理论力学(第2版)习题答案

2023年12月30日发(作者：宝马5系2021款配置)

各章习题(计算题)部分答案

第1章 略

第2章

2-1

FR?3.284kN，cos(FR,i)?206.3?，cos(FR,j)?116.3?

2-2

T3?16.2kN，??30?

2-3

??48.2?，FRx?4.96kN

2-4

Fx1?86.6N，Fy1?50N

Fx2?30N，Fy2??40N

Fx3?0N，Fy3?60N

Fx4?56.6N，Fy4?56.6N

2-5

FR?0

2-6(a)

FAx?7.07kN，FAy?3.54kN，FB?3.54kN

(b)

FAx?0，FAy?5kN，FB?5kN

(c)

FAx?9.33kN，FAy?4.33kN，FB?6.12kN(垂直于支撑面，指向简支梁)

2-7

Fmin?15kN，FN?25kN

2-8

FAx?0.866kN，FAy?0.5kN，TBD?1kN

2-9

FNA?1.732kN，FNC?3.464kN，AC?1.5m

2-10

FAB?0，FAC?34.36kN

2-11

FBC?2-12

FNE233G，FAx??G，FAy?G

336?G?F

5

2-13

FNC?FND?3G

2-14

FAB?231N，FAE?115.5N，FBC?231N，FBD?84.5N

PP2-15 (a)

FAy??，FB?

33(b)

FA?FB?2P (FA，FB方向相反，组成一力偶)

3(c)

FA?FB?0

7773kN，FAB?3kN，FOA?3kN，FBC??7kN

3362-17

FAx??1 905N，FAy?1 905N，FCx?1 905N，FCy??1 905N

2-16

F1?2-18

FAx?3 571N，FAy??3 571N，FCx??3 571N，FCy?3 571N

·312·

理论力学

2-19

M2?4kN?m，FA?FB?1.155kN

第3章

3-1

FAx?2 400N，FAy?1 200N，FBC?848.5N

3-2

F\'，MO?260N?m

R?012121M?ql

3-3(a)

F\'， (b)

，M?qa?qaF\'?qlOORRq22

3-4(a)

FAx?

(b)

FAx403803kN，FAy?40kN，MA?120kN?m，FNC?kN

33?0，FAy??2.5kN，FBy?15kN，FDy?2.5kN

3-5 当??60?时，FABmin?3-6

FAx?0，FAy4Pr

L?2qa，MA?qa2

3-7 (a)FAx?2 400N，FAy??1 000N，FDx??2 400N，FDy?2 000N

(b)FAx??2 400N，FAy??1 000N，FDx?2 400N，FDy?2 000N

3-8

FAx??FBy?5(1?3)14?203?4?53kN，FAy?kN，FBx?kN，

33322?53kN

3PLPLPL3-9

FAx??，FAy?P，FBx?，FBy?P，FD?，FC?2P

2r2r2r32qa

3-10

FRE??qa，FBD?223-11

FAx??FCx??2.3kN，FAy?FCy?1kN

3-12

FAC??3-13

FBC第4章

4-1

FT?20kN，FOA??10.4kN，FOB??13.9kN

4-2

Mx?2.54kN?m，My?1.46kN?m，Mz?0

4-3

Mz(P)?0

4-4

MAB(P)?Pasin?sin?

4-5

TA?TB?TC?2PP，FEF?0，FBD??

33FF?，FDE?

22W

34-6

T?1kN

，FAx?0，FAy??750N，FAz??500N，FBx?433N，FBZ?500N

4-7

F1?F6??F，F3?F，F2?F4?F5?0

·312

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各章习题(计算题)部分答案

4-8

M1?·313·

MMMMbcM2?M3，FAy?3，FAz?2，FDx?0，FDy??3，FDz??2

aaaaa4-9

FAx?4kN，FAz??1.46kN，FBx?7.9kN，FBz??2.9kN

4-10

FOx??5kN，FOy??4kN，FOz?8kN，

MOx?32kN?m，MOy??30kN?m，MOz?20kN?m

4-11 (a)

FN1?0.412kN，FN2?0.213kN，FN3?0.375kN

4-12

xC??r1r222(r21?r22)，yC?0

4-13 (a)

xC??58.9mm，yC?0 (b)

xC?79.7mm，yC?34.9mm

4-14

xr1r22C??2(r2，yC?0

1?r22)4-15

F?0，F1PPAxAy??2(P1?P2)，FAz?P1?22，FCx?0，FCy?0，FCz?22第5章

25-1

F?Gfsmin1?f2，??arctanfs

s5-2

F?Psin??+?m?cos??-?m?，???m

5-3 (1) A先滑动，(2) A、B一起滑动

5-4 能保持平衡，FS?201N

5-5

f?0.223

5-6

??arcsin3πf4?3πf

5-7

FPP1?fsin??cos?，F2?f，故F1?F2

sssin??cos?5-8

Qmin?8.45kN

5-9

P?4.35N

5-10

?≤9.926?

