基礎物理(二a) 第四章

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

⋟ਣ⊮ġ ġ ⣀ᔅཽ‫ݎ‬ġ ĵĮIJġ ⣀ᔅཽ‫ݎ‬റ࿉ġ

ġ ĩΚĪ࿳ԥЖΩۢࡢ(Law of Universal Gravitation)Ȉġ Aˣ⭂佑烉 (1)䈃枻㚨㖑㲐シ⇘炻㚰䎫⽒叿役Ụ⚻⼊䘬年忻丆⛘䎫忳廱炻娵䁢㚰䎫⽭⭂㚱㛅⎹⛘䎫䘬≈ 忇⹎炻Ṏ⎴㗪⽭㚱䓊䓇㬌≈忇⹎䘬ἄ䓐≃⬀⛐ˤ (2)1687 ⸜炻䈃枻㍸↢叔㚱⺽≃⭂⼳烉 ⬯⭁ᷕảỽ℟㚱岒慷䘬䈑橼悥㚫䚠Ḻ⏠⺽炻⺽≃䘬慷ῤ冯ℑ䈑橼 䘬岒慷Ḁ䧵ㆸ㬋㭼炻␴⼤㬌攻嶅暊䘬⸛㕡ㆸ⍵㭼炻㬌斄Ὢ䧙䁢叔 㚱⺽≃⭂⼳ˤ (3)㗇䎫冯䈑橼攻䘬叔㚱⺽≃炻䧙䁢慵≃(Gravitational force)ˤ GMm Bˣ斄Ὢ⺷烉 F烌 2 R Cˣ槿嫱烉 䓙⃳⌄≺忙㛇⭂⼳

R3 烌K1 T2

GMm 4S 2 R m 烌 R2 T2

Î T 2烌

R3 K1

K K K m GMm 烌m u 4S 2 R u ( 31 )烌m u 4S 2 u ( 21 )烌 2 2 2 R R R R K m KM GMm Î F烌 2 ὅἄ䓐≃冯⍵ἄ䓐≃⭂⼳ F ␴ M ㆸ㬋㭼炻⚈㬌 F烌 2 2 烌 3 2 R R R F烌

F烌

Dˣ妶婾烉 (1)叔㚱⺽≃怑䓐㕤岒溆炻ㆾ㗗⛯⊣䘬䎫橼ˤ (2)⛯⊣䎫橼攻䘬叔㚱⺽≃炻⎗夾䁢岒慷普ᷕ㕤䎫⽫(ㆾ岒⽫)炻⚈㬌岒溆冯䎫橼䘬嶅暊䓙䎫⽫ 䬿崟ˤ (3)℞Ṿ⼊䉨䘬䈑橼炻暨ẍ⽖䧵↮嗽䎮炻ᶵ傥⽆岒⽫䬿崟ˤ

ġ ĩΡĪ࿳ԥЖΩۢࡢ‫ޠ‬ᔗңȈ Aˣ㚰䎫⮵⛘䎫㴟㲳䘬叔㚱⺽≃炻⎗妋 慳㼖㯸䎦尉烉 (1)⛘䎫堐朊䁢㴟㯜炻⎗冒䓙㳩≽ˤ ⚈㬌月役㚰䎫䘬ᶨ朊炻⚈䁢㚰䎫 䘬叔㚱⺽≃炻侴ἧ⼿㴟㯜僓暊⛘ 䎫炻⚈㬌 A 嗽䘬㯜ỵ⋯檀炻侴 CˣD 嗽䘬㯜ỵ旵Ỷˤ 137

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

(2)B 嗽䘬㴟㯜䓙㕤⛘䎫℔廱䓊䓇䘬暊⽫≃炻ἧ⼿㴟㯜僓暊⛘䎫炻⚈㬌 B 嗽䘬㯜ỵ⋯檀ˤ (3)䓙㕤㚰䎫⺽≃⍲⛘䎫℔廱暊⽫≃䘬䳸㝄炻ἧ⼿⛘⽫冯㚰䎫忋䶂䘬ℑ䪗䁢㻚㼖(⤪⚾ᷕ AˣB ℑ嗽)炻侴✪䚜䘬ℑ“⇯䁢徨㼖(⤪⚾ᷕ䘬 CˣD ℑ嗽)ˤ (4)䓙㕤⛘䎫冒廱㭷⣑ᶨ⚰炻⚈㬌ᶨ⣑㚫㚱ℑ㫉㻚㼖ˤ Bˣ⎗槿嫱⼿⇘⃳⌄≺忙㛇⭂⼳烉 GMm 4S 2 R Î GMT 2烌4S 2 R 3 m 烌 R2 T2 Cˣ⎗㯪⼿⎬㗇䎫堐朊䘬慵≃⟜⻟⹎ g烉 劍㗇䎫岒慷䁢 M炻ᶼ㗇䎫䘬⋲⼹䁢 R F烌

F烌

GMm 烌mg R2

Î

Ũ烌

Î

R3 GM 烌 烌 K(⭂ῤ) 2 T 4S 2

GM R2

Dˣ枸㷔埴㗇年忻炻妋慳埴㗇ᶵ夷⇯䘬忳≽ʇʇ㓅≽䎦尉(perturbation)烉 (1)埴㗇昌Ḯ⍿⣒春䘬⺽≃⢾炻ṵ⍿℞Ṿ㗇䎫⺽≃䘬ἄ䓐炻㓭忳埴䘬年忻᷎朆⸛㹹䘬㚚䶂炻 侴⛐忳埴䘬年嶉⏰䎦⽖⮷ᶵ夷⇯䘬嬲⊾炻㬌䎦尉䧙䁢㓅≽䎦尉ˤ (2)䓙㕤䘤䎦㗇䎫忳埴䘬年嶉㚱㓅≽䎦尉炻⚈㬌䘤䎦Ḯ㕘埴㗇炻ἳ⤪烉⣑䌳㗇ˣ㴟䌳㗇ˣ⅍ 䌳㗇䫱㗇䎫ˤ Eˣ⇑䓐叔㚱⺽≃妋慳暁㗇忳≽烉 (1)⬯⭁攻䘬暁㗇怈暊℞Ṿ㗇橼䘬ἄ䓐炻ℑ㗇橼岒慷↮⇍䁢 m1ˣm2炻ℑ㗇橼ᾅ㊩ᶨ⭂䘬嶅暊 R炻ℑ㗇橼ẍ⼤㬌攻䘬叔㚱⺽≃炻⼤㬌Ḻ丆ℙ⎴䘬岒⽫㕳廱ˤ (2)ℑ㗇橼Ḻ丆ℙ⎴岒⽫䘬㕳廱⋲⼹冯㗇橼䘬岒慷ㆸ⍵㭼炻⚈㬌 m1 ⇘岒⽫䘬嶅暊䁢 r1炻m2 ⇘岒⽫䘬嶅暊䁢 r2炻⇯ m2 m1 r1烌 R r2烌 R m1為m2 m1為m2

r1 烉r2烌

m2 m1 R烉 R烌m烉 2 m1 m1為m2 m1為m2

(3)ℑ㗇橼Ḻ丆ℙ⎴䘬岒⽫㕳廱炻⚈㬌㗇橼冯岒⽫⿮⏰ᶨ䚜䶂炻㇨ẍℑ㗇橼䘬忙㛇⽭䚠䫱炻 奺忇⹎⽭䚠䫱烉 F烌

Gm1m2 4S 2 r1 m2 4S 2 m1m2 4S 2 m m R R 烌 烌 u 烌 1 1 R2 T2 T 2 m1為m2 (m1為m2 )T 2

Î T 2烌

4S 2 R 3 G(m1為m2 )

Î

T烌

4S 2 R 3 R 烌 2S R G(m1為m2 ) G(m1為m2 )

