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һѾָʱҵĻеġƷʱתΪңʣֵʣƷҲתΪҡʱҰתΪҵʣֵתΪʱ׷ӵʵҪءʱһѭڣṩĲƷǣڵʱϷҲȻȫϳ֣ڿʱѾڵʱУʱѾĵĹ̶ɲ̳ΪػҵҲϱֳ

ٶһʱ=400c+100vʣֵ=100ĩƷƷ=400c+100v+100m600תΪҡУ400cתΪʱʵʽ100vתΪͶ⡪ٶȫʣֵۡ100mͨʱʵҪཻתΪ׷ӵĲʱҪٶ1һļ£ҶְִܵĲʱԿһµĹҵҵǣҲڿʼǰʵʻۺǰʣ
551
ֵҵתҵҪһܳʱ䡣2ٶʵǰѾĹģУΪҪʹ(Իʽصʣֵ)ܹתΪʱҪأЩҪرгϿ򵽵ƷʹЩҪزΪƷ򣬶ǰ죬ҲʲôֻǴԺ󣬲ֻڶʵʽ˹ģԺҲ˵ԭѾԺ󣬲Żǽ֧ǱǿܴڵģҲǵҪдڵģΪֻҪжĴ̼ƷǰԤȹԤȳۣǵͿʵʽСǣһĻҾһĿûлҵ¾ѾڣΪұʵҪءǶӡЩƱġ

磬ʱAһڻڰЩƷƷʱͰΪʣֵеߵǲƷƷʣƷתΪңҲƷʽʣֵתΪңֻγһֿܵµĻʱǿܵģΪԲҪתΪʱҪءǣʵֻǽ˼򵥵ĻأֻزʵҪءԣĻֻǴͨȡͨĻҡȻⲢųƱͨұڽ֮ͨǰһصһ֡ʱAĻأܵµĻʱͬϵĻһ׷ӵƸǣͨȡġǰͨеĻңǰػҵɲ֣߿ǹʵĻʽʹ
552
ϻƷתΪңʹĳһʱҵĲʱֻͨЩͬµĲƸӼƷͨĹ۵ҲΪÿתʮΣʵʮͬƷֵͲֻԭеļֵĳеߣʮֵĳеһûлңЩƷǴڣңۻתһλתʮΣǻ(߻ĥ)ֻڽУڽƷʣƷʣֵĳеߵʱµĲƸ(ܵĻ)ŻᱻңֻȫµĽƷͨŻµĿܵĻʱĻҲϡ

ȻԻʽصʣֵ׷ӵµƸҪִеְܣǴµĿܵĻʱ(Ժǻ֪ʣֵ𽥻һ⣬µĻʱ)

ԻͨȡΪػΪƷڳԺûнŽйˣձеģǾƺڿӦôĶΪУ̱뿴ձģΪÿһʱܹڻ۹̣ÿһ˶ΪػҶûҪ

ٶĸֱ߽֮ͬͨеģǲԵģΪ⣬ͨ໥˶ɵģĩͱֻĽ(
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)߿ʼҼٶ˶ȫʣƷ(ȫʣֵĳе)ͻתУʱԼм䰴طȻԻʽڵʣƷʣֵȻĽĻΪߵĲƷҪְִܵʱǲѾˣѾʹˡֳϣԽʽʣֵΨһĻʱҶҪȡǵʣƷתΪҵĲϡֽʱѵеʣƷҪӡƱУˣʣֵͼֵԣҪӼΪʽȫʣֵȡּٶ˻˵ձͬʱγɻصĿԣǶ˵߷⡪ǰһ

ڽǰҪѵI(ϵ)Ļۺ͵II(ϵ)ĻǴӵI࿪ʼ

IIĻ

1
ȻͶڹɵIҵŵʱͶÿһĲҵڵĲͬĵʱǵ䲻ͬҲѾְִܵʱ䲻ͬȫƲǵĹģгϵȵȲ˵ʣֵ
554
תΪܵĻʱ̵Ĳͬ׶ΣֻʱҪǵְִܵʱҪµĹҵҵ(ʽ)ˣһʱҲϵذǵѾӵӦĿܵĻʱתΪʱҲͨʣֵĻһĻϣ׷ӵĲʱҪأһʱȻ¿ܵĻʱءˣʱǻģһΪߣһΪߣÿһжֻһá

磬AB(Դһϵ)600(=400c+100v+100m)ѾƷ600ɻ600100ʣֵ100ͨȡԻʽ100ҲʣƷֵ100ĳеߵĻʽظһʼҲʱҵĻǰѳʣƷ100õĻҴͨȡץסA淢ͨϣʱA'A''A'''ֻͬءˣϣұͨȡ۳ػһܵĻʱҲͨϰΪʹҵ˶ֹͣʹһ򳤻̵ʱʧȥͨǱע⣬ԶƷͨʱƷĻǰڼ򵥵ƷͨѾ˻أеĻǴʵͨеĲ֣Ȼһֻı仯ӻ١ͬػҺͬĻأ
555
ʱ̵һء

ƶ£ЩܵʱǻеȵȵУΪɹ֧ʱɴʱʱҲǱĶδ֣ܶģĶ(˼)ǾͿ⣬ΪʲôǶԴ˸е㡣

ǣAֻܽأΪʣƷ˵ֻΪߣΪ߳֡ԣʣƷҪתΪҵʣֵĳеߡֻصǰᡣֻIڲֳͨϣΪܲƷһֵʣƷʵʽܲƷʵʽһǵI಻ʱһҪصʵʽҲ˵ϵϵķ롣Ͼͻ֪BB'B''ȵУʲôִʲôְܡ

Ҫסһ㣺Aͨȡ൱ʣֵĻңһ棬ҲƷͶͨûԴ˴ͨȡƷˣBB'B''ȵȾܹѻͶֻͨȡƷϣƷʵʽ;˵Ҫ뵽BB'ȵĲʱĹ̶ҪػҪȥġAдζBͶʡԣܵΪ϶࣬ΪͶʲ㡣һ㣬漰ʣƷBB'ʱ̸

