南京航空航天大学大学物理练习册答案.pdf

1 0-1 (1) m)42(m)10412(jiijiba vvvvvv v +=+=+ 2042 22 =+=+ba v v =4 .63 2 4 arctan (2) m)422(m)10412(jiijiba vvvvvv v +=+= 510422 22 =+=ba v v =3 .10 22 4 arctan (?) 0-2 (1) 1207248)68()126(=+=jijiba vvvvv v (2) kkkjijiba vvvvvvvv v 609636)68()126(=+=+= 0-3 (1) m5=+ccba vv v v (2) ba v v Q?0=ba v v (3) kijba vvvv v 1243= 0-4 (1) ktjeit t r t vvv v 5cos106)23( d d 22 += ?0=t?jr v v 3=?kji t r vvv v 1062 d d += (2) 1401062 d d 222 =+= t r v (3) 18)106()3( d d =+=kjj t r r vvv v v (4) ikjj t r r vvvv v v 30)106()3( d d =+= 1-1 (1) jti tr vv v )32(3 2 +=?jti t r v vv v v 43 d d +=?j t r a v v v 4 d d 2 2 = s2=t?jir vv v 116+=?jiv vv v 83 +=?ja v v 4= (2) jijijirrr vvvvvv vvv 63)53()116( 12 +=+=?4563 22 =+=r v ? ?x? =4 .63 3 6 arctan (3) ji jji t rr v vv vvv vv v 23 1 3)53( 1 01 1 += + = =?ji ji t rr v vv vv vv v 63 1 63 2 12 2 += + = = (4) 3 x t =?3 9 2 3 3 2 2 2 +=+ = xx y i v 2 j v 4 ba v v + 2 1-2 t t x vx10 d d =? = tx ttx 01 d10d?15 2 += tx 2 d d t t y vy=? = ty tty 0 2 2 dd?2 3 1 3 +=ty jtitr vv v )2 3 1 () 15( 32 +=?jti tv vv v 2 10+=?jti t v a vv v v 210 d d += s2=t?jir vv v 3 14 21 +=?jia vv v 410+= 1-3 ? (1) jti ttavv vv vvv 46 0 +=+= jtittjiitatvrr vvvvv vvvv 2222 00 2)310()46( 2 1 10 2 1 +=+=+= (2) 2 2ty =? 2 2 y t =? 2 3 10 y x+=?)10( 3 2 =xy 1-4 ?x?x? x ? x xx H h =?x hH H x =?V hH H t x hH H t x v = = d d d d 1-5 2 63 d d d d d d d d x x v v t x x v t v a+=? += xv xxvv 0 2 0 d)63(d? 32 23 2 1 xxv+=? 3 46xxv+= 1-6 BvA t v a= d d ? = vt t BvA v 00 d d ?)1 ( Bt e B A v = 1-7 (1) 2 m/s2 d d = t v a?m/s28 d d t t x v+=? += tx ttx 852 d)28(d?m1808 2 +=ttx (2) m/s8 0 =v?m180 0 =x 1-8 3 4 d d t t = ? 2 12 d d t t = ? 2 12tRRat=? 62 16 tRRan= s1=t? 2 m/s12= t a? 2 m/s16= n a?m/s201612 22 =+=a amF v v =?N2201 . 0= maF v ?F v ? =13.53 12 16 arctanarctan t n a a 1-9 ctb t s v+= d d ?c t v at= d d ? R ctb R v an 22 )( + = nt aa =?c R ctb = + 2 )( ? c bRc t = 3 1-10 (1) ?r?rd? rrnd2? v rrn t d2 d =? CD ? min4 .69s4166)2 . 26 . 5( 130 6500 )( d2 d 222 1 2 2 2 1 = = RR v n v rrn tt R R (2) 2 r v =?cm0 . 5=r? 2 /s26 0 . 5 130 =? nr v rn v r v t r r v t 3 2 22 22d d d d = cm0 . 5=r?rad/s/s1031. 3 650052 130 23 3 2 = = 1-11 ? vvv vvv += (1) ? 0 1 = x v v ? km/h36 2 iv x v v = (2) km/h4 .6260tan3660tan= ? vv vv km/h7260cos/3660cos/= ? vv vv 1-12 ?BBAA vvv vvv += km/h917 60cos800100028001000 60cos2 22 22 = += += ? ? ?BA BA BA vvvvv 6543. 0 917 5 . 0800100030sin sin = = = BA BA v vv ? ? =9 .40 ? A ? B ?9 .40? 1-13 ? vvv vvv += (1) =60 10. 1 55. 0 arccosarccos ? ? v v s1050 60sin1 . 