(4)ℑ㗇橼Ḻ丆岒⽫㗪䘬↯䶂忇䌯烉 v1烌

2S r1 m2 G (m1為m2 ) 1 G R) u 烌2S ( 烌 m2 T m1為m2 2S R R R(m1為m2 )

v2烌

2S r2 m1 G (m1為m2 ) 1 G R) u 烌2S ( 烌 m1 T m1為m2 2S R R R(m1為m2 )

v1 ġ烉v2 烌 m2

G G 烉m1 烌 m2 烉m1 R(m1為m2 ) R(m1為m2 ) 138

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

ġ ĩήĪЖΩள኶ ň অ‫ޠ‬ข໕Ȉġ Aˣ䈃枻䓇⇵᷎ᶵ䞍忻⺽≃ⷠ㔠 G ῤ䘬⣏⮷ˤ Bˣ1798 ⸜⌉㔯徒大炻⛐⮎槿⭌ᷕẍ㈕䦌墅伖嫱⮎ℑ䎫橼攻䡢⮎㚱叔㚱⺽≃⬀⛐炻᷎ᶼ⼿⇘⺽ ≃ⷠ㔠 G 䘬㔠ῤˤ Cˣ㷔慷㕡㱽烉 (1)⤪⚾炻ℑ柮⮷䎫 m ẍ䳘䶂ㆠ⎲炻ἧ℞㈕㒢⇘朄㬊⸛堉ˤ (2)ℑ柮慵慹Ⱄ䎫 M 军㕤 m 㕩炻冯 m 嶅暊 Rˤ (3)m 冯 M 䓙㕤⺽≃䚠⏠炻ἧ⼿ㆠ䶂㈕廱⮷奺⹎ 'T1 ˤ (4)䦣≽ M 军 m 䘬⎎ᶨ“炻ṵ䵕㊩嶅暊 R炻ἧㆠ䶂㛅⍵㕡⎹ ㈕廱 'T 2 ˤ (5)⍾ 'T1 ⍲ 'T 2 䘬⸛⛯ῤ炻⎗㷃⮹婌ⶖˤ Dˣ⮎槿䳸㝄烉 炼 (1)㷔⼿⺽≃ⷠ㔠 G ῤ烌6.74×10 11NȆm2炾kg2ˤ 炼 (2)㬌㷔慷ῤ冯℔娵ῤ 6.67×10 11NȆm2炾kg2 ㍍役ˤ

ġ ᢏ‫܉‬ዑఽȈġ ____1.䈃枻㍸↢叔㚱⺽≃⭂⼳炻᷎㷔⼿⺽≃ⷠ㔠ˤ ___________________________________________________________________ ____2.⺽≃ⷠ㔠䁢 9.8m炾s2ˤ __________________________________________________________________________ ____3.ℑ慹Ⱄ䎫ⷞ㚱暣匟㗪炻ℑ䎫橼攻⎒㚱朄暣≃炻㰺㚱叔㚱⺽≃ˤ __________________________________________________________________________ ____4.⛘䎫丆㖍忳埴㗪炻⛐役㖍溆䘬叔㚱⺽≃慷ῤ㚨⮷ˤ __________________________________________________________________________ ____5.喳㝄⍿慵≃句ᶳ炻㗗䓙㕤喳㝄⍿⛘䎫⺽≃⣏㕤⛘䎫⍿喳㝄䘬⺽≃ˤ __________________________________________________________________________ ____6.䘤䎦㴟䌳㗇ᷳ⇵炻⣑㔯⬠⭞奨㷔⣑䌳㗇忳埴炻䘤䎦℞年忻㚱㓅≽䎦尉炻㍐㷔⣑䌳㗇䘤䓇 ῷ暊䘬䎦尉㗗叔㚱⺽≃⭂⼳䘬䳸㝄ˤ __________________________________________________________________________ ____7.暊⛘檀⹎ᶨᾳ⛘䎫⋲⼹⣏⮷䘬檀⹎炻㇨⍿慵≃䁢⛘堐䘬ᶨ⋲ˤ __________________________________________________________________________ ____8.⮯ℑ䎫橼䘬岒慷≈᾵炻侴⼤㬌攻嶅暊ḇ≈᾵炻⇯叔㚱⺽≃嬲䁢⍇㚱䘬 2 ᾵ˤ __________________________________________________________________________

139

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

1 ⚃ᾳ岒溆岒慷↮⇍䁢 mˣmˣmˣ2m炻㌺⛐㬋㕡⼊䘬奺ᶲ炻⤪⎛⚾炻⇯ 2m ⍿ ≃⣏⮷䁢ỽ烎 Gm 2 3Gm 2 (B) (A) 2 L L2 ˰䫼㟰˱烉D

(C)

( 2為1)Gm 2 L2

(D)

(2 2為1)Gm 2 L2

(E)

(2 2為ij)Gm 2 ˤ L2

2 ⶚䞍ℑ⮎⽫⚻䎫䘬䚜⼹↮⇍䁢 6R ␴ 2Rˣ⭮⹎ᷳ㭼䁢 4烉3ˤ䎦⛐⮯ℑ⮎⽫⚻䎫䵲⭮㌺↿炻⶚ 䞍⮷䎫䘬岒慷䁢 m炻⇯⣏ˣ⮷ℑ䎫攻䘬叔㚱⺽≃䁢 (A)

Gm 2 R2

(B)

2Gm 2 9R2

(C)

8Gm 2 9R2

(D)

9Gm 2 2R2

(E)

9Gm 2 4R2

˰䫼㟰˱烉E

3 怲攟䁢 L 䘬㬋ℕ怲⼊炻⛐枪奺↮⇍伖ᶨ⚢⭂䘬岒溆炻⎬岒溆䘬岒慷⤪⎛⚾炻 ⇯⛐ℕ怲⼊ᷕ⽫嗽㓦伖岒慷䁢 m 䘬岒溆炻℞㇨⍿䘬叔㚱⺽≃䁢 9GMm 7GMm (B) 2 L2 L ˰䫼㟰˱烉ł (A)

(C)

5GMm L2

(D)

3GMm L2

(E)

GMm ˤ L2

4 㚱 ABCD ⚃ ᾳ 䈑 橼 岒 慷 䚠 ⎴炻䫱 攻 嶅 ㌺ ㆸ ᶨ ↿炻⤪ ⎛ ⚾ ˤ ⇯ ᶳ ↿ 㔀 徘 ỽ 侭 㬋 䡢 烎 (⣂ 怠 ) (A)A ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ ⣏ 㕤 B ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ (B) A ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ 䫱 㕤 C ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ (C) B ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ 䫱 㕤 C ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ (D)A ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ 䫱 㕤 D ㇨⍿䘬⺽≃慷ῤ

(E)B ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ ⣏ 㕤 D ㇨ ⍿ 䘬 ⺽ ≃ 慷 ῤ ˤ

˰䫼㟰˱烉ACD

140

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

5 ⣒ 春 䘬 岒 慷 䲬 䁢 10 3 0 ℔ 㕌 炻 㚰 䎫 䘬 岒 慷 䲬 䁢 10 23 ℔ 㕌 炻 ⛘ 䎫 䘬 岒 慷 䲬 䁢 10 25 ℔ 㕌 炻 ⣒ 春 冯 ⛘ 䎫 ⸛ ⛯ 嶅 暊 䲬 䁢 10 11 ℔ ⯢炻⛘ 䎫 冯 㚰 䎫 ⸛ ⛯ 嶅 暊 䲬 䁢 10 9 ℔ ⯢炻⇯ ⛘ 䎫 ⍿ ⇘ ⣒ 春 䘬 ⺽ ≃冯㚰䎫䘬⺽≃㭼⣏䲬䁢 (A)10 3 烉 1 (B)1 烉 10 3 (C)10 4 烉 1 (D)1 烉 10 5 (E)10 5 烉 1 ˤ

˰䫼㟰˱烉ł

6 ⛐戨㱛䲣ᷕ炻㗇⹏丆戨㱛䲣ᷕ⽫ᷳ年忻⋲⼹䘬䩳㕡冯忙㛇⸛㕡ᷳ㭼䁢 k炻叔㚱⺽≃ⷠ㔠䁢 G炻 ⇯戨㱛䲣ᷳ䷥岒慷䁢劍⸚烎 4S 2 4S 2 K (B) GK G ˰䫼㟰˱烉Ń (A)

(C)

2S K G

GK 4S 2

(D)

(E)

GK ˤ 2S

7 `姕⛐⣒春䲣ᷕ㇨㚱埴㗇年忻䘮䁢⚻年忻ˤṲ劍䘤䎦ᶨ㕘埴㗇炻⛘䎫岒慷䁢㬌埴㗇䘬 8 ᾵炻 ⛘䎫⋲⼹䁢㬌埴㗇䘬 4 ᾵炻⛘䎫丆⣒春䘬⸛⛯年忻攟⹎䁢㬌埴㗇䘬 2 ᾵炻⇯⣒春⮵⛘䎫䘬叔 㚱⺽≃⣏⮷䁢⣒春⮵㬌埴㗇䘬劍⸚᾵烎 (A)

1 4

(B)