5-11

x?120cm

5-12

Q?R2(sin??f)L≤P≤Q?R2(sin??f

scos?scos?)L5-13

Pmin?147.5N

5-14

49.61N?m≤MC≤70.39N?m

5-15

b?11cm

5-16

sin??fscos?cos??fQ≤P≤sin??fscos?Q

ssin?cos??fssin?5-17

??arcsinfsr(1?f2

s)b

a313·

·

·314·

理论力学

5-18

P?500N

5-19

fs≥0.15

5-20

b?7.5mm

第6章

6-1

vx?lk(coskt?sinkt)，vy??lk(coskt?sinkt)；

ax??lk2(coskt?sinkt)，ay??lk2(coskt?sinkt)

6-2 (1)

s?0；v?R?；a??0，an?R?2

1331R?2，an?R?2

R；v?R?；a???2242(3)

s?R；v?0；a???R?2，an?0

(2)

s?6-3 直角坐标法：

vy?2R?cos2?t；vx??2R?sin2?t，x?Rcos2?t，y?Rsin2?t；ax??4R?2cos2?t，ay??4R?2sin2?t

自然坐标法：s?2R?t；v?2R?；a??0，an?4R?2

6-4

xM?(l?b)sin?t，yM?(l?b)cos?t；6.5

xM(l?b)22?yM(l?b)22?1

(x?a)(b?l)22?yl22?1

6-6

xB?rcos?t?l2?(rsin?t?h)2，yB??h

uu2b222x?b；a??3 6-7

v??xx6-8

??arctan(rsin?0t)

h?rcos?0t?n6-9 当t?0s时，vM?15.7cm/s；aM?0，aM?6.17cm/s2

?n当t?2s时，vM?0；aM??12.3cm/s2，aM?0

6-10

xC?all?vt222，yC?avtl2?v2t2；vC?av

2lesin2?t2226-11

y?esin?t?R2?e2cos2?t；v?e?[cos?t?2R?ecos?t6-12

x?0.2cos4tm；v??0.566m/s；a??2.263m/s2

bvvt6-13

??arctan0rad；??2022rad/s

b?v0tb]

6-14

??25t2；v?120m/s；an?36 000m/s2

6-15

??8rad/s；???38.4rad/s2

6-16 转轴O的位置位于正方形的中心；??1rad/s，??1rad/s2

111n?6-17

vC?r?；aC?r?2，aC?r?

422·314

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各章习题(计算题)部分答案

n?6-18

vM?1.2m/s；aM?7.2m/s2，aM?0.6m/s2

6-19

vC?0.377m/s

5000?26-20

?2?rad/s2；a?592.2m/s

2d6-21

??3.2rad

·315·

6-22

h1?2mm

lb?26-23

?2?0，?2??

r2n?6-24

vAB?0.2m/s，aAB?0.05m/s2；vC?0.2m/s，aC?0.267m/s2，aC?0.05m/s2

226-25

a1?2r?0，方向沿AO1；a2?4r?0，指向轮心

第7章

7-1

x\'?vt，y\'?acos(kt??)，轨迹方程为y\'?acos(7-2

vM?2R?cos?，方向水平向左

7-3 (a)?2?3.09rad/s； (b)?2?1.82rad/s

kx\'??)

v3v23v3lv7-4 (1)?OC?，vC?；(2)aK?

4b4b4b7-5 当??0?时，v?0；当??30?时，v?100cm/s，向右；

当??90?时，v?200cm/s，向右

7-6

vBC?1.26m/s；aBC?27.4m/s2

7-7

vCD?10cm/s；aCD?34.6cm/s2

7-8

aa?(r?2???)2?(r?)2

7-9

v?233e?，方向向上

27-10

??1.732rad/s，???8.66rad/s

27-11

v?0.173m/s，a?0.05m/s

7-12

vM?0.173m/s，aM?0.35m/s2

7-13

vBC?7-14

vCD?πnrcos?15sin?2

103r?2

937-15

va?346.5mm/s；aCD?1400mm/s2

r?；aCD?第8章

8-1

??