︽ָǰʱһֿƷĲͬɲֵĽҲЩɲ֮ͨ(ͨͬʱʱԼʱ
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ָĲͬʽʱɱʱ̶ʱʱʱƷʱ)ǰǽΪƷĵ򣬻߽ΪƷĵʵϣξѧũѧɺǵ˹óѧٶֻƷƷн̶֪ʱһͶ룬ְִܵȫʱھͲø£ԭʽãļֵ𽥵ԻʽѾ֪IIcĹ̶ʱ(IIcȫʱֵתΪڼֵI(v+m)ȵҪ)ڸµǰᣬһIIcҪɻʽתΪʵʽĹ̶ֵĵӦImĵһIIcҪΪҵĹ̶()ֵֵĵӦImĵбеǰǣIIcĵ򣬰ֵ˵IIcĵȣͬImIIc1ֵĵҲIIc2ֵĵ(520521ҳ)Ȼͻ⵽ƻһĵһĵͬеǰǣImAA'A''ĻصĲֵĵImBB'B''ҪػתΪ׷ʱҪصĲֵĵ򱣳ƽ⡣

ȻƽγߺΪͬȼֵ֣߳ߺΪͬȼֵ֣߳ԣһصڹʱԤҵġ¹֮ǰѳ۵һǾƷƷĲֵͬĽԣʵƽҪ
557
ȡڻཻƷͬȵļֵ

ǣȻֻǵĽףһǴĵһǴĵ֪ʱϣƷ׾ֵ̬仯ԣƽֻµǰ²ܱ֣ļֵҪ͵ļֵƷʱһʽʵѾʱлҲֶͨεãҲʱãͬʱֻʽеġʹӶҲʹ(Ǽ)еĳЩЩתΪͬɹʧתΪͬΣĿԣΪԷʽУƽⱾһżȻԣִӹ׾ѧǿġ⡱ֻΪʱƶȱ绤Ĺʡ־⣬ʵǷǳżȻģʹﵽҲȶģݼŵġ

ǻ֪IvIIcӦֵʱǶIIc˵IIƷɵIͬȼֵƷڵIIʱҷ棬ƷĳºԵIͬȼֵƷĹΪġֲǻᷢģǵI͵IIʱǵƷתвǻཻƷIIcƷ۸IĹˣIĹǵΪƷߺIIcIIcǵΪƷߺ͵IĹIIcõĻңΪƷߺ͵IʱIʱIvΪƷߺIIcֻڳƷIԻʱʽĿɱʱIʱIvΪƷߺ͵IIʱ
558
ĩͶĹϾΪƷߺ͵IĹIĹ˵ΪƷ(ϵ)͵IIʱĩǾ͵ΪƷߣǵͶߣ͵Iʱ

IĹҪϵṩͶIƷʱһҪתΪɱʱĻʽIIƷʱһҪòʱIIcʵҪһбҪǰǻΪģǣһΪӵĹΪýġ̣˴˶еֻཻһ̡̱ͨĸԣֳͬɹʧԭ

2׷ӵĲʱ
ʣƷʣֵĳеߣռߣIʱңǲѷĵġòŰκηʽԤһƷͿԵõԤ(avance)ũѧɿѾʱҪʵֵļֵһʽˣIʱԤģǵĲʱͿɱʱ˲ͨԼͶΪǱ˲ʱһ´ľƷʽӦļֵ֣Ϊǲ˿ɱʱֵң˻ԼʣͶṩһʣƷʽڵʣֵ̳ͨʣƷγ˻أγ׷ӵĿܵĻʱ￼ĳϣʣƷһʼϵϹɵġʣƷֻBB'B''
559
(I)Уִ׷ӵĲʱְܡǣڳǰڻAA'A''(I)ѾǱڵ׷ӵĲʱˡֻI෽ļֵĩǾȻڼķΧڣΪûʹ׷ʱǱڵ׷ӵĲʱ(ʣƷ)ҲûʹñڼϺķѵĸʣͶֻʹõʣͶʽֻ÷ʽľʡIcϣIIcϵģϵϣϵϵġڼ£ǰǵIȫʣֵΪ뻨ڵIIƷϣԣֻԼʵʽ²ʱIIcϹɵġˣΪ˴ӼɵIҪܹΪII첻ʱҪأӦضΪI첻ʱҪءֹûѵģǣڵIЩƷΪһʵֹɾЩ

ɴ˵óֵֻۣʻڼڲġ˵ʻǣֱڵIϵϵġڵIǱڵ׷ʱĴϵĵI๤˵ʣͶˣAA'A''(I)Ǳڵ׷ӻʱγɣ̳ͨǵĲҪκʱ֧ʣƷҲֻ׷ӵĵIϵĻʽ

Ǳڵ׷ʱڵǰĳ(Ϊǽ֪
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׷ʱ԰ȫͬķγ)Ǳʾ̱󣬼ʱҪһʽϽе

ˣ׷ӵǱڻʱͨϵĴģǱڵ׷ʱĶ෽Ľͱ֣ʱγɱԲҵʱҷκ׷ӻ֧Ϊǰġ

AA'A''ȵ(I)Ǳڵ׷ʱǱڵĻʱ(ػ)תǵʣƷ̳ģûйΪķеĵƷģתǿͨȡԼγӦĻɵġֻأߵĳϳ⣬ƸӣֻĿǰΪֹͨеĻҵְܵĸı䡣ǰΪְִֶͨܣΪֶΣΪγɵġǱڵ»ʱְִܡˣ׷ӻʱγɺһй˴֮ûκϵġ

ɴ˻ԵóۣѾһְִܵʱ(ʱͶʣƷĴ)Խ࣬ͶӶѸļֶԽչʣƷڼֵڼֵֵʹüֵԽĩжҲԽ

1AA'A''ȵеʣƷʽǱڵ׷ʱ

2AA'A''еҪתΪҵʣƷǱڵ׷ӻʱˣ˵ˣ֪
561
ͨϵʣֻ֪ʱʱʣǾһ֤ʲ׼ѧҲ˽ǵƶȵĻ

ʱAA'A''(I)ֱռеʣƷʱۼʵȻҪBB'B''ȵ(I)УʵʸְִܣĩӼɵĻҵʽΪػңΪֻγɵǱڻʱʱǾԷģʽȻƽнУȴ֮⡣ʱһ(dead weight)ΪǱڻʱʣֵȡͼƶȺм֤ȯҵŬĿꡣƶȺм֤ȯԴڵĻʱɴһʽʱϵĽ̺;޴ķչ˼Ӱ졣