1 2

(C)1 (D)2 (E)4

᾵ˤ

˰䫼㟰˱烉D

8 岒慷 4m 冯 m 䘬ℑ岒溆 AB 䚠嶅 d炻Ṳ⛐℞忋䶂ᶲ伖ᶨ岒慷 2m 䘬岒溆 C炻ἧ C ㇨⍿䘬慵≃ ␴䁢 0炻⇯ AC 䁢 1 1 (A) d (B) d 2 3 ˰䫼㟰˱烉ń

2 (C) d 3

(D) (3炼 2 )d

(E) (2炼 2 )d ˤ

9 ⤪⎛⚾炻岒慷⛯䁢 m 䘬ᶱᾳ㗇䎫㕤怲攟䁢 d 䘬㬋ᶱ奺⼊ᶱ枪溆炻ἄ⢾㍍⚻䘬䨑 ⭂忳廱炻㭷ᶨᾳ㗇䎫⍿≃⣏⮷䁢ỽ烎 Gm 2 Gm 2 (B) 2d 2 d2 ˰䫼㟰˱烉Ņ (A)

(C)

3Gm 2 2d 2

(D)

3Gm 2 d2

(E)

3Gm 2 2d 2

141

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

栆1.㚱ᶨ岒慷 M ⚻䑘炻⋲⼹䁢 R炻⛐䑘⽫伖ᶨ岒慷 m ᷳ䈑橼炻䈑橼㇨⍿⚻䑘䘬⺽≃䁢ỽ烎 (A)

GMm R2

GMm (B) 2R2

(C)

GMm 4R2

(D)

2GMm R2

(E)0ˤ

栆2.㝸㗇䎫䘬岒慷㗗⛘䎫䘬 3 ᾵炻⋲⼹㗗⛘䎫䘬 2 ᾵炻⛐⛘䎫堐朊⍿≃⣏⮷ F 䘬䈑橼炻伖㕤娚 㗇䎫堐朊㗪炻⇯⍿叔㚱⺽≃⣏⮷䁢ỽ烎 3 (A) F 2

3 (B) F 4

9 (C) F 4

4 (D) F 9

2 (E) F ˤ 3

栆3.㝸㗇䎫䘬岒慷䁢 M炻㗇䎫⋲⼹䁢 R炻劍ᶨ刀⣒䨢凡岒慷 m炻嶅暊㗇䎫堐朊 R炻⇯⣒䨢凡㇨⍿ ⺽≃䁢ỽ烎(`姕慵≃ⷠ㔠䁢 G) GM (B) R2

GMm (A) R2

GMm (C) 2R2

GMm (D) 4R2

GMm (E) 2R ˤ

栆4.劍㚱ᶨ埴㗇丆叿⿮㗇 S ἄ㨊⚻年忻忳≽炻⇯ᶳ↿㚱斄埴㗇⤪⚾炻劍 SD 烌8 SA 炻⇯埴㗇⛐ A 冯 D 嗽⍿叔㚱⺽≃⣏⮷䘬㭼䁢 (A)1烉1 (B)1烉8 (C)8烉1 (D)16烉1 (E)64烉1ˤ

栆5.㈧ᶲ柴炻㚱斄埴㗇⛐⚾ᷕ⎬溆䘬≈忇⹎慷ῤ䘬㔀徘炻ỽ侭㬋䡢烎 (A)㇨㚱溆悥ᶨ㧋⣏ (B)溆 A 嗽㚨⣏ (C)溆 B 冯溆 F 嗽㚨⣏ (D)溆 C 冯溆 E 嗽㚨⣏ (E)溆 D 嗽㚨⣏ˤ

栆6.⭮⹎⛯⊣䘬Ḵ⎴⽫䎫㭤䘬岒慷↮⇍䁢 M1 ⍲ M2炻℞⋲⼹↮⇍䁢 R ⍲ 3R炻⛐嶅䎫⽫ 2R 嗽炻岒 慷䁢 m 䘬岒溆炻℞㇨⍿䘬⺽≃䁢劍⸚烎 GM1m (A) 4R2

GM2m (B) 4R2

(C)

G(M1為M2)m 9R2

GM1m (D) 9R2

GM2m (E) 9R2 ˤ

1 栆7.姕⛘䎫䘬⋲⼹䷖⮷ 2 炻⭮⹎ᶵ嬲炻⇯⛘䎫ᶲ䈑橼慵慷嬲䁢⍇Ἦ䘬 (A)2 (B)

1 2

1 (C)4 (D) 8

1 (E) 4

᾵ˤ

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Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

栆8.岒慷 M ⋲⼹ R ᷳ⛯⊣⮎⽫䎫炻㊾⍣䚜⼹䁢 R 䘬ℏ↯⮷䎫炻⮯ᶨ岒慷 m 䘬岒溆伖㕤⮷䎫䎫⽫炻 ⇯ m 冯∑检䎫橼攻䘬叔㚱⺽≃䁢ỽ烎 GMm (A) 4 R2

GMm (B) 2 R2

3 GMm (D) 4 R2

2 GMm (C) 3 R2

7 GMm (E) 8 R2 ˤ

栆9.⋲⼹䁢 R 䘬戃䎫掌ㆸᶨ䨢⽫䎫炻ἧ䨢⽫䎫堐朊冯戃䎫堐朊⢾↯炻᷎ 忂忶戃䎫䘬䎫⽫炻⤪⎛⚾炻劍掌䨢⇵岒慷䁢 M炻Ṳ嶅戃䎫ᷕ⽫ 2R 嗽炻㚱ᶨ⮷岒溆 m炻⇯⮷岒溆⍿⇘戃䎫䘬叔㚱⺽≃䁢劍⸚烎 (A)

7 GMm 36 R 2

(B)

5 GMm 36 R 2

(C)

1 GMm 6 R2

(D)

1 GMm 9 R2

(E)

2 GMm ˤ 9 R2

栆10.岒慷⎬䁢 9Mˣ4M 䘬 AˣB ℑ⿮㗇䚠嶅 L炻劍ℑ侭怈暊℞Ṿ㗇䎫炻Ṳ㚱ᶨ䀓䭕⛐㬌ℑ⿮㗇 忋䶂ᶲ㇨⍿⺽≃䁢暞炻⇯䀓䭕冯 B 㗇䎫嶅暊䁢ỽ烎 2 4 3 9 (A) 5 L (B) L (C) L (D) Lˤ 13 5 13

栆11.岒慷冯⛘䎫䚠⎴ᷳ⎎ᶨ㗇䎫冯⛘䎫䄼⎰ㆸ⣏⮷ᶵ嬲ᷳ㕘㗇䎫⼴炻Ṣᷳ橼慵⮯ (A)⡆≈ 1 ᾵

1 (B)⡆≈ 3 ᾵

(C)ᶵ嬲

1 (D)㷃⮹ 2

1 (E)㷃⮹ 3 ˤ

栆12.⚃ᾳ岒溆㌺↿⤪⚾炻ᶼ mA 2 ℔㕌ˣmB 1 ℔㕌ˣmC 暞炻⇯ D 岒溆岒慷䁢 (A)2 (B)4 (C)6 (D)8 (E)10 ℔㕌ˤ

3 ℔㕌炻劍 C 岒溆㇨⍿䷥慵≃䁢

栆13.⮯⭮⹎䚠⎴䘬⣏ˣ⮷⮎⽫䎫月⛐ᶨ崟炻⤪⎛⚾ˤ⶚䞍⮷䎫䘬岒慷䁢 m炻⇯ ⣏ˣ⮷ℑ䎫攻䘬叔㚱⺽≃䁢 (A)

Gm 2 R2

(B)

2Gm 2 3R 2

(C)

8Gm 2 9R2

(D)

4Gm 2 16 R 2

(E)

9Gm 2 ˤ 25 R 2

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Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

⒇ࠣⓌ◈ġ Κȃ൑ΚᒶᐆᚡȈġ ____1.⚃ᾳ岒溆㌺↿⤪⎛⚾炻ᶼ mA 3 ℔㕌ˣmB 1 ℔㕌ˣmC 2 ℔㕌炻劍 B 岒溆㇨⍿䷥慵≃䁢暞炻⇯ D 岒溆岒慷䁢 (A)3 (B)4 (C)6 (D)8 (E)9 ℔㕌ˤ 1 4

____2.⛘䎫⋲⼹䁢 R炻劍㝸Ṣ⛐嶅⛘堐檀 R 嗽炻℞慵慷䁢⛐⛘堐嗽ᷳ⸦᾵烎 (A)

1 4

(B)

