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Российский государственный гидрометеорологический университет

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Теоретическая механика

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1.2 Вал условие ФЗО

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Равновесие вала

Горизонтальный вал весом G может вращаться в цилиндрических шарнирах A и B. К шкиву 1 приложено нормальное давление N и касательная сила сопротивления F , пропорциональная N . На шкив 2 действуют силы натяжения ремней T1 и T2. Груз Q висит на нити, навитой на шкив 3. Определить силу давления N и реакции шарниров в условии равновесия вала (в Н ). Учесть веса шкивов P1, P2, P3. Все нагрузки действуют в вертикальной плоскости. Силы даны в Н, размеры — в см.

Вариант А

						F~
								~			*y

	z			T~2				N	q		Q d
	z			T~2		?			q	3	Q d
	6			α H			q
				HY	2		q	1			c

	A				q
						?T~1	a
B			pb						b
B			x
	pb	-
		-

F = 0.1N, T1 = 40, T2 = 21, P1 = 36, P2 = 30, P3 = 34, Q = 10, G = 20,

α = 60◦, R1 = 18, R2 = 12, R3 = 13, a = 22, b = 23,

c = 26, d = 23.

Вариант Б

~1 α

F = 0.3N, T1 = 70,

P2 = 30, P3 = 38,

, P1

= 136

= 46

= 22,

= 35,

◦

= 60

1 = 30,

, R

a = 24, b = 28,

-T~2

= 12,

= 14,

d .

= 31

= 28

Вариант В

F = 0.1N, T1 = 30,

= 57,

P1 = 26,

2 = 20,

3 = 24,

α H-

α = 45 , R1 = 16,

T~2

= 18,

= 15,

◦

R2 = 10, R3 = 11,

?T~1 a

, d .

a = 22, b = 25,

= 27

= 23

Вариант Г

T~2

Q d

α H

B-

F = 0.1N, T1 = 30, T2 = 16, P1 = 36, P2 = 30, P3 = 34, Q = 10, G = 15,

α = 60◦, R1 = 18, R2 = 12, R3 = 13, a = 22, b = 23,

c = 26, d = 23.

Вариант			Д

					~					*y
		6								3
					T1				q	3
	z							2	q	Q d
		~					q
		F	6	A			q		-b
		~			pb					c
	N		1						~	c
									T2
B	-		-q			a
B	x
		bp

F = 0.2N, T1 = 40, T2 = 76, P1 = 22, P2 = 10, P3 = 14, Q = 22, G = 20,

α = 30◦, R1 = 26, R2 = 8, R3 = 9,

a = 22, b = 26, c = 27, d = 26.

Вариант

F = 0.2N, T1 = 70,

= 137, P1 = 32,

= 45◦

= 28

= 20,

3 = 24,

, R1

-T~2

Q = 18,

= 35,

= 10

= 11

d .

a = 22,

= 25,

= 27

= 26

Вариант

F = 0.4N, T1 = 40,

= 24,

= 40,

2 = 30,

3 = 38,

α H

α = 60 , R1

= 18,

T~2

= 26,

= 20,

◦

?T~1

R2 = 12, R3 = 14,

d .

a = 24, b = 29,

= 32

= 25

Вариант З

	z		T~1 α				3	A
	z		T~1 α				3	pb
		F~ ?
		F~ ?						Q
		6 N~			2	q		Q
		1		q
				q		-		b

		-q
						~
B	x					T2
		pb				a
						a

*y	F = 0.3N, T1 = 40,
	T2	, P1	,
		= 23	= 36

dP2 = 20, P3 = 28, Q = 26, G = 20,

c		◦
		α = 45 , R1 = 28,
		R2 = 10, R3 = 12,
		a = 24, b = 29,
		c = 31, d = 28.

Вариант

F = 0.4N, T1 = 50,

= 29

= 46

P2 = 30, P3 = 38,

= 26,

= 25,

◦

1 = 30,

= 60

, R

R2 = 12, R3 = 14,

T~1

a = 24, b = 29,

= 32

= 28

Вариант К

						F~
				HY			~			*y
				HY		1
	z			T~2			N	q		Q d
	z			T~2		?		q	3	Q d
	6			α H			q
					2		q			c

	A				q
						?T~1	a
B			pb					b
B			x
	pb	-
		-

F = 0.1N, T1 = 40, T2 = 21, P1 = 26, P2 = 20, P3 = 24, Q = 26, G = 20,

α = 45◦, R1 = 16, R2 = 10, R3 = 11, a = 22, b = 27,

c = 29, d = 23.

Вариант

F = 0.4N, T1 = 50,

T2 = 29, P1 = 20,

2 = 10,

3 = 18,

Q = 26, G = 25,

α = 30◦, R1 = 14,

R2 = 8, R3 = 10,

= 24,

= 29,

= 30

= 25

Вариант

F = 0.3N, T1 = 60,

= 33

= 36

P2 = 20, P3 = 28,

= 26,

= 30,

-T~2

α = 45◦, R1 = 28,

= 10

= 12

a = 24, b = 29,

= 31

= 28

Вариант

F = 0.1N, T1 = 30,

T2 = 57, P1 = 42,

2 = 30,

3 = 34,

T~1 α

Q = 18, G = 15,

= 60◦

= 30

, R1

-T~2

R2 = 12, R3 = 13,

a = 22, b = 25,

-q

c = 28, d = 26.

Вариант

F = 0.4N, T1 = 50,

T2 = 29, P1 = 40,

2 = 30,

3 = 38,

Q = 10, G = 25,

F ?