1 1000 60sin 10001000 = = = ? vv t (2) =4 .63 55. 0 10. 1 arctanarctan ? ? v v m500 10. 1 1000 55. 0 1000 = ? ? v vx ?m500? 2-1 x y ? v v ? v v ? v v 30 ? ?A v v ?B v v BA v ? v 30 ? v v ? v v ? v v ? v v ? v v ? v v 4 (1) (2) ? A ? = = = BA BBB AAA TT amgmT amTgm 30cos 60cos ? 2 m/s12. 0 30cos60cos = + = BA BA mm gmgm a? (3) N502)12. 060cos8 . 9(10060cos=+=amgmT AA 2-2 ? n F? ? R v mmaF nn 2 =? ? t v mFn d d = t v R v d d 2 =? =t Rv v v v d d 0 2 ? t R v v v 0 0 1 + = 2-3 (1) (a) = = = TTT amgmT amTgm 21 222 111 ? g mm mm a 21 21 + =, g mm mm agmT 21 21 2 2 )( + =+= (b) = = gmFT amgmT 1 22 ? g m mm a 2 21 = (2) ? a ? = += = TTT aamgmT aamTgm 21 222 111 )( )( ? )( 21 21 ag mm mm a+ + = )( 2 )( 21 21 2 ag mm mm aagmT+ + =+= 2-4 (1) ?y? y v mv t v mkmvmg d d d d 2 =? + = v v y kvg vv y 0 2 0 d d? 2 2 0 ln 2 1 kvg kvg k y + + = ?0=v? g kvg k y )( ln 2 1 2 0 max + = (2) ? y v mvkmvmg d d 2 =+? = vy y kvg vv y 0 2 d d max ? g kvg k yy 2 max ln 2 1 =? k eg v yyk )1 ( )(2 max = ?0=y? 2 1 2 0 00 1 = += g kv vvy 2-5 5 ?m? l m =?y?v? y v mv t v myg d d d d =? = vy a vvmyyg 0 dd? l ayg m ayg v )()( 2222 = = ?ly =? l alg v ly )( 22 = = 2-6 = = =+ TTT amamgmT amTamgm 21 2222 1111 )( )( ? )( 21 21 ag mm mm a+ + = )( 2 )( 21 21 2 ag mm mm aagmT+ + =+= 2-7 ?(?)?m?0= a = = 0cos 0sin mgN maN ? 22 gamN+= 2-8 ?m? 2 2 R m =?x?o?x? ?xd?xxRmd2d 22 =? 3 4 d 2 d 0 220 R xxRx mm mx x R R c = 2-9 ? LayLyg=)(?g L Ly a = 2 ?ga Ly 3 1 3 2 = = y v v t y y v t v g L Ly a d d d d d d d d2 = =? = L b v yLy L g vv 3 2 0 d)2(d? += 22 9 22 bbLL L g v ?(?) ?bBC =? L bLbL m b b bL bL yc 2 22 22 )( 22 + = + = ?LBC 3 2 =? Lyc 18 5 = ? 2 2 1 )(mvyymg cc =?)(2 2 cc yygv=? += 22 9 22 bbLL L g v 3-1 6 (1) s)(N68d)430(d 2 0 2 0 =+= tttFI xx (2) 300230d)430(d 2 00 =+=+= tttttFI tt xt ?(s)86. 6=t (3) 1212 mvmvppI=?(s)86. 6=t?s)(N300=I (m/s)20)1010300( 10 1 )( 1 12 =mvI m v 3-2 (1) + = 75355 502 tt tt F?50t?t t v m2 d d =? = 5 00 d2d 1 ttvm v ?(m/s)25 25 1 = m v 75t?355 d d +=t t v m? += 7 5 d)355(d 2 1 ttvm v v ?(m/s)35 2 =v (2) s)(N35)107( 2 1 d 7 0 =tFI? 212 mvmvmvI=?(m/s)35 2 =v 3-3 ? jivmvmvmm vv vvv 8064)( 221121 +=+=+? jiv vv v 108 += (cm/s)8 .12108 22 =+= vv v ?x? =3 .51 8 10 arctan 3-4 ? 0)(=+VMmv?MVmv =? = tt tVMtvm 00 dd?s?S?m?M? = t tvs 0 d? = t tVS 0 d?MSms =? SRs=? R Mm m S + = ?m?M? v M Mm Vvv + =+=? + = tt tv M Mm tv 00 dd?s M Mm R + =?M? R Mm m sRS + = 3-5 rmvL =? mr L v =? 2 2 2 22 1 mr L mvEk=? e M? r mM GE e p = ? r v m r mM G e 2 2 =? 2 mv r mM G e =? 2 2 2 2 2 2 22mr L mr L mr L EEE pk =+= 3-6 (1) j tbi ta t r v vv v v cossin d d += )cossin(j tbi tamvmp vv vv +=?tbtamppcossin 222 += v (2) kabmj tbi tamj tbi taprL vvvvv vv v =+=)cossin()sincos( 3-7 7 (1) 0 vmrL vv v = ? 