5 4

(C)

25 16

(D)

16 25

(E)1ˤ

____3.ᶱᾳ岒慷⎴䁢 M 䘬岒溆炻ỵ㕤怲攟䁢 L 䘬䫱怲ᶱ奺⼊䘬枪溆ˤ⛐叔㚱⺽≃⼙枧ᶳ炻忁ᶱ 岒溆⛐⢾㍍㬌䫱怲ᶱ奺⼊䘬⚻⼊年忻忳廱炻ᶼṵᾅ㊩⼤㬌攻䘬嶅暊炻⇯⎬岒溆㇨⍿䘬叔 㚱⺽≃ᷳ⣏⮷䁢⣂⮹烎 3GM 2 L2

(A)

(B)

2GM 2 L2

(C)

GM 2 L2

(D)

GM 2 2 L2

(E)

2GM 2 ˤ L2

____4.劍䓚㗇䎫岒慷䁢ḁ㗇䎫岒慷䘬 16 ᾵炻侴ℑ侭忋⽫䶂攟䁢 a炻䎦㚱ᶨ䀓䭕〘忳埴军㬌忋⽫ 䶂ᶲ嶅䓚㗇䎫ᷕ⽫嶅暊䁢 b 㗪炻㗇䎫⮵䀓䭕ᷳ⺽≃␴〘䁢暞炻⇯ a 䁢 b 䘬劍⸚᾵烎 (A)0.25 (B)1 (C)1.25 (D)1.5 (E)2ˤ ____5.ℑ柮大䒄月⼿⼰役炻Ữ叔㚱⺽≃⌣デ奢ᶵ⇘炻ᷣ天䘬⍇⚈㚨⎗傥䁢ỽ烎 (A)叔㚱⺽≃⭂⼳⎒怑䓐㕤㗇䎫 (B)叔㚱⺽≃ⷠ㔠⣒⮷ (C)大䒄㇨⍿⛘⽫⺽≃⣒⮷ (D)大䒄䘬⺽≃䚠Ḻ㉝㴰 (E)大䒄㇨⍿㐑㒎≃怈⣏㕤⛘⽫⺽≃ˤ ____6.ᶨ⸛朊⛸㧁⍇溆 O炻岒慷 m 䘬岒溆ỵ㕤⛸㧁( 3 d , 0)嗽炻ℑᾳ岒慷 M 䘬岒溆ỵ㕤⛸㧁(0 ,為d)⍲(0 , d)嗽炻⤪⚾炻⇯暁 M 䲣䴙冯 m ᷳ 攻䘬叔㚱⺽≃⣏⮷䁢ỽ烎 (A)

GMm 4d 2

(B)

GMm 2d 2

(C)

3GMm 4d 2

(D)

3GMm 8d 2

(E)

GMm ˤ 8d 2

____7.冒⛘朊戃䚜⎹ᶲ䘤⮬ᶨ岒慷䁢 Mˣ慵慷䁢 W 䘬䀓䭕炻䔞嶅⛘朊 h 檀⹎㗪炻℞岒慷∑ᶳ 炻慵慷嬲䁢

M 4

W 炻⇯ h 䁢⛘䎫⋲⼹ᷳ⸦᾵烎 64

(A)2 (B)2.5 (C)3 (D)3.5 (E)4ˤ ____8.㝸㗇䎫䘬岒慷㗗⛘䎫䘬 3 ᾵炻⋲⼹㗗⛘䎫䘬 2 ᾵炻⛐⛘䎫堐朊 24 kgw 䘬䈑橼炻伖㕤娚 㗇䎫堐朊㗪炻⇯慵慷嬲䁢劍⸚ kgw烎 (A)4

(B)6 (C)12 (D)18 (E)20ˤ

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____9.㝸㗇䎫℞⸛⛯⭮⹎冯⛘䎫䚠⎴炻⋲⼹⇯䁢⛘䎫ᷳℑ᾵炻⛐⛘䎫堐朊⍿≃⣏⮷ F 䘬Ṣ⇘娚 㗇䎫堐朊㗪炻℞⍿叔㚱⺽≃⣏⮷䁢ỽ烎 1 (A) F 4

1 (B) F 2

(C)F

(D)2F

(E)4Fˤ

____10.⤪⚾炻AˣBˣCˣD 䁢⚃ᾳ⣏⮷⎗⾥䔍䘬⮷护䎈炻℞岒慷㭼 䁢 A烉C烌3烉2炻B烉D烌5烉1炻嶅暊㭼 rAB烉rCD烌3烉2炻⇯ AˣB 攻冯 CˣD 攻䘬叔㚱⺽≃㭼 FAB烉FCD ㅱ䁢 (A)5烉1 (B)6烉5 (C)10烉9 (D)16烉9 (E)10烉3ˤ 2 ____11.姕⛘䎫䘬⋲⼹ˮ䷖⮷䁢 R ˯㗪炻`姕⭮⹎ᶵ嬲炻⇯⛘䎫ᶲ䈑橼慵慷嬲䁢⍇Ἦ䘬 3 (A)

2 3

(B)

3 2

4 9

(C)

(D)

9 4

(E)

1 9

᾵ˤ

____12.䎫岒慷⣏䲬㗗㚰䎫岒慷䘬 81 ᾵炻⛐䘣㚰梃凡忂忶㚰⛘ᷳ攻炻㚰䎫␴⛘䎫⮵⬫⺽≃䚠䫱 䘬ỵ伖㗪炻梃凡暊攳㚰䎫ᷕ⽫␴⛘䎫ᷕ⽫䘬嶅暊㭼䁢 (A)1烉3 (B)1烉9 (C)1烉4 (D)1烉10 (E)1烉8ˤ ____13.ᶨᾳ岒慷䁢 1000 ℔㕌䘬堃㗇炻⛐嶅⛘朊䁢⚃ᾳ⛘䎫⋲⼹䘬檀⹎嗽丆⛘䎫忳埴炻⇯㬌堃 㗇⍿⇘䘬⛘䎫⺽≃䁢劍⸚℔㕌慵烎 (A)40 (B)60 (C)80 (D)100 (E)0ˤ ____14.⮯⭮⹎䚠⎴䘬⣏ˣ⮷⮎⽫䎫月⛐ᶨ崟ˤ⶚䞍⮷䎫䘬岒慷䁢 m炻⮯⭮⹎ ⛯⊣䘬⣏䎫㊾⍣ᶨ悐↮炻⤪⎛⚾炻⇯㬌㗪⣏ˣ⮷ℑ䎫攻⺽≃䁢 (A)

Gm 2 4R2

(B)

2Gm 2 9R2

(C)

4Gm 2 81R 2

(D)

23Gm 2 9Gm 2 ġ (E) ˤ 36 R 2 25 R 2

____15.(103 ⬠㷔) ᶨ凔娵䁢戨㱛䲣ᷕ⽫㚱ᶨᾳ崭⣏岒慷䘬湹㳆ˤ㚱ṃ⣑㔯⬠⭞Ộ妰忁湹㳆䘬 岒慷⣏䲬㗗⣒春䘬⚃䘦叔᾵炻⣒春暊㬌崭⣏岒慷湹㳆䘬嶅暊䲬䁢 28000 ⃱⸜ˤ⤪㝄⣒ 春ˣ娚崭⣏岒慷湹㳆冯⛘䎫㌺ㆸᶨ䚜䶂炻ᶼℑ侭⮵⛘䎫䘬ᷣ天⼙枧⎒㚱叔㚱⺽≃炻⇯ 忁ᾳ崭⣏岒慷湹㳆␴⛘䎫ᷳ攻䘬叔㚱⺽≃炻⣏䲬㗗⛘䎫␴⣒春ᷳ攻叔㚱⺽≃䘬⣂⮹ ᾵烎(1 ⃱⸜⣏䲬㗗 6.4×104 ⣑㔯╖ỵ) 炼 炼 炼 (A)1.2×10 12 (B)2.5×10 7 (C)2.2×10 3 (D)4×106 (E)8.1×1011ˤ 1 2

____16.劍⛘䎫⋲⼹䁢 R炻䀓䭕䓙⛘朊✪䚜⋯檀炻䔞℞岒慷∑ᶳ↢䘤㗪 炻䀓䭕暊⛘朊檀⹎〘䁢 R炻⇯㬌㗪䀓䭕㇨⍿⇘叔㚱⺽≃䁢↢䘤㗪䘬⸦᾵烎 (A)

1 2

(B)

