. W!ic! tatement belo$ bet repreent t!i cenario& A' T!e uark are tied toget!er by nontretc!able tring. (' T!e uark are tied toget!er by elatic tring. C' T!e uark mo%e independently of eac! ot!er. )' T!e force bet$een t!e uark !a a 19r , be!a%ior like gra%ity. E' T!e potential energy of a uark decreae $it! eparation. An: ( Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: +umerical >6. 2n maga"ine car tet an important indicator of performance i t!e "ero to 6; mp! ; to 46.6 km9!' acceleration time. A time belo$ 6 i conidered to be e7tremely uick. 2f a car $it! ma 1;; kg $ere dropped %ertically from a great !eig!t !o$ long $ould it take to go from "ero to 6; mp! and $!at $ould t!e magnitude of t!e c!ange in gra%itational potential energy be during t!i time& +eglect air reitance' A' ,.= and 1=. k? )' ;.= and 6> ? (' ,.= and 6> k? E' ,.= and 1=. ? C' ,.= and 6> ? An: ( Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: Conceptual >=. W!ic! potential energy %eru diplacement cur%e bet repreent t!at of an e7tended
Page 19
Chapter 6: Work and Energy
pring&
A' 1 An:
(' ,
C'
)'
E'
C
Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: Conceptual >>. T!e potential energy function for a coner%ati%e force acting in t!e x direction on a particle i !o$n belo$. T!e number of point $!ere t!e net force on t!e particle i eual to "ero are
A' (' C' An:
( and ). C and E. ( C ) and E. C
)' A and 5. E' any point bet$een C and ).
Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: +umerical >4. T!e potential energy function for a coner%ati%e force acting in t!e x direction i !o$n in t!e figure on t!e rig!t. W!ere $ould t!e particle e7perience a force directed to t!e rig!t&
Page 20
Chapter 6: Work and Energy
A' (' C' An:
bet$een A P ( and E P 5 bet$een ( P C and C P ) bet$een ( P C and ) P E A
)' at point ( and ) E' at point C and E
Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: +umerical 4;. A ma m i releaed from a !eig!t >; cm from t!e rig!t-!and ide of t!e track !o$n in t!e diagram at rig!t. T!ere i only friction acting along t!e !ori"ontal portion ; cm eit!er ide of t!e midpoint * $it! a kinetic coefficient of friction of mk ;.. )etermine i' !o$ many time doe t!e ma m pa t!roug! t!e midpoint * and ii' !o$ far from t!e midpoint doe it come to ret.
An:
A' 6 .1 m )
(' 6 ., m
C' ., m
)' .1 m
E' 1 , cm
Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: +umerical 41. A ma m i releaed from a !eig!t 6; cm from t!e rig!t-!and ide of t!e track !o$n in t!e diagram at rig!t. T!ere i only friction acting on t!e ma on t!e !ori"ontal portion cm eit!er ide of t!e midpoint * $it! a kinetic coefficient of friction of mk ;.. )etermine $!at i t!e %elocity of t!e block t!e firt time it pae t!roug! t!e midpoint and on $!ic! ide of t!e midpoint doe it top&
Page 21
Chapter 6: Work and Energy
An:
A' . m9 Q E
(' .4 m9 Q
C' .4 m9 F
)' ,.4 m9 F
E' ,.4 m9 Q
Section: 6- Statu: +e$ to t! edition Topic: Motential Energy Type: +umerical 4,. A ma m i releaed from a !eig!t = cm from t!e rig!t-!and ide of t!e track !o$n in t!e diagram at rig!t. T!ere i only friction acting on ma along t!e !ori"ontal portion ; cm eit!er ide of t!e midpoint * $it! a kinetic coefficient of friction of mk ;.. )etermine !o$ !ig! it reac!e t!e econd time it pae o%er to t!e left ide and in $!ic! direction i it mo%ing $!en it top&
An:
A' ,= cm Q (
(' .; cm Q
C' ,= cm F
Page 22
)' .; cm F
E' 1 cm Q