00 4 3 lmvrmvL= (2) ?o? ) 4 1 ( 4 1 ) 4 3 ()2( 4 3 4 3 0 lmllmllmv+=? l v 19 12 0 = 3-8 (1) 0= mgF?mgF =?(J)980dd 10 0 10 0 = ymgyFA (2) mamgF=?)(agmF+=?(J)990d)(d 10 0 10 0 =+= yagmyFA (3) 0)2 . 0(=gymF?gymF)2 . 0(=?(J)882d)2 . 0(d 10 0 10 0 = yymgyFA 3-9 (1) (J)27d)43(d 3 0 3 0 =+= xxxFA x (2) ? 2 2 2 1 3 2 2 1 2 1 2 1 mvmvmvA=+=?(m/s)3 2 2 = m A v (3) ? )(m/s5 . 2 6 343 2 = + = m F a x x 3-10 ? t v mbtF d d =? = vt vmtbt 00 dd? m bt v 2 2 =?Tt =? m bT v 2 2 = ? m Tb mvmvmvA 82 1 2 1 2 1 42 22 0 2 =+= ?t m bt tvxd 2 dd 2 =? m Tb t m bt btxFA T x 8 d 2 d 42 0 2 = 3-11 (1) rT v v d?0d=rTAT v v ?T v ? =+=+= 2 1 sind)d(ddd)( y y F mglymgj yi xjmgrgmrgmTA vvv vvvv v (2) sin)( 12 mglyymgEp=? (3) ? 2 2 1 sinmvmgl=?sin2glv = 3-12 (1) B x A F= 2 ?0=F? B A x = 0 (2) ) 11 (dd 0 2 11 00xx Ax x A xFA x x x x = ?)(dd 022 00 xxBxBxFA x x x x = 1 A? 2 A? 8 (3) ABBx x A xxB xx AxB x A xFE x x x x p 2)() 11 (d)(d 0 0 2 00 +=+= 3-13 ? ? ? 1 v? ? 10 )(cosvmmmv+=? mm mv v + = cos 0 1 ? 2 v? ghmmvmmvmm h gmm)()( 2 1 )( 2 1 sin cos)( 2 2 2 1 +=+ ) 1cot(2 cos 2 0 2 + + = gh mm mv v 3-14 (1) ?A?A?B?v? 22 0 )( 2 1 2 1 vmmkx BA+ =? BA mm K xv + = 0 (2) A?B?A? m x? 22 2 1 2 1 mA kxvm=? BA AA m mm m x k m vx + = 0 3-15 ? 2 2 1 )sin1 (mvmgR=?)sin1 (2 2 = gRv? R v mmg 2 sin=? 3 2 sin=?=8 .41 3 2 arcsin?gRgRv 3 2 )sin1 (2= 3-16 ? = += sin245sin 2 cos245cos 2 0 0 0 0 0 000 vm v m vm v mvm 0 0 368. 0225 4 v v v=?= =7 .28 4 45sin arcsin 0 v v 3-17 (1) ? v ?V? MVmv =?v M m V =? 222 2 1 2 1 2 1 MVvmmv+=? M mM vv = (2) ? vv = ? ? ? =coscosvmmv?=?2? ? 0 m 0 v x y ? 0 2m 2 0 v v 9 4-1 )7( 12 d 2 d 2 d 21 2 2/ 22 2/ 0 212 mm L xx l m xx l m mxJ L L L m +=+= 4-2 ? cosRr =? cosddRh = ? dcosdd 332 Rhrm= ? dcos 2 1 d 2 1 d 552 RmrJ= 25 3 5 2/ 0 55 2/ 0 2 5 2 3 4 15 8 15 8 dcosd 2 1 2mRR R m RRmrJ= 2222 5 7 5 2 mRmRmRmRJJ=+=+= 4-3 (1) ? 222 51) 2 ( 2 1 2mRR l mmRJ= += (2) 2222 67.61 6 64 51 12 1 mRmRmRMlJJ=+=+= 4-4 sin 2 3 3 1 sin 2 2l g ml l mg J M = d d d d = t ? = 00 dd?)cos1 ( 3 = l g ? 2 2 1 )cos1 ( 2 J l mg=?)cos1 ( 3 = l g 4-5 cos 2 cos 4 )3(mg ll gmmM=? 2222 3 1 ) 4 ( 12 1 ) 4 (3ml l mml l mJ=+= cos 2 3 3 1 cos 2 2l g ml mg l J M = 4-6 (1) ?r?rd? rrgfd2d=? ? rrgfrMd2dd 2 =? mgRR R m grrgM R 3 2 3 2 d2 3 2 0 2 = 10 (2) g R mR mgR J M 3 4 2 1 3 2 2 =? g R t 4 3 00 = = 4-7 (1) ? /smkg102. 05 . 01001d30sind 2 020 0 02. 0 0 = tlFtM oo ? /smkg1d 2 0 0 = t oo tMJJJL (2) rad/s3 3 1 1 2 = = ml J L 4-8 (1) ? O ? J v mlvml+=30sin 22 1 30sin 2 1 ?rad/s3 118