1 4

(C)

1 6

(D)

1 8

(E)

1 10

᾵ˤ

____17.怲攟䁢 a 䘬㬋ᶱ奺⼊枪溆↮⇍㓦伖岒慷䁢 2MˣMˣM 䘬ᶱᾳ岒溆炻劍⛐㬌ᶱ奺⼊⸦ỽ ᶲ䘬慵⽫㚱ᶨ岒慷䁢 m ᷳ䈑橼炻⇯㬌䈑橼㇨⍿⇘叔㚱⺽≃䘬⎰≃⣏⮷䁢⣂⮹烎 (A)

2GMm a2

(B)

3GMm a2

(C)

4GMm a2

(D)

9GMm a2

(E)

3GMm ˤ 2a 2

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ΡȃӼ२ᒶᐆᚡȈġ ____1.ᶳ↿㔀徘ỽ侭㬋䡢烎(ㅱ怠ᶱ枭) (A)叔㚱⺽≃怑䓐㕤ảỽ䈑橼攻䘬ἄ䓐≃ (B)慵≃ⷠ㔠 G 㗗䈃枻㇨㷔↢䘬 ≃⭂⼳⎗ẍ妋慳埴㗇忳≽

(D)叔㚱⺽≃㗗冒䃞䓴䘬➢㛔ἄ䓐≃ᷳᶨ

(C)叔㚱⺽

(E)慵≃ⷠ㔠 G 晐

⛘溆侴嬲ˤ ____2.⎛⚾䁢⌉㔯徒大㷔⭂ G ῤ䘬⮎槿䣢シ⚾炻ᶳ↿㔀徘ỽ侭㬋䡢烎 (ㅱ怠ᶱ枭) (A)㬌墅伖䧙䁢㈕䦌 (B)⚾ᷕ 4 ᾳ䎫䘬岒慷グ⮷グ⤥ (C)⸛朊 掉⮯⃱䶂⍵⮬㗗䁢Ḯ慷↢廱≽䘬奺⹎ (D)⚾ᷕ⯢㧁㒢㓦䘬ỵ 伖グ役グ⤥

(E)㬌⮎槿⎗槿嫱叔㚱⺽≃⭂⼳䘬㬋䡢⿏ˤ

____3.斄㕤慵≃ⷠ㔠䘬㔀徘ỽ侭㬋䡢烎(ㅱ怠ℑ枭) (A)慵≃ⷠ㔠⣏䲬㗗 9.8 ℔⯢炾䥺 2 (B)嶅暊⛘堐グ怈炻慵≃ⷠ㔠グ⮷ ↢侭䁢䈃枻

(D)慵≃ⷠ㔠䘬╖ỵ䁢

䈃枻 ℔⯢2 ℔㕌2

(C)慵≃ⷠ㔠㷔

(E)䈑橼月グ役炻ᷳ攻䘬叔㚱⺽≃グ

⣏炻Ữ慵≃ⷠ㔠ᾅ㊩⚢⭂ˤ 1 6

____4.姕㚰䎫堐朊䘬慵≃⟜⻟⹎䁢⛘䎫堐朊慵≃⟜⻟⹎䘬 炻ᶳ↿㔀徘ỽ侭㬋䡢烎(ㅱ怠ᶱ枭)ġ (A)⛐㚰䎫堐朊岒慷䁢 1 ℔㕌䘬ⱑ䞛炻ⷞ⚆⛘䎫⼴䧙℞岒慷䁢 6 ℔㕌ġ (B)⛐㚰䎫ᶲ慵慷 䁢 2 ℔㕌慵䘬ⱑ䞛炻℞岒慷䁢 12 ℔㕌ġ (C)冱慵怠ㇳ⛐㚰䎫ᶲ⎗冱岒慷 150 ℔㕌䘬䈑橼炻 ⇯⛐⛘䎫ᶲ⎗冱岒慷 25 ℔㕌䘬䈑橼ġ (D)冱慵怠ㇳ⛐⛘䎫ᶲ⎗冱 100 ℔㕌慵䘬䈑橼炻⛐ 㚰䎫ᶲ⎗冱 600 ℔㕌慵䘬䈑橼ġ (E)⣒䨢Ṣ⛐⛘䎫ᶲ⎗嶛 2 ℔⯢檀炻⇯⛐㚰䎫ᶲ⎗嶛 12 ℔⯢檀ˤ ____5.⬯⭁ᷕ㚱 AˣBˣC ᶱᾳ䈑橼炻⤪⎛⚾炻⇯ᶳ↿䚠斄㔀徘ỽ侭㬋䡢烎(ㅱ怠ᶱ枭) (A)A ㇨⍿䘬⺽≃慷ῤ䁢

2Gm 2 11Gm 2 ġ (B)A ㇨⍿䘬⺽≃慷ῤ䁢 ġ 4r 2 r2

(C)B ㇨⍿䘬⺽≃慷ῤ䁢

4Gm 2 8Gm 2 ġ (D)B ㇨⍿䘬⺽≃慷ῤ䁢 ġ r2 r2

(E)B ㇨⍿䘬⺽≃㕡⎹⎹⎛ˤ ____6.⶚䞍㚱 AˣB ℑ柮㗇䎫炻A 㗇䎫䘬⋲⼹㗗 B 㗇䎫䘬 3 ᾵炻⭮ ⹎Ṏ㗗 B 㗇䎫䘬 3 ᾵炻娎⓷ᶳ↿怠枭炻ỽ侭㬋䡢烎(ㅱ怠ℑ枭) (A)A 㗇䎫橼䧵㗗 B 㗇䎫䘬 27 ᾵ (B)A 㗇䎫䘬岒慷㗗 B 㗇 䎫䘬 9 ᾵ (C)岒慷ᶵ嬲䘬㝸䈑橼⛐ A 㗇䎫堐朊㇨⍿䘬慵≃ 㗗⛐ B 㗇䎫堐朊ᶲ䘬 9 ᾵ (D)劍ℑ㗇䎫攻㚱叔㚱⺽≃Ḻ䚠ἄ䓐炻⇯ B 㗇䎫㇨⍿䘬叔㚱 ⺽≃㭼 A 㗇䎫⍿⇘䘬叔㚱⺽≃⣏ (E)劍 A 㗇䎫冯 B 㗇䎫ᷳ䎫⽫䚠嶅䁢 d炻⇯ᶨ⣒䨢㡕 ⛐嶅暊 B 㗇䎫

4 3 d 嗽㇨⍿䘬叔㚱⺽≃⎰≃䁢暞ˤ (˰姣˱䎫橼℔⺷ V烌 S R 3 ) 5 3

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Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