Ѿְִܵʱ(ʣƷְִܶ)ܶԽתΪǱڻʱʣƷҲԽ󡣵ǣÿǱڻʱʱʱķҲͻףˣʱԸѸٵرͶһҵҵͬһʱУһЩ(μŲļͥԱȵ)Сʱķָȫ뿪ԭеʱԱΪµĻʱͶһµĶҵ

ʣƷAA'A''ȵ(I)ȡõʣƷ̵ֱӽ̳ڼҲҪԤʱͿɱʱ⣬ԽһͨΪΪǰᣬΣΪģṩʵʵ
562
Ǳڵ׷ʱ෴أBB'B''ȵ(I)ȴͬ1AA'A''ȵȵʣƷֻBB'B''ȵвʵΪ׷ӵĲʱְִ(ҰʱһҪأ׷ӵͶ׷ӵĿɱʱƲ˵)2ʣƷҪBB'B''ȵУҪһͨΪǱ빺ʣƷ

ڵһ㣬Ӧָ󲿷ʣƷ(Ǳڵ׷Ӳʱ)ȻAA'A''(I)ڵģҪһ꣬ʱ򣬲ܹʵBB'B''(I)Ϊҵʱְִܣڵڶ㣬һ⣺ͨĻǴ?

ȻBB'B''ȵ(I)ĲƷʵʽͬһ̣ԶԼһʣƷͻӦֱ(ûͨΪý)תΪǵʱΪʱ׷Ҫؽ̡ǣӦҲûаAA'ȵ(I)ʣƷתΪҡƲЩ˵ĩǴ?֪AA'ȵһͨ۸ԵʣƷγǵĻأѾﵽĿ꣺ػһ۵ġǱڵĻʱӦʵΪ׷ӵĻʱְִܡһǾֻﶵȦˡȻǣBȵ(I)ǰͨȡ۵ĻǴ?

ȻǴӿѾ֪I͵IIʱбһңԱ㽻ǵʣƷڼУΪϵĻңᰴո
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ʱΪƷԤĻҵĶ٣صʱУУͬĻһٳ֣ǵְܸıˡAȵȺBȵ(I)ṩңԱʹʣƷתΪ׷ӵǱڵĻʱҽذγɵĻʱΪֶͶͨʱǽǵѲҪ

ΨһǰǣеĻ(ٶͨٶȵȵȲ)ҪӦܶͨҪҲҪӦػҵĴҪˣ֪ģǰڼ򵥵ƷͨҲǱ߱ġػҵְǲͬġеĻҲ1ΪʱУһвƷ(ĹԼѵƷ)ΪƷģԱͨӼΪҵĽ׶Σ2ΪʱϣƷʱֵԵ󣬶ޱѸٵ3ΪĿɱʱ벻תΪʱ4Ϊ»ʱγɺͬʱǵĻصĲϱֳɵġֻҲϵĲ㣬ŵԭΪ˽ʹòȱݶֵûһֽҵת䣬¶ս׶ɭֽϵıʱ׶ΣͨռҪλƶȵĽ׶ΣȫõģĩȻԽͨΪƶȵ׶ΣҲõġһ棬׷ֻҪʱӡʱ٣ͻ᲻ڱȽϳʱڣڼ̵ʱƷ۸ֽҵĹҲˡһ棬ûϵæøֲͼʩʵĽͨһԵСС޶ȣΪԼĽ̵ĻҲӦӡֻͬڽƷС

ǱڵµĻʱܶʱBB'B''ȵ(I)
564
ܱ˴˹ͳǵĲƷ(ǵĲʣƷ)£ΪʣƷͨԤĻңBȵΪǸԵƷͨԤĻҵͬһصǸСΪֶ֧ͨģĩֻǵ˴˲ʱ֧ҪǣһҪٶԭʼʽĽͨΪһأĵ֮ƶڱΪʶĵڹ̵һأŻΪƶ֮ڵĶŻȻʽԺӳʽֳ

3׷ӵĿɱʱ
Ϊֻ׷ӵĲʱҪת뿼׷ӵĿɱʱ

ڵһѾϸʱĻϣͶ׼õģڱҪʱù˵ͶͿƶͶˣʱûбҪһֻҪٶγɵĻʱпתΪɱʱĲ֣ӦתʱܻҵͶڵһһʱûлۣܹһ֮ģǣҪضϵʱۣˣҪȡʣֵ׷ʱתҲҪȡΪʱ

ܹһֽʣֵΪǱڵĻʱֻۣҪﵽҪֱܹתΪµĿ
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ʱΪȳʣƷͬأֱܹӰתΪʱҪءںһֳϣͱҵʱĸҪأ˵ٶÿ߶ΪȻĳƷг߼ٶÿ߶ΪϣʵΪǰģҲʣƷΪǰģǰһϣʣƷʵʴڵģںһϣʣƷǱڵشڵģܹӦġ

IIIIĻ
ǼٶAA'A''(I)ǰǵʣƷҲڵIBB'B''ȵȡǼٶA(I)ʣƷתΪңڰʣƷIIBֻܹΪA(I)B(II)Ժ󣬲ŹϣҲ˵ֻΪⷽеǵIIcܹƷʱʽתΪʱʵʽֻΪIvImһ֣ʽڵIIcһཻڣAImתΪңֽûнУ෴أAͨImӵIIõĻҴͨȡIIcˣA(I)Ȼγ׷ӵǱڻʱһ棬B(II)ȴͬȼֵһֲʱƷʱʽϣܹתΪʱʵ
566
ʽ仰˵B(II)һƷȥһƷȥⲿƷȥͲܰĲʱȫתΪʽˣⲿƷ˵ʣֹʣ谭ⲿƷǹģ