2r28-2

vC?15.6cm/s,vD?17cm/s

·315·

v1?v2，vO?v1?v2

·316·

理论力学

8-3

vC?87.7cm/s

8-4

?OB?3.75rad/s，?I?6rad/s

48-5

vA?600mm/s，vB?200mm/s，vC?20010mm/s；?ABC?rad/s，

3?BD?0.5rad/s

8-6

?AB?2rad/s，?AB??57.8rad/s2；?BC??6.67rad/s，?BC?192.6rad/s2

22(R?2r)vCRv?C8-7

aA?，aBx?2aC，aBy?

(R?r)r(R?r)r8-8

aB?8-9

vC?1222

r?0，?O1B??0223r?0，aC?3r?02

1228-10

v?1.15l?0

8-11

?O1C?6.186rad/s，?O1C??78.17rad/s2

32m/s，aCD?m/s2

153n2?8-13

aB?400cm/s，aB??170.5cm/s2，aC??170.5cm/s2

8-12

vCD?33v273v2ve3v18-14

?OC?，?OC?；vE?v，aE??

?8b224bOB4b28-15

aB?1960mm/s2，?AB?9.8rad/s2

R?08-16

vC?3R?0，方向向左；?O1B?，逆时针转向

r8-17

aC?RRv2，224

a?4a(R?r)?vB22(R?r)(R?r)3?010(9?43)2?0

；aB??39n2?28-18

aB，aB?2a?0?a(3?0?2?0)

8-19

?B?8-20

vB?2m/s，vC?2.828m/s，aB?8m/s2，aC?11.31m/s2

第9章

9-1

?max?gf

r9-2

nmin?67r/min

v09-3

v?

12kv1?0gvv9-4

x?bcoskt?0cos?sinkt，y?0sin?sinkt

kk19-5

x?v0tcos?，y?v0tsin??gt2

2·316

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各章习题(计算题)部分答案

·317·

v0(1?e?kt)

k9-7

t?2.02s，s?7.07m

9-8

F?17.2N

9-6

s?9-9

FAC?9-10

Fmax9-11

a?mL2mL2(?a?g)，FBC?(?a?g)

2a2a?5.84kN，Fmin?5.36kN

Wsin??fcos?

g，FN?cos??fsin?cos??fsin?F0m?2(1?cos?t)

9-12

x??0t?第10章

110-1 (a)

p?mL?，方向水平向右；(b)

p?mR?，方向水平向右；(c)

p?me?，2方向垂直于OC的连线；(d)

p?mvC，方向水平向右

10-2

Fx?30N

10-3

F0?P1?P2?10-4

v?v1?P2?2P1a1

2gm1vr

m1?m2v010-5

t?

g(sin??f\'cos?)10-6

p?l?(5m1?4m2)，方向与曲柄垂直且向上

2m1l?2k??xx?sin?t 10-7

?m?m1m?m110-8

s?R

210-9 (1)

xC?P3L?(P1?2P2?2P3)Lcos?t2(P1?P2?P3), (2)

yC?(P1?2P2)Lsin?t2(P1?P2?P3);

P1?2P2?2P3L?2

2g10-10 椭圆

4x2?y2?l2

FOxmax?10-11 (1)

x?G?2W2G?2Wl?

lsin?t (2)

Fxmax?gP?W?G10-12 向右移3.77cm

10-13

Fox?(m3gsin??10-14

a?

RRm3a)cos?，Foy?m1g?m2(g?a)?(m3gsin??m3a)sin?

rrm2b?f(m1?m2)g

m1?m2·317·

·318·

理论力学

10-15

sA?17cm，向左移动；sB?9cm，向右移动

10-16

Foxmaxr?2?F?(G1?2G2)

2g10-17

FOx??第11章

4mR24mR2(?cos???sin?)，FOy?mg?(?sin???cos?)

3?3?13111-1 (a)

L0?ml2?，(b)

L0?mR2?，(a)

L0?mR2?

22311-2

a?0.8m/s2，FT?28.62kN，FOy?46.26kN

1111-3 (1)

LO??Ml2??mR2??ml2?，(2)

LO??Ml2??ml2?