____7.ᶳ↿㚱斄ˬ慵≃˭䘬㔀徘炻ỽ侭㬋䡢烎(ㅱ怠ℑ枭) (A)䈑橼䘬慵慷Ἦ冒㕤⛘䎫⺽≃䘬ἄ䓐炻㇨ẍ⛘䎫⺽≃⍰䧙䁢慵≃炻Ữ慵≃㰺㚱㕡⎹⿏ (B)ᶵ侫ㄖ䨢㯋旣≃炻2 ℔㕌冯 1 ℔㕌䘬䈑橼⛐⛘堐嗽冒䓙句ᶳ㗪㇨⍿䘬≃炻2 ℔㕌㗗 1 ℔㕌䈑橼䘬 2 ᾵ (C)㇨媪ˬ⣙慵䉨ン˭㗗㊯ˬ㰺㚱⍿⇘⛘䎫⺽≃䘬ἄ䓐˭ (D)丆⛘䎫 ἄ䫱忇⚻␐忳≽䘬Ṣ忈堃㗇炻晾ἄ䫱忇忳≽炻Ữṵ⍿⛘䎫⺽≃ἄ䓐 (E)䈑橼⛐⛘䎫⍿慵 ≃㇨䓊䓇䘬≈忇⹎慷ῤ冯㛔幓䘬岒慷␴⛘䎫岒慷䘬Ḁ䧵ῤ㚱斄ˤ ____8.斄㕤叔㚱⺽≃䘬㔀徘ỽ侭㬋䡢烎(ㅱ怠ᶱ枭)ġ (A)⛘䎫⛐役㖍溆䘬㗪῁㇨⍿⣒春䘬⏠⺽≃庫怈㖍溆⣏ġ (B)䈑橼⛐⛘⽫㇨⍿叔㚱⺽≃庫 ⛘堐⣏ġ (C)叔㚱⺽≃䘬慷ῤ冯ℑ岒溆岒慷Ḁ䧵ㆸ㬋㭼ġ (D)䈑橼劍ⷞ㚱暣匟炻⇯叔㚱⺽ ≃㚫庫ᷕ⿏䘬䈑橼⣏ġ (E)叔㚱⺽≃℔⺷㍸↢侭䁢䈃枻ˤ ____9.㝸埴㗇丆⣒春℔廱䘬年忻䁢ᶨ㨊⚻年忻炻⤪⎛⚾㇨䣢炻⇯ᶳ↿ ⒒ṃ㬋䡢烎(ㅱ怠ℑ枭) (A)A 溆㇨⍿䘬叔㚱⺽≃㚨⣏ġ (B)C 溆㇨⍿䘬叔㚱⺽≃㚨⣏ġ (C)B 溆㇨⍿䘬叔㚱⺽≃⣏㕤 D 溆ġ (D)B 溆㇨⍿䘬叔㚱⺽≃䫱㕤 D 溆ġ (E)B 溆㇨⍿䘬叔㚱⺽≃⮷㕤 D 溆ˤ ____10.ᶳ↿㚱斄叔㚱⺽≃ᷳ婒㱽炻ỽ侭㬋䡢烎(ㅱ怠ℑ枭) (A)䈑橼⛐⛘朊ᶲ⍿⛘䎫ἄ䓐ᷳ叔㚱⺽≃慷ῤ␴⛘䎫ᷳ冒廱䃉斄 (B)䈑橼ᷳ慵慷⯙㗗 ⬫㇨⍿䘬叔㚱⺽≃慷ῤ炻␴䈑橼䘬岒慷ㆸ⍵㭼 (C)䈑橼⛐⛘朊ᶲ㇨⍿䘬叔㚱⺽≃㕡⎹ 䁢ℑ䈑橼ᷳ忋⽫㕡⎹ (D)⬫䘬ἄ䓐⬀⛐㕤ảシℑ䈑橼ᷳ攻 (E)ℑ䈑攻ᷳ叔㚱⺽≃慷 ῤ␴℞嶅暊ㆸ⍵㭼ˤ ____11.㚱 ABCD ⚃ᾳ䈑橼岒慷䚠⎴炻䫱攻嶅㌺ㆸᶨ↿炻⤪⎛⚾ˤ ⇯ᶳ↿㔀徘ỽ侭㬋䡢烎(ㅱ怠ℑ枭) (A)A ㇨⍿䘬⺽≃慷ῤ⣏㕤 B ㇨⍿䘬⺽≃慷ῤ (B)B ㇨⍿䘬⺽≃慷ῤ⣏㕤 C ㇨⍿䘬⺽ ≃慷ῤ (C)A ㇨⍿䘬⺽≃慷ῤ䫱㕤 B ㇨⍿䘬⺽≃慷ῤ (D)A ㇨⍿䘬⺽≃慷ῤ⮷㕤 B ㇨⍿䘬⺽≃慷ῤ (E)B ㇨⍿䘬⺽≃慷ῤ䫱㕤 C ㇨⍿䘬⺽≃慷ῤˤ ____12.⛘䎫岒慷 81Mˣ㚰䎫岒慷 M炻ℑ侭忋⽫䶂攟⹎䁢 d炻姕䀓䭕ỵ伖⛐ℑ㗇䎫忋⽫䚜䶂ᶲ炻 劍ℑ㗇䎫⮵䀓䭕⺽≃慷ῤ䚠⎴炻㬌㗪䀓䭕冯㚰䎫嶅暊䁢 a炻⇯ a 䫱㕤⣂⮹烎(ㅱ怠ℑ枭) (A)

d d d d d ġ (B) ġ (C) ġ (D) ġ (E) ˤ 10 9 8 7 6

____13.`姕⛘䎫⋲⼹䁢 R炻ᶳ↿Ḽᾳ岒溆炻⒒ℑᾳ岒溆⍿⇘⛘䎫䘬叔㚱⺽≃䚠⎴烎(ㅱ怠ℑ枭)ġ (A)嶅暊⛘堐 R炻岒慷 m ᷳ䈑橼ġ (B)嶅暊⛘堐 2R炻岒慷 2m ᷳ䈑橼ġ (C)嶅暊⛘堐 3R炻岒慷 2m ᷳ䈑橼ġ (D)嶅暊⛘堐 3R炻岒慷 4m ᷳ䈑橼ġ (E)嶅暊⛘堐 4R炻岒慷 4m ᷳ䈑橼ˤ ____14.㚱 ABCD ⚃ᾳ䈑橼岒慷䚠⎴炻䫱攻嶅㌺ㆸᶨ↿炻⤪⎛⚾ˤ⇯ᶳ↿㔀 徘ỽ侭㬋䡢烎 (ㅱ怠ℑ枭) (A) A ㇨⍿䘬⺽≃慷ῤ⣏㕤 B ㇨⍿䘬⺽≃慷ῤġ (B) B ㇨⍿䘬⺽≃慷ῤ⣏㕤 C ㇨⍿䘬⺽ ≃慷ῤġ (C) A ㇨⍿䘬⺽≃慷ῤ䫱㕤 B ㇨⍿䘬⺽≃慷ῤġ (D) A ㇨⍿䘬⺽≃慷ῤ⮷㕤 B ㇨⍿䘬⺽≃慷ῤġ (E) B ㇨⍿䘬⺽≃慷ῤ䫱㕤 C ㇨⍿䘬⺽≃慷ῤˤ

147

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

____15.`姕⛘䎫䘬⋲⼹䁢 R炻㝸䈑橼⛐⛘堐䘬慵慷䁢 W炻⇯ᶳ↿㔀徘ỽ侭㬋䡢烎(ㅱ怠ᶱ枭)ġ (A)娚䈑橼⛐暊⛘堐 R 嗽䘬慵慷䁢

W W ġ (B)娚䈑橼⛐暊⛘⽫ 2R 嗽䘬慵慷䁢 ġ 4 2

(C)娚䈑橼⛐暊⛘堐 2R 嗽䘬慵慷䁢

W ġ (D)娚䈑橼⛐⛘⽫嗽䘬慵慷䁢 0ġ 4

(E)䈑橼嶅⛘堐䃉䩖怈嗽䘬慵慷䁢 0ˤ ____16.劍ℑ岒溆岒慷䘮䁢 M炻䚠嶅 R炻⼤㬌攻叔㚱⺽≃䁢 F炻ᶳ↿㔀徘ỽ侭㬋䡢烎(ㅱ怠ᶱ枭) (A)劍ℑ岒溆岒慷䁢 Mˣ2M炻䚠嶅 R炻⼤㬌攻䘬叔㚱⺽≃䁢 2Fġ (B)劍ℑ岒溆岒慷䘮䁢 M炻䚠嶅 2R炻⼤㬌攻䘬叔㚱⺽≃䁢

F ġ (C)劍ℑ岒溆岒慷䘮䁢 2M炻䚠嶅 R炻⼤㬌攻䘬 2

叔㚱⺽≃䁢 2Fġ (D)劍ℑ岒溆岒慷䁢 Mˣ2M炻䚠嶅 2R炻⼤㬌攻䘬叔㚱⺽≃䁢

F ġ 2

(E)劍ℑ岒溆岒慷䘮䁢 2M炻䚠嶅 2R炻⼤㬌攻䘬叔㚱⺽≃䁢 Fˤ ____17.ᶳ↿㚱斄慵≃䘬㔀徘炻⒒ṃ㬋䡢烎(ㅱ怠ᶱ枭) (A)䈑橼䘬慵慷Ἦ冒㕤⛘䎫⺽≃䘬ἄ䓐炻㇨ẍ⛘䎫⺽≃⍰䧙慵≃ (B)ᶵ侫ㄖ䨢㯋旣≃炻 2 ℔㕌䘬䈑橼⛐⛘堐嗽冒䓙句ᶳ㗪䘬≈忇⹎㗗 1 kg 䈑橼䘬 2 ᾵ (C)⯙⛘䎫⢾悐侴妨炻 䈑橼䘬慵慷晐暊⛘檀⹎䘬⡆≈侴㷃⮹ (D)⎴ᶨ䈑橼⛐⛘䎫ᶲ䘬慵慷␴㚰䎫ᶲ䘬慵慷 䚠䫱 (E)㼖㯸䘬㻚句ḇ㗗慵≃忈ㆸ䘬䳸㝄ˤ ____18.⶚䞍ˬ叔㚱⺽≃˭℔⺷䁢 F