ˣϣA(I)׷ӵǱڻʱȻʣƷ(ʣֵ)תɻҵʽǣʣƷ(ʣֵ)Ǽ󣬻ǹģI(v+m)Σmһ֡ձIIcԱIIcܹĹģСA(I)ʣƷB(II)ʱȻѾʵʽB(II)ṩ˲ʱӦļֵ֣ͬʱͨȡ˻ңûн򲹳ʹB(II)ľͬȼֵƷȥˣǿǵI͵IIʱҶͬڣĩA(I)ʣƷתΪǱڻʱǱʾB(II)ľͬȼֵƷʱתΪ()ʱⲻǱʾǱڵĹģǱʾܵ谭ҲǼ㡣ΪA(I)ʣƷγɺͳ۱ǼԾڼĻϣҲֻΪ󣺵IγǱڵ׷ӻʱ(ԴӵIIĹ۵ѲЧ)IIƷתΪʱ(ԶԵII˵Եʣ)IĻʱʣII㡣IѾ㹻II࣬IIӦԽֻǵIIǰһƷδ꣬еĻҶȱٴI๺ͬģϡIĻһ۵һѭвƷ
567
һ㣬ض̸ֻҪָ˵ʱǵǰǣI͵IIȫʣֵΪ뻨ġǣʵϣʣֵһΪ뻨һתΪʱֻǰ£ʵʵĻۡǿеһ˵Ǻʱıìܵһֻ룬ΪֻٶʱĿĺͶѣʣֵľȡʱۡáֽΪĻȻִӹ׾ѧҪ˼롣

ڣҪȽϸؿһµIIĻۡ

IIcĵһѣɵIIƷʱһɲתΪIIĲʱʵʽйصġǲǰĹʽ

(1000v+1000m)I

2000IIc

IʣƷһ룬1000/2m500ImΪʱI࣬ڵIⲿʣƷͲܲIIcκβ֡תΪ(תΪϵĳϣڵI͵II֮ⲿͨзģʵʵĻĽҲ˫ƷλⲻͬԵIĹΪý1000IIcl000IvеĲ)ҪڵI౾Ϊ׷ӵáͬʱڵI͵IIְܡʱҲܼȰʣƷļֵϣͬʱֶʣƷѣʱˣ2000IIcģѲ2000I(v+m)ֻ1500(1000v+500m)I500IIcͲܴ
568
ƷʽתΪII()ʱǵIIͻᷢʣʣĳ̶ǡIѾĳ̶ӦIʵ۵µIIϲ㣬IIӦǲġͬʱ500ImûӦIIcˣIIǰһƷҲû(ʣ)ǰһͬǣIIصĻ䣬IʱҵĸѼ500Iʱ500ңԹʣµIIcIʱҵѲ䣬ʵ500Ҽ500IʱҵƷȫ꣬ж500ңӦõϼ500IIʣҲصطӦIϣµIĹڵIIϵ1000Ҳǲֵأ1000ҲԿɱĻʱʽصIʱСʱӦӦֱ䶯ݵĽϣ簴ͬĲʱɱʱʣֵıԱؿĽᷢչʲôزIʱҽᷢΪͼģҲܵ谭ﻹҪע⣬IʵֻмʽоٵҪֻΪ󣬱˵һ󣬽вͬϰˡ

˿ͼرѣΪʱҲֿСֱתΪʱ500IIcԶԶʣ෴أһҪҪأҪһֱǺˡѾ֪ҴϻˣͨȡⲿֵΪпγɵI»ʱֵΪʹĵĹ̶ʱļֵʱڻʽϡǣΪڹʽıмٶһлҺһƷһʼֻǴڵI͵IIʱУˡҾӪߡмңҲֻѶֱӲμƷĽ׼ԣڸ߱вγƷ棬ԱʹתˣIIʱҲֿе500IIcģϵƷƷʹаѹУҲǴһɵһꡣͬʱҲеѻ𣬲ڽù⣬㿪ʼʹǴӽ
569
쵽죬ҲǲܵġΪƷ桪Ȼб䶯벻ϵγɣǵIIʱ߱ӵл׼ʱʹпܼǵ̣ǵʱһʱҪƷʽϡռٶǰȫҵҵһģԣǱӵ׷ӵĻʱʱ̵ĸְɸʱҶִʱǴеġ

Ƕ˵ķǣ1ƷҪԣԵI͵IIеʱ˵õġΪƷǵֻڣǲͬƷֻ΢ϵġIIƷĴԵIƷдΪǰġǺһִҲͱضһĴǣǰ涼ǵͲᷢκα仯2ڵII෽棬ʱһƷĩͬڵII෽棬꿪ʼʱҲһõƷˣڷʱԭΪıʱǱ߶۳ǼȻȫҲͰѽתһƷڣǣҲһѽȥõƷ۳ʵһƽȵܲƷΪǷĶ󡣡3ڿʱûҪرܵѣһʵ֤漰һ֮ԷֻڵIĸҪ֮(˵)˲ͬϣûϵı仯͸ܷģ
570

IIIùʽ˵
ǰйʽѧǱͷùʱرĹߡ

ʽ(a)

I4000c+1000v+1000m=6000

II1500c+376v+376m=2252

ϼ=8252

ҪָƷܶ8252Сڵһʽܶ9000ǾԼٶһöܶ˵һʮܶѡһСڵһʽܶΪҪ˵ģ(ָֻýϴͶе)Ʒľ޹أҲΪҪ˵һƷ˵ģҪǰǣȶƷĸҪѾ˲ͬϣְܹͬ涨ˣֵ˵ֻǼıģǼĸּȶҪصǵʵĹ涨ָıԺŷĹģǰᡣһԶղķ˹պ֮ʱ۵ۣڵһ(22µ5)Ѿһ۵ڲҵʱ²ҵʱĿܡԺҪ̸һ㡣

ڿɱʱͲʱ֮ıͬʱǶԹʽıԲͬ磺
571
ʽ(b)