33111-4

LO?(2m?M)l2?sin2?

311-5

n?480r/min

11-6

??Jz?ma2Jz?mr2?0

11-7

FN?11-8

?1?11-9

a?Pr?0

fgt02(R2M?R1M\')

(m1?m2)R12R2(Mi?PR)RPRg2

?(J1i2?J2)cosgkt

3(P1?3P2)11-10

??11-11

a?11-12

??11-13

a?11-14

v?11-15

a??0lWM?W1Rsin?gR，FT?W1sin??1a

2gJ0g?W1Rm2r2?m1r1m1r12?m2r22?JOg

m1(R?r)2m1(R?r)2?m2(R2??2)g，F?(?2?Rr)m1m2gm1(R?r)2?m2(R2??2)

213gh，FT?mg

3341gsin?，F??mgsin?

7711-16

aC?0.355g

11-17

a?F?f(m1?m2)g

m2m1?3·318

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各章习题(计算题)部分答案

11-18

a?m1r?fm2Rmg?m1a，FTB?fm2g?m2R1r2?m22R?M?2gr，FTA?m1ra

QL211-19

Fsin?12a2gsin?ND?12a2?L2，aCx?gcos?，aCy?12a2?L2

11-20

FNB?36.33N

11-21

FO1x?FO2x?0.516P，FO1y?1.434P，FO2y?1.164P

12章

12-1

WAB?mgr0(1?cos?)，WAC?mgr0(cos??sin?)

12-2

WF?12990.4J，Wf??10500J

12-3

W12??2.06J，W23?2.06J，W31?0

12-4 (a)

T?16ml2?2，(b)

T?322122324mR?，(c)

T?4mR?，(d)

T?4mvC，12-5

W重?10J，W重?5.03J

12-6

T?16ml2?2sin2?

12-7

f?hs?s

1212-8

??2M??m2gr?(sin??fcos?)rm2m

1?212-9

v?3gh

12-10

vA?3m[M??mgl(1?cos?)]

3Mπg?(W212-11

v1?3W2?3W3)vA?W

1?W212-12

v?2gsM/R?W1sin?W，a?M/R?W1sin?g

1?WW1?W12-13

v8ghC?5，aC?45g

12-14

F?9.8N

12-15

??3m1?6m2g3mmsin?，??m1?6m2gcos?

1?32lm1?3m22l12-16

vm3ghC?23m8m，F?(3m1?4m2)m3g1?4m2?33m1?4m2?8m

312-17 (1)

??2(M?m1gRsin?)m(6m， (2)

F1Mcos??m2gRsin2?)(3mOx?1?2)R22(3m?m；

12)RFmm(3M?m2g?12gRsin?)Oy?(3m?sin?

1?m2)R

·319·

319·

第

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·320·

理论力学

12-18

v?第13章

2(mgh?2kh)3m2，a?41mg?4kh，Fs?kh?mg

3m36232W13-2

a?g，FT?

332PgPQ13-3

a?，F?

2P?3Q2P?3Q13-1

a?gsin?

13-4

a?22Tcos?1g，FN?P?Tsin?，Fs?Tcos?

3P313-5

??3g13-6

FADbcos??asin?3322(b?a)sin2??44.5N，FBE?54N

???mr2??2cos?sin??M 13-7

(J?mr2sin2?)?r?233322213-8

M?

(m1?2m2)gr?m2r?，FOx??m1r?，FOy?(m1?m2)g?(m1?2m2)444413-9

??0?时，FAx??2329N，FBx?1 382N，FAy?FBy?19.62N

??180?时，FAx?1223.8N，FBx??592N，FAy?FBy?19.62N

2213-10

FAx??3mr2?0，FAy?mgr,FBx?mr2?0，FBy?mgr

12125g，F?mg

17179g3g213-12

?1?，?2??，FOx?0，FOy?mg

77l7l13-11

aC?aCx?第14章

14-1

P/Q?ctg?/2

14-2

FAx?(3ctg?/2)P

14-3

FA?P/2

14-4

Q?Pctg?

14-5

Q?P/4?50N

214-6

F1?F2l／(acos?)

14-7

FAx?0，FAy?5kN，mA?21kN?m

14-8

P?18.66kN

Fl14-9

x?a?()2

kb14-10

FAx?2(kN)，FAy?3.804(kN)，MA??24(kN?m)，FB?18.588(kN)

·320

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