Gm1m2 炻劍℞ᷕ r ẋ堐䈑橼攻岒⽫䘬嶅暊ˤ⇯斄㕤㬌⺷䘬 r2

㔀徘炻ᶳ↿ỽ侭㬋䡢烎(ㅱ怠ᶱ枭) ġ (A)G 䧙䁢慵≃ⷠ㔠ġ (B)椾⃰䓙劙⚳⌉㔯徒大㇨㍸↢ġ (C)㬌⺷怑䓐㕤岒溆⮵岒溆攻䘬 ⺽≃妰䬿ġ (D)㬌⺷怑䓐㕤ℑ⛯⊣⚻䎫橼攻䘬⺽≃妰䬿ġ (E)㬌⺷ᷕ䘬 G ῤ椾⃰䓙䈃枻 䴻⮎槿㷔⼿ˤ

ĵĮIJŠ࿳ԥЖΩŠዀྦ๏਱Ȉġ ᜹ᚡȈ 1.E 2.B 3.D 4.E 5.B 6.A 11.A 12.C 13.C Κȃ൑ΚᒶᐆᚡȈ 1.E 2.D 3.A 4.C 5.B 6.C 11.A 12.B 13.A 14.D 15.A ΡȃӼ२ᒶᐆᚡȈ 1.ACD 2.ACE 3.DE 4.BCE 11.AE 12.AC 13.AD 14.AE

7.B

8.B

9.A 10.A

7.C 8.D 9.D 10.E 16.D 17.B 5.BCE 6.AC 7.AD 8.ACE 9.BD 10.AD 15.ADE 16.ADE 17.ACE 18.ACD

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Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

ĵĮijġ ੕⯶Ὲ㈔‫ݐݎ‬ネ༦ġ

ġ ĩΚĪ२ΩĩňųŢŷŪŵźĪȈġ Aˣシ佑烉 (1)⛘䎫⮵䈑橼䓊䓇䘬叔㚱⺽≃:炻⌛䁢䈑橼䘬慵≃ˤ (2)慵≃䘬慷ῤ⌛䁢慵慷炻ẍ w 堐䣢ˤ (3)⛐⛘堐旬役䘬⎴ᶨ檀⹎(h)炻⮯岒慷⇍䁢 m1ˣm2 䘬 AˣB ℑ䈑橼䓙朄㬊句ᶳ烉 䓙㕤䈑橼⍿⛘䎫䘬叔㚱⺽≃ ὅ䈃枻䫔Ḵ⭂⼳(忳≽⭂⼳) F1烌

GMm1 R2 F1烌m1a1

GMm2 R2 F2烌m2 a2

F1烌

GMm1 GM 烌m1a1 Î a烌 1 2 R2 R

F2烌

F2烌

GMm2 GM 烌m2 a2 Î a2烌 2 2 R R

GM R2 䈑橼⛐⛘堐旬役⍿慵≃ἄ䓐㗪炻䓊䓇䘬≈忇⹎慷ῤ␴䈑橼䘬岒慷䃉斄炻 㬌≈忇⹎䧙䁢慵≃≈忇⹎(acceleration of gravity)炻ᶨ凔ẍ g 堐䣢ˤ a1烌a2烌

Bˣ斄Ὢ⺷烉 w烌F烌

GMm r2

g烌

GM r2

w 烉䈑橼䘬慵慷烊 r 烉䈑橼⇘⛘⽫䘬嶅暊 ╖ỵ䁢䈃枻(N) ╖ỵ䁢℔⯢(ŮĪ

G 烉⺽≃ⷠ㔠 6.67 u10

炼11

M 烉⛘䎫岒慷 N<m

2

kg 2

ġġġġġġġķ u IJı 24 kg

ġ ĩΡĪ२Ωൠ஽࡚ĩňųŢŷŪŵŢŵŪŰůŢŭġŇŪŦŭťĪȈġ Aˣシ佑烉 (1)䈑橼⛐㗇䎫䘬旬役炻⍿⇘㗇䎫䘬⺽≃ἄ䓐炻ἧ䈑橼℟㚱慵≃炻℞ 㕡⎹⿮㊯⎹㗇䎫䘬䎫⽫ˤ (2)㗇䎫䘬旬役炻㭷╖ỵ岒慷㇨⍿䘬叔㚱⺽≃炻䧙䁢娚㗇䎫䘬慵≃⟜ ⻟⹎炻ẍ g 堐䣢ˤ (3)嶅暊㗇䎫グ怈炻⇯㇨⍿䘬叔㚱⺽≃グ⮷炻⚈㬌慵≃⟜⻟⹎グ⮷ˤ Bˣ斄Ὢ⺷烉 GMm 2 F GM (1)慵≃⟜⻟⹎ g烌 烌 r 烌 2 m m r GMm GM g烌 2 烌mg 2 r r ⎗䞍㗇䎫旬役䘬慵≃⟜⻟⹎⌛䁢䈑橼⛐娚ỵ伖䘬慵≃≈忇⹎ˤ

(2)䈑橼䘬慵≃≈忇⹎烉

F烌

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Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

ġ ĩήĪӵ౩‫ޠ‬२Ωൠ஽࡚Ȉ Aˣ⶚䞍⛘䎫⋲⼹䁢 R炻⛘䎫岒慷䁢 M炻⇯⛘䎫堐朊䘬慵≃⟜烉 GM (6.67 u10炼11 )(6 u 1024 ) ẋℍ㔠ῤ⎗⼿ 烌 ɼ9.8 m 2 g s R2 (6.4 u 106 ) 2 Bˣ⛐⛘䎫⢾悐炻嶅暊⛘⽫ r 嗽烉 g烌

g烌

GM r2

䔞 r グ⣏㗪炻g ῤグ⮷ˤ

⎗䞍嶅暊⛘⽫グ怈炻g ῤグ⮷炻g ῤ␴ r 2 ㆸ⍵㭼ˤ Cˣ⛐⛘䎫ℏ悐炻嶅暊⛘⽫ r 嗽烉 ⛐⛘䎫ℏ悐 r 嗽炻ℏ悐䘬岒慷傥䓊䓇慵≃⟜ `姕⛘䎫⭮⹎䁢⛯⊣炻ᶼ⭮⹎䁢 U炻侴⛘䎫ℏ悐䘬岒慷䁢 M1炻 4 ⇯ M1烌 S r 3 u U 侴 3

4 M烌 M烌 S R 3 u U 3

r3 4 3 4 3 3 3 ⚈㬌 M 1 烉M烌 S r u U 烉 S R u U烌r 烉R Î M1烌 3 M R 3 3 GM 1 G r 3 M GM g烌 2 烌 2 ( 3 )烌 3 r r r R R

⎗䞍 g ␴ r ㆸ㬋㭼炻

(1) 䔞 r烌0(⛘⽫嗽) 㗪炻g烌0 Î ⛘⽫嗽䘬慵≃⟜䁢 0ˤ (2) ⛘䎫ℏ悐䘬 g ῤ␴ r ㆸ㬋㭼炻⌛ 1 1 ⛘䎫ℏ悐 r烌 R嗽 炻g ῤ䁢⛘堐䘬 1炾2炻䫱㕤 g ˤ 2 2

ġ ᢏ‫܉‬ዑఽȈġ ____1.崌忻䘬慵≃≈忇⹎㭼⊿㤝⣏ˤ ___________________________________________________________________ ____2.劍㝸㗇䎫冯⛘䎫岒慷䚠⎴炻⇯㝸㗇䎫橼䧵グ⣏炻℞⛘堐慵≃⟜グ⣏ˤ __________________________________________________________________________ ____3.⎴ᶨ䈑橼炻岒慷␴慵≃≈忇⹎ㆸ㬋㭼ˤ __________________________________________________________________________ ____4.劍㝸㗇䎫冯⛘䎫⭮⹎䚠⎴炻⇯㝸㗇䎫⋲⼹グ⣏炻℞⛘堐慵≃⟜グ⮷ˤ __________________________________________________________________________ ____5.嶅暊⛘ᶨᾳ⛘䎫⋲⼹䘬檀⹎炻℞慵≃⟜㚫嬲ㆸ⛘堐䘬 1炾2ˤ __________________________________________________________________________