I4000c+875v+875m=5750

II1750c+376v+376m=2502

ϼ=8252

ʽƺΪгģʣֵȫΪ뻨ûл(a)(b)ϣƷļֵͬģֻ(b)ĳϣĸҪְϣʹ밴ͬĹģٿʼ(a)ĳϣȴѾ˹ģʻ(b)ĳϣ(875v+875m)I=1750I(v+m)1750IIcʱû(a)ĳϣ(1000v+1000m)I=2000I(v+m)1500IIcʱȴһ500ImIлۡ

Ǹϸطʽ(a)ٶI͵II඼ʣֵһתΪ׷ʱҪأΪ뻨Ϊ1000Imһ=500ҪֻʽΪ׷ӵĻʱͶ룬Ҳ˵ҪתΪ׷ӵʱԣֻ(1000v+500m)IΪ뻨ˣIIcҲֻ15001500I(v+m)1500IIc֮ĽоΪΪĹѾˣ4000IcҲٿ죬Ϊ4000IcΪ¿ʼ(һҪĹģ)еϣͬҲΪĹ̲ˡ

ΨһҪоģ500Im(376v+376m)IIһҪI͵IIԵڲϵһҪ֮˶ΪǼٶIIʣֵҲһҪۣӦ188תΪʱ1/4=47ҪתΪɱʱƣ˵48ҪתΪɱʱʣ
572
140ҪתΪʱ

һ⣬Ĵڱͨļ˵ȻԵ֣Ϊͨļ⣬һƷҪһƷ˵ƷҪͻҽҪһƷ140IImܹתΪʱֻΪƷImоͬȼֵĲԶImҪͬIImĲ֣Ϲɣϻ߼ȽIҲIIֻIIֲܹ֮УֻڵII෽ĵΪȫдǿʣƷ500ImҪڵIĻϣˣͬIIƷ仰˵IЩʣƷͬʱۣѡˣIIֽ140Im(ǣ500ImͬIIƷôII༴ʹǮҲ140ImʹǵI500ImȫΪʱҪó100תΪɱʱӶ100IImཻôII໹40Imȱڡ)õĻңΪԺIIƷIصܹԵIۣδءңÿУֻҪǹģֹ̾ǲϷġԵII˵ΪĿҪĻԴȪǴ?

ǣII»ʱγɡγɰʵʵĻۣʱʵʻ۵ʵȱΪ򵥵Ļءһ鲻ë֮ء

ȣ376IIvԤͶϵĻʱ376ڵIIƷ˹ϵΪʽĿɱʱصIIʱСϷ뿪ֻص(ʱҵǮ)βѭתĻҡˣⲻǻһ۵ԴȪҲ
573
ͨȡԱγġǱڵµĻʱ

ûʲôͼ?

ǲҪǣ͵IȣIIһŵ㣺IIʹõĹˣII๺ԼƷIIͶߣͬʱԼʹõͶ߳ƷߡˣIIʱܹ

1򵥵ذѹѹ͵ƽˮƽ¡IʱҵĹ֮ͬˣΪɱʱĻʽְִܵĻңһͬһ̵ĲϷгΪIIĻصһԴȪӶγǱڵ׷ӻʱһԴȪżȻթȡõ󣬵Ȼ￼ʱγɵ޹ءҪǣʵ֧(¾ɱʱ)ʱҵĺĳ֧ģһϵ²ò֧ġˣ˵ͱųˡǼٶ376vǵIIķѵĿɱʱǾͲӦΪ˵һ⣬ͻȻ͵͵ظıǵļ裬⵹(ִ)ӹ׾ѧҳõַ˵ֻԤ350v376v

2һ棬IIΪȵI໹һŵ㣺ͶߣͬʱԼĹ˳ƷߡÿһҵҶṩʮԵʵ֤ŵ㣬֧Ĺʣʵȴһʵ﹤ƣһαͨİ취(ҲܷɵĴ)еһڲӦƷȼٶ仰˵͵磬Ӣ(
574
һ㣬Ҫоǡ˵ִӡ)ǣǵ1ֻͬαװһ£ػ۵ؽеġˣҪǰһһųｲģʵ֧Ķ֧Ĺʡ

֪ڶʱп͹۷ʱеĳЩر۵Ϊڣųϵѡڶִӹ׾ѧ۽зʱҲеĳЩرʵļǰΪڣųϵѡȻǰЩĿ˼һֻΪųҪĸţǹʵֵǣҵĴʲ׼Ҿ󺰴Уƺұ˵ڡʱۡһмٶʱ֧Ͷʵʼֵ(Ǵ󶼲)ԩЩʱ!(ﲻô͸ҵĿһлĻ)

ˣҪﵽĿģ376IIvǲеġ

ǣ376IImƺСֻͬһʱһǱ˴˳ۺͱ˴˹ϡֽĻңֻΪְִֶͨܣĽУֻұ밴ոйصԤͨеصǸʼղϵͨͬһ

ҪͨȡֻγǱڵ׷ӵĻʱֻͨ;ǣIIһʱƭһʱңַȡеĻңԱǰ߾ִӹ׾ѧġҵҲܡ֪»ʱγɣҪֻͨҪĳЩĻҴͨȡΪػʹ԰ѻ͵µIIһʱҵ׷ӻʱγɣԺһʱҵֱӵĻʧһҲııʡIIƭһʱһòһЩ˶ѡ
575
ǣҪIImһֱ֣ڵIIתΪµĿɱʱģǽڱµĽβ(IV)о

1һ

(A)Ĺʽ
I4000c+1000v+1000m=6000

II2000c+500v+500m=3000

ܶ=9000

(B)ģĿ˹ʽ
I4000c+1000v+1000m=6000

II1500c+750v+750m=3000

ܶ=9000

ٶڹʽ(B)УIʣֵһ뼴500ۡˣȣ(1000v+500m)I1500I(v+m)Ҫ1500IIcIµ4000c+500mҪڻۡ(1000v+500m)I1500IIcǼһ̣ڿʱѾˡ

Ǽٶ500Im400ҪתΪʱ100ҪתΪɱʱҪڵIڲʱ400mĽѾˣֱܹӲIcIǣ

4400c+1000v+100m(һҪתΪ100v)бʱѵ500m

II෽Ϊ˻۵ĿģҪI๺100Im(ϵʽ)γɵII׷ӲʱIIΪĿĶ֧100ңתΪI׷
576
ɱʱĻʽIʱ4400c+1100v(Իʽ)=5500

IIĲʱ1600cIIҪʱͱͶ50vĻµͶӶʹĿɱʱ750ӵ800IIӵĲʱͿɱʱ150Ҫɸòʣֵˣ750IImУֻʣ600mΪIIʱҵѻǵƷڻ£

II1600c+800v+600m(ѻ)=3000

150mѾתΪ(100c+50v)IIʵʽȫ빤˵ѣ100ΪIĹ(100Iv)ѣ50ΪIIĹ(50IIv)ѡʵϣΪIIܲƷҪԻʽ100ʣֵҪԱҪϵʽʵǰĹģʼģIĿɱʱ100ͻͨǵĹ˵֣صIIࣻIIƷе100mתI࣬ͬʱְƷе50תĹˡ

Ϊ۵ĿĶıϣڱ£

I4400c+1100v+500ѻ=6000

II1600c+800v+600ѻ=3000

ܼͬ=9000

Уʱǣ

I4400c+1100v()=5500

II1600c+800v()=2400

ϼ=7900
577
ڿʼʱǣ

I4000c+1000v=5000

II1500c+750v=2250

ϼ=7250

ʵʻϽеģ˵ѾӵʱʵʽڵڶʱǾ͵ó

I4400c+1100v+1100m=6600

    II1600c+800v+800m=3200

ϼ=9800

ٶIͬһлۣ550mΪ뻨550m1100IvҪ1100IIcΣ550ImҲҪʵΪͬĵIIƷϼ1650I(v+m)ǣIIҪĲʱֻ=1600ˣ50800IImв䡣ƲҲ˵ĩ׵Ľ£

I4400c+550m(Ҫʱʣֵ)⻹ʱҺ͹˵ѻ1650(v+m)ƷIIcʵ֡

II1650c(е50ǴIImȡ׷ӵ)+800v+750m(ʱҵѻ)

ǣIIvcԭеıĩͶ50cͻҪͶ25vֱ750mȡˣǵó

II1650c+825v+725m

I550mҪʱǰı440γɲʱ110γɿɱʱ110ƱҪ725IImȡ˵ֵ110ϽɵIĹѣɵIIʱѣˣҲֻðǲ
578
ѵ110mתΪʱˣ725IImֻʣ615IImǣII110תΪ׷ӲʱʱǻҪ׷ӵĿɱʱ55ͱٴǵʣֵȡ615IImмȥֻʣ560IIʱѡԣһʵĺͿܵתԺڵʱֵǣ

I(4400c+440c)+(1100v+110v)=4840c+1210v=6050

II(1600c+50c+110c)+(800v+25v+55v)=1760c+880v=2640

ϼ=8690

ҪʹؽУIIͱȵI۵ÿ죬ΪI(v+m)ҪƷIIcĲ֣ͻΨһ֮IIcӵÿ졣Ŀǰ(Iʱ500055006050IIʱ225024002640)һ㡣

ϲ¼УһʱǾ͵ó

I4840c+1210v+1210m=7260

II1760c+880v+880m=3520

ϼ=10780

ʣֵʲ䣬IȾͻ1210vʣֵһ=605ϼ=1815Ϊ뻨ѻֱIIc5555Ҫ880mȡʣ82555IImתΪIIcʱҪIImп۳ӦĿɱʱ=27 1/2ѵ797 1/2IIm

IҪʱ605m484תΪʱ121תΪɱʱҪIImп۳IIm=797 1/2۳ʣµ676 1/2ˣII121תΪ
579
ʱΪˣҪпɱʱ60 1/2ͬҪ676 1/2п۳ʣѵֻ616

ʱʱǣ

Iʱ4840+484=5324

ɱʱ1210+121=l331

IIʱ1760+55+121=1936

ɱʱ880+27 1/2+60 1/2=968

ϼƣ

I5324c+1331v=6655

II1936c+968v=2904

ܼ=9559

ʱĲƷǣ

I5324c+1331v+1331m=7986

II1936c+968v+968m=3872

ϼ=11858

ظּ㣬ѷȥ͵óһʱĲƷ

I5856c+1464v+1464m=8784

II2129c+1065v+1065m=4259

ϼ=13043 

һʱĲƷǣ

I6442c+1610v+1610m=9662

II2342c+1172v+1172m=4686

ϼ=14348

ģڼ䣬I͵IIʱѾ5500c+1750v=7250ӵ8784c+2782v=11566Ҳǰ100:160֮ˡʣֵԭ17502782Ѿ()ʣֵԭڵI500ڵII600ϼ=1100һ꣬ڵI732ڵII745ϼ=1477ˣǰ100:134֮ˡ
580

2ڶ
ڼٶƷ9000ƷȫǴڲҵʱҽ׼еƷʱпɱʱͲʱһƽ1:5ǰǣʱѾķչӦͶҲѾķչģڴǰѾڹ˽׼˿ڹʣҲѾ˷չʱѷĳƷͻỮ£

I5000c+1000v+1000m=7000

II1430c+285v+285m=2000

ϼ=9000

ڼٶIʱֻʣֵһ=500һ(1000v+500m)I=1500ҪתΪ1500IIcΪIIcֻ=1430Ҫʣֵﲹ70285IImȥ215IImǵó

I5000c+500m(ʱʣֵ)+ʱҺ͹˵ѻ1500(v+m)