150

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

____6.劍⛐㝸㗇䎫ᶲ䘬慵≃⟜⻟⹎⎒㚱⛘䎫䘬 1炾2炻⇯㝸Ṣ⛐娚⛘䘬橼慵䁢⛘䎫䘬 2 ᾵ˤ __________________________________________________________________________ ____7.⮷䞛⫸⽆䨢ᷕ句ℍ㶙ḽᷕ炻慵≃≈忇⹎㚫徸㻠⡆⣏ˤ __________________________________________________________________________ ____8.⎒㚱⛐⛘⽫䘬⛘㕡炻䈑橼䁢⣙慵䉨ンˤ __________________________________________________________________________ ____9.⛘䎫⛐役㖍溆㗪炻暊⣒春㚨役炻⚈㬌⛘䎫ᶲ䘬Ṣ慵慷㚫庫怈㖍溆㗪䘬慵慷慵ˤ __________________________________________________________________________ ____10.嶅暊⛘⽫グ役炻慵≃⟜⻟⹎グ⣏ˤ __________________________________________________________________________

1 ᶨᾳ⭮⹎⛯⊣䘬㗇䎫炻↮塪䁢 8 ᾳ⭮⹎ᶵ嬲ˣ岒慷䚠䫱䘬㗇䎫ˤ⇯㭷ᾳ㗇䎫堐朊䘬慵≃≈忇 ⹎嬲䁢⍇Ἦ䘬⣂⮹᾵烎 (A)2 (B)8 (C)

1 2

(D)

1 4

1 (E) ˤ 8

˰䫼㟰˱烉C

2 㝸㗇䎫岒慷 M炻⋲⼹ R炻℞⛘堐慵≃⟜⻟⹎䁢 gˤ娎⚆䫼ᶳ↿⓷柴烉 (1)䓚㗇䎫岒慷 3M炻⋲⼹ R炻暊⛘ R 嗽慵≃⟜⻟⹎䁢____________ˤ (2)ḁ㗇䎫岒慷 4M炻⋲⼹ 2R炻暊⛘ R 嗽慵≃⟜⻟⹎䁢____________ˤ (3)᷁㗇䎫岒慷 2M炻⋲⼹ 2R炻⛘堐慵≃⟜⻟⹎䁢____________ˤ ˰䫼㟰˱烉

3 `姕㝸㗇䎫䘬慵≃≈忇⹎䁢⛘䎫䘬 4 ᾵炻娎⚆䫼ᶳ↿⓷柴烉 (1) 䈑 橼 冒 檀 ⹎ h ἄ 冒 䓙 句 橼 炻 ℞ 句 ⛘ 忇 ⹎ 慷 ῤ 䁢 ⛘ 䎫 䘬 ____________ ᾵ ˤ (2) 㝸 Ṣ 䘬 ✪ 䚜 嶛 帵 檀 ⹎ 䁢 ⛐ ⛘ 䎫 䘬 ____________ ᾵ ˤ (3) 㝸 Ṣ 䘬 橼 慵 䁢 ⛐ ⛘ 䎫 䘬 ____________ ᾵ ˤ

˰䫼㟰˱烉

151

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

4 ⤪⎛⚾炻㚱ℑ岒溆岒慷↮⇍䁢 Mˣ2M炻䚠嶅 4rˤ娎⚆䫼ᶳ↿⓷柴烉 (1)A 溆ỵ伖冯ⶎ岒溆 M 䚠嶅 r炻℞慵≃⟜⻟⹎䁢____________ˤ (2) B 溆ỵ伖䁢ℑ岒溆ᷕ溆炻℞慵≃⟜⻟⹎䁢____________ˤ ˰䫼㟰˱烉

5 岒慷䁢 M 䘬䀓䭕⛐⛘堐䘬慵慷䁢 W炻䘤⮬⼴岒慷㚫晐䅫㕁ἧ䓐侴㷃⮹炻劍⛐嶅⛘堐 嗽炻岒慷∑ᶳ

R 2

M 炻⇯㬌㗪䀓䭕㇨⍿䘬慵≃䁢____________ˤ 4

˰䫼㟰˱烉

6 ⶚䞍 g 䁢⛘堐ᷳ慵≃⟜⻟⹎炻⇯嶅暊⛘堐 h( h R 炻R 䁢⛘䎫⋲⼹)檀嗽ᷳ慵≃⟜⣏⮷炻庫⛘ 堐ᶲᷳ慵≃⟜⮷ġ R2 2h R 2R 2 (B) ġ (C) ġ (D) g g g g R h h2 h2 ˰䫼㟰˱烉B

(A)

(E)

2h 2 gˤ R2

7 姕⛘䎫⋲⼹䁢 R炻㝸⣒䨢凡⛐年忻⋲⼹ 4R 䘬⚻⼊年忻ᶲ䑘丆⛘䎫忳≽炻凡ℏ⣒䨢Ṣ⛐⛘堐㗪 岒慷䁢 80 ℔㕌炻⇯⛐娚嗽 (1)⣒䨢Ṣ㇨⍿⛘䎫⺽≃䁢____________℔㕌慵ˤ (2)⣒䨢Ṣ䘬⎹⽫≃䁢____________℔㕌慵ˤ (3)⣒䨢Ṣ䘬夾慵䁢____________℔㕌慵ˤ (4)⣒䨢Ṣ䘬岒慷䁢____________℔㕌ˤ ˰䫼㟰˱烉łńņ

152

Ŝ唺㜾⎸汧ᾼ卹䋅䭠ⴇŞġ ⦉䪝䏸䖕ŠijłŠ䲻⡪䱯ġ 喻㢘イ␪ġ

栆1.ᶨᾳ⭮⹎⛯⊣䘬㗇䎫↮塪䁢 64 ᾳ⭮⹎ᶵ嬲ˣ岒慷䚠䫱䘬㗇䎫炻⇯㭷ᾳ㗇䎫堐朊䘬慵≃≈忇 ⹎嬲䁢⍇Ἦ䘬⣂⮹᾵烎 (A)1 (B)2 (C)

1 2

(D)

1 4

1 8

(E) ˤ

栆2.㝸㗇䎫⸛⛯⭮⹎冯⛘䎫䚠⎴炻⋲⼹⇯䁢⛘䎫 2 ᾵炻⛐⛘䎫ᶲ慵慷䁢 48 ℔㕌慵䘬Ṣ⇘娚㗇䎫 㗪炻℞慵慷䁢 (A)24 (B)36 (C)48 (D)72 (E)96

栆3.䀓㗇岒慷䲬䁢⛘䎫䘬

℔㕌慵ˤ

1 1 ᾵炻⋲⼹䲬䁢⛘䎫䘬 ᾵ˤṲ⛐⛘堐嗽ẍ⻰䯏䦌䟅䡤慵慷㗪炻⻰䯏 2 10

Ỡ攟慷䁢 xˤ劍⛐䀓㗇堐朊ἄ䚠⎴㷔慷㗪炻⻰䯏Ỡ攟慷䁢ỽ烎 (A)0.1x

(B)0.2x

(C)0.3x

(D)0.4x

(E)0.5xˤ

栆4.䓚ˣḁℑ㗇䎫䘬岒慷䚠䫱炻Ữ⋲⼹㭼䁢 1烉2炻⇯䓚ˣḁ㗇䎫堐朊䘬慵≃≈忇⹎㭼䁢 (A)1烉1 (B)1烉2 (C)2烉1 (D)1烉4 (E)4烉1ˤ

4 栆5.⶚䞍⛘䎫⋲⼹䁢 R炻⸛⛯⭮⹎䁢 U炻ᶼ叔㚱⺽≃ⷠ㔠䁢 G炻䎫橼橼䧵䘬斄Ὢ⺷䁢 V烌 S R 3 炻 3 ⇯嶅暊⛘堐 R 嗽䘬慵≃≈忇⹎慷ῤ䁢劍⸚烎 1 3

(A) S G U R

2 3

(B) S G U R

4 3

(C) S G U R

(D)

4S G U 3R

(E)

S GU 3R

ˤ

1 2

栆6.㝸埴㗇橼䧵䁢⛘䎫䘬 8 ᾵炻⸛⛯⭮⹎䁢⛘䎫䘬 ᾵炻⛐⛘䎫堐朊䘬䈑橼ἄ冒䓙句橼⇘忼⛘ 朊暨㗪 4 䥺炻⇯⛐娚埴㗇堐朊ἄ䚠⎴檀⹎䘬冒䓙句橼暨㗪 (A)1 (B)2 (C)4 (D)8 (E)16 䥺ˤ

153