II1430c+70m(ʱʣֵ)+285v+215m

Ϊ70IImֱӲIIcԣΪƶ׷ӵĲʱҪһɱʱ70/5=1414ҲҪ215IImп۳ʣµ201IImǵó

II(1430c+70c)+(285v+14v)+201m

1500I(v+1/2m)1500IIcĽǼḶ́
581
һѾˡﻹָĳЩЩԻᷢл۵УI(v+1/2m)ǵIIcIIcIImһ

ԶȻѻΪǰᣬI(v+m)ʹIIcIIcȣΪ1IѾһʣƷԼʱе5/6תΪʱԣͬʱõII5/62IҪʣƷΪIIлʱĲʱṩϣIIΪIĿɱʱṩȫһɱʱӦƶɵIԼ׷ӲʱǲʣƷ֪ʵʵĿɱʱͶɵģˣ׷ӵĿɱʱҲͶɵġIʱҲūΪǽҪʹõ׷ͶII๺ҪϵĴֱҪϡԼ͵IIнסǣ˵ʱҵĹ۵㿴׷ͶֻƱҪе׷ͶϺάֶΣǵĿɱʱʵʽ(ָIʱ)ԼֱӻֻΪ׷ͶµĻʱһǰͶǵʱҶͶ˵ͳΪIIƷĹֶΣͶҵֳɵϡ

˵һ£ʱǵıͶѻҵķʽͶʵֻҵĵIIƷǸе⡣ǣ̸Ļͳ̸磬Ӣפʢٹʹ³ɵġ˵
582
塷{һֿ}1879ʮµ׷һƪ˼£д

ĻϷĽƷѾ𣬿ǲ֪ʹǣûΪЩƷκг{ÿʱҵȻԸ⹤˹Ʒ}ûκ˵Ϊʲô˲ӦЩ׬ǮͬһʦʦҽʦһϣõͬƷ{ʦʦҽʦȷʵ԰ԼԸõƷ}ǹ˲ʼڣúġ潡ķΪߵĵλⲻ׵⣬ΪȫûгͶʱķΧƻɿȥȡ飬յԼ͵ԵԼĵλ(ŮפʹפڹĹҵı桷1879׶ذ404ҳ)

ӳͶʱ䣬ʹ˽Լ͵ԵԼĵλΪһߵֺġ潡ķܡΪҪΪʱƷһߣȡǹƻֹҪʱòġ𽡿ķͶʱ?ϧۣƷóֱӺĹ˴򽻵ʵСʵ﹤ơڸʽʵ﹤лסһʱͬʱǹ˵ķˡ

λͨʱ峢߹˽׼λĵĵ³ɵ£ͬһл̸˹˾ģ޷֯ŮĹᣬӵйĹɷݹ˾УЩŮԱΪùɷݹ˾ġɷݹ˾ƶŮκŮʮǰ
583
ᡣƶȵľǣ˾ر𾯲ڸѲߣԷΥʮԺκŮ׼ᡣκŮ׼ڹɷݹ˾ĵطסޡڵÿһݣÿܸ˾ʮԪҵڣǾһֺǺεҸ

豸õŮи١֯ͶʮСʱŮ˵ҪϢ˵Ҫˣм䣬֡赸Ҫá(412ҳ)

ǣʹ˳ΪһߵҪܣһ㡣³ɵʹɡ˹(Ҹ)Ƶɷݹ˾λŷĲ͵ƷʤӢƷָ

ڼ۸ϣҲҪʤӢѾˣǹϵģǱнϵ͵ļ۸ֻҪǵĸֵļ۸ˣǵͶҲˣǾͻнϵ͵ļ۸񣡡(427ҳ)

͹ʺӳͶʱ䣬߹˵λʹΪߵֺġ潡ķʵʣֻ˲ſΪһĻͷĽʹƷ졪г

ˣIʣƷΪIIṩ׷ӵĲʱһIIҲҪΪIṩ׷ӵĿɱʱͿɱʱ˵IIԱҪϵʽܲƷĴ󲿷֣رʣƷĴ󲿷ʱͼΪIΪԼлˡĳɡͼΪԼΪIлˡͿԷνġ֡ˡ
584
ʱΪУI(v+m)=IIcٲʱǲʣƷϵIIĲʱ׷Ӳ֣II޶ȣǵI౾ʵʻۣʵȱٵ޶ȡ

ǻعղſһص㣺IIcСI(v+1/2m)СڵIƷΪϵĲ֣ˣں1500I(v+m)ʱIIһʣƷ=70ɴʵ֡1430IIc£ҪͬȼֵI(v+m)IIļпܽУһ㣬ǲҪп졣ǲ70IImͲֶԵI˵ϲ룬ΪѶƷ飬ԵII˵ͲڼĲʱƷʱʽתΪʵʽֱӵĻ۹̣һʣƷϵʽתΪʱʽI70(ΪʣֵתĻ׼)70IImII಻ҹ70Im70Ϊʱĩ70ȻκٽĲƷı֣׷ӲƷı(ǵIIʣƷı֣׷ӲƷʣƷһ)ǣһII෽ֻһۣͬʱʽȥ70ImıˡˣIᷢԵʣͬII෽ͬʱӦġ
585
ǣǰƲ˵ڴӵIĻ70ûͨII෽湺70ImصֻǲֵػصIʱ70ڵIIȫػֵ߲س䵱׷ӵǱڻʱڵI͵II֮ƷĻಹʹصǰ˫κν˵õġǣе£ֻʱġһʱ׷ӻұܶΪ׷ӻʱְִܵƶ£ֽʱĻʱ磬ڵIµҵϣӦʵͣڵIҵе׷ӲƷΣӦָ70ImIIĲʱͬʱҪIIĿɱʱ14ӡIʣƷImֱӲʱIcһԵIIѾнһʱΪǰģҲ˵ԵIIɱҪϹɵǲʣƷΪǰġ

˵ڵڶУ500ImҪʱ9000ƷΪĿģ밴ķֻ֡ƷѻͨƲܡ

I5000c+500m(ʱʣֵ)+1500(v+m)ѻ=7000Ʒ

II1500c+299v+201m=2000ƷܶΪ9000ƷƷ

ʱĹ£

IҪʱ500mֳ5/6=417c+1/6=83v
586
83vIImȡһͬ򲻱ʱҪأҼӵIIcȥIIc83ҪIIvҲ831/5=17ˣڽ֮ǵó

I(5000c+417m)c+(1000v+83m)v=5417c+1083v=6500

II(1500c+83m)c+(299v+17m)v=1583c+316v=1899

ϼ=8399

IʱѾ6000ӵ65001/12IIʱѾ1715ӵ1899ӽ1/9ֳIIϿ졣

ϣڶյõʱǣ

I(5417c+452m)c+(1083v+90m)=5869c+1173v=7042

II(1583c+42m+90m)c+(316v+8m+18m)v=1715c+342v=2057

ʱõĲƷǣ

I5869c+1173v+1173m

II1715c+342v+342m

IǰһʣֵһĩI(v+1/2m)=1173v+587(1/2m)=17601715IIc45ˣͨͬתIIcIIcͻ45ӶҲҪIIv1/5=9Σʱ587ImҲǷΪ5/61/6Ϊ489c98v98ҪIIĲʱ98ҪIIĿɱʱ1/5=20ˣǵó
587
I(5869c+489m)c+(1173v+98m)v=6358c+1271v=7629

II(1715c+45m+98m)c+(342v+9m+20m)v=1858c+371v=2229

ʱ=9858

ˣʹIʱ6000ӵ7629IIʱ1715ӵ2229ʱ7715ӵ9858ѧŶʾԿѭļʡ

3ʱIIcĽ
ɼI(v+m)IIcĽвͬ

ڼʱ߱ȣ뻥ಹΪǰ˵ģͲܲܵš

ڻʱҪǻʡϸϣǶٶIĻ=1/2mIÿ걣ֲ䡣ֻǼٶʱֳɿɱʱͲʱıᷢ仯Σ

1I(v+1/2m)=IIcˣIIcСI(v+m)I޷ˡ

2I(v+1/2m)IIcϣҪһҪIImһӦּӽIIcʹIIcܶ=I(v+1/2m)ĽԵII˵ĲʱļѾǻۣĲʱѾԽIϵǲʣƷͬʱII໹
588
ʣƷȡһӦĿɱʱ

3I(v+1/2m)СIIcϣIIûֽͨȫĲʱԱͨI๺򣬲ֲܲ㡣ǣҪIIɱʱĽһۣΪĲʱֹֻͨԭȫһ棬Iн׷ӻʱһʱңȴѾֻֽͨ۵һ֡

ǰI(v+m)=IIcǰͬʱǲݵ(ִӹ׾ѧ׷ġ⡱Ҳͬʱݵ)ȻⲢų1011ĲҵĳһܶСǰһܶºǰһȽϣҲûСˣ˿ÿȻֳ£ֻӦӵĲ۲ȫʣֵ1500ʱŻᷢ£ͲʱĻۣʵʵʱˣʱ۵ʵųIIc=I(v+m)һԡʱУȻܷڹȥһϵڼл۵ĽIIcI(v+m)ȣI(v+m)˵IIʣˣֻͨһδָܻƽ⣬ʱɵIIתƵIࡣIIԼһֲʱũҵʹԼӣҲıI(v+m)IIcĹϵڵI͵II֮ĽУIIcֺIcһԿ졣IIĲƷһֿΪϽI࣬ҲıʵʡⲿֲƷͻ͵Iṩһ
589
ϻԸ(ϵߺϵ)֮ĽдġܸŵĿ죬ĩӦôһʼͰִ˫۳

ˣʱУI(v+m)IIcȣ˵߲ڽʱIm/xImΪIʱҵ뻨Ĳ֣ĩI(v+m/x)ͿԵڡڻСIIcǣI(v+m/x)СII(c+m)ǵIIʱIImαԼѵĲ֡Լ

Ӧָڹڻ۵УͲʱƷʱһֵּ˵ʱļֵûеõȷ˵»۵ĲʱĹ̶ֻ֣𽥵ءڵءЩ̶ҪصĲͬʶԲͬĳ̶ȼƷʱģˣԭϺͰƷȵȴƷʱƷʱĺܴһĲɲֺͿɱʱߵĲɵġ(ɲֵתǿԵģˣԼٶһ֮ڣԼɹ̶ʱתǲֵּתʮƵṩƷܶڼֵϺͽʱȡ)ڻֻø϶ԭϵĵطͶҪvͱȻΪƷʱĽϴɲ֡ڼʱʣֵǰʱģ̶ɲڵתƵƷȥļֵĶ޹ءǣڵÿƷʱļֵ˵ֻǰղʱĹ̶ĶѼֵƽתƵƷȥĳ̶ȣѲʱĹ̶ּڡ
590

IV˵
ԵII˵ԭʼĻԴȪǵIIIcһֽнv+mֻڽ߻ʣֵתΪIϣӶʱv+mŲIIࡣһ棬ֻнԼⷽĻһյвߵ׷ӿɱʱǲʣֵŽII࣬γµػңṩµֶΣʹI๺򣬶ҪֱIۡԴڽI(v+m)ĻУҪ۳һֽIIĳЩҪԭϵȵȣ֮ǵĲʱĲҪءΪ˽ڵI͵II֮ĽУ³ϳʱγɵĻصҪأԵI˵ֳϣImһֵءûӦĹII࣬ΪII׷ӲʱãԵII˵ֳϣI෽Ϊȡ׷ӵĿɱʱҲΣֳϣIΪ뻨ǲʣֵܺIIcIImһֱȥתΪҡI(v+m/x)IIcIIcΪļͲҪõIƷIImѾIѵĲ֡ڣڵIIʱ֮ĽУֻֽIImĻཻڶ̶ܹγɻ
591
?֪IIڲֱ֮ӵĻۣIImһֱתΪɱʱ(Iڲֱ֮ӵĻۣImһֱתΪʱ)ֻҪָIIĲͬڲĻۣԼÿеÿʱҵĻۣǴڲͬĽ׶ΣѾԵõ˵ˣӦı䶯ҲȫڵIࡣһ滹ڻءֻĽ׶ΣһȴѾʵֻĽ׶ΡȻ׷ӵĿɱʱͶ׷ӵͶϣͶЩ»أ׷ӵġѵϵ˹ϡͬЩ˵ĻӦҲص㣬ǻѻһ

592

Ŀ¼ 