= 60◦

, R1

= 18

R2 = 12, R3 = 14,

α H

a = 24, b = 25,

- pb

= 28,

= 25.

Вариант

F = 0.4N, T1 = 50,

= 98,

= 26,

= 30◦

= 26

= 10,

3 = 18,

, R1

Q = 14,

= 25,

= 8

= 10

T~1

d .

a = 24,

= 26,

= 27

= 28

Вариант

F = 0.4N, T1 = 50,

= 29,

= 30,

2 = 20,

3 = 28,

Q = 10, G = 25,

R2 = 10, R3 = 12,

= 24,

= 25,

1 c

= 45◦

, R1

= 16,

d .

= 27

= 25

Вариант

F = 0.4N, T1 = 40,

= 30, P3

= 38,

= 24

= 44

= 10,

= 20,

T~1

= 12, R3

= 14,

= 60◦

, R1

= 26,

-q

d .

a = 24, b = 25,

= 28

= 27

Вариант Т


					~					*y
		6								3
					T1				q	3
	z							2	q	Q d
		~	N				q
		~		B			q		-
		F ?		B					b
			~		pb					c
		1							T2
			x
		pb
A			-q			a

F = 0.3N, T1 = 30, T2 = 18, P1 = 26, P2 = 10, P3 = 18, Q = 10, G = 15,

α = 30◦, R1 = 26, R2 = 8, R3 = 10, a = 24, b = 25,

c = 26, d = 28.

Вариант У

F = 0.3N, T1 = 60,

α H

T2 = 117, P1 = 40,

= 60◦

= 18

T~2

= 30,

= 38,

, R1

Q d

Q = 18, G = 30,

a = 24, b = 27,

?T~1a

R2 = 12, R3 = 14,

= 30

= 25

Вариант

F = 0.4N, T1 = 40,

= 30, P3

= 38,

, P1

= 77

= 46

T~1 α

= 18,

= 20,

◦

α = 60 , R1 = 30,

c = 30, d = 28.

-q

R2 = 12, R3 = 14,

a = 24, b = 27,

Вариант Х

α H-

T~2

B-

F = 0.4N, T1 = 30, T2 = 57, P1 = 40, P2 = 30, P3 = 38, Q = 18, G = 15,

α = 60◦, R1 = 18, R2 = 12, R3 = 14, a = 24, b = 27,

c = 30, d = 25.

Вариант

F = 0.2N, T1 = 40,

= 22,

= 16,

2 = 10,

3 = 14,

α H

α = 30 , R1

= 14,

T~2

= 26,

= 20,

◦

?T~1 a

R2 = 8, R3 = 9,

, d .

a = 22, b = 27,

= 28

= 23

Вариант

F = 0.1N, T1 = 50,

F ?

= 26,

= 28,

= 45◦

= 20

= 20,

3 = 24,

, R1

= 26,

= 25,

α H

a = 22, b = 27,

- pb

= 29,

= 24.

R2 = 10,

= 11,

Вариант

F = 0.1N, T1 = 30,

= 58,

= 40,

= 60◦

= 26

= 30,

3 = 34,

, R1

= 14,

= 15,

T~1

a = 22, b = 24,

R2 = 12,

= 13,

-q

-T2

c = 27, d = 25.

Вариант

F = 0.2N, T1 = 40,

T2 = 76, P1 = 38,

P2 = 30, P3 = 34,

6T~2

Q = 22, G = 20,

◦

= 60

, R1 = 22,

α H2

R2 = 12, R3 = 13,

a = 22, b = 26,

-q

c = 29, d = 24.

?T~1

Вариант

F = 0.3N, T1 = 60,

T2 = 33, P1 = 30,

= 20

= 28

Q = 26, G = 30,

◦

α = 45 , R1 = 16,

?T~1

2 = 10,

3 = 12,

= 24,

= 29,

c = 31, d = 25.

Вариант

F = 0.4N, T1 = 50,

T2 = 96, P1 = 22,

P2 = 10, P3 = 18,

Q = 22, G = 25,

= 30◦

= 18

, R

R2 = 8, R3 = 10,

a = 24, b = 28,

= 29,

= 26.

Вариант

F = 0.2N, T1 = 50,

T2 = 27, P1 = 42,

P2 = 30, P3 = 34,

Q = 10, G = 25,

◦

α = 60 , R1 = 30,

R2 = 12, R3 = 13,

T~1

= 22,

= 23,

c = 26, d = 26.

Ответы

	N	XA	ZA	XB	ZB
1	198.889	85.664	1094.760	-55.275	-744.058
2	53.778	331.006	-269.630	-581.405	389.496
3	45.000	60.562	-223.085	-65.257	311.280
4	165.556	-45.237	-658.206	69.793	964.905
5	17.308	-157.933	66.787	44.625	-16.889
6	84.286	-288.045	-141.146	17.262	203.791
7	77.222	135.898	863.013	-93.009	-612.575
8	57.381	-20.580	66.590	-13.490	92.507
9	51.333	174.753	-325.815	-226.521	517.149
10	297.500	138.551	1522.972	-93.951	-1084.321
11	76.429	14.274	-100.909	41.412	311.837
12	69.286	-58.303	-131.379	3.662	298.238
13	30.000	-52.179	20.033	-60.801	100.967
14	54.444	32.571	119.257	3.706	103.073
15	23.462	-396.832	-72.855	250.370	113.169
16	51.563	17.917	-71.619	23.214	265.676
17	31.923	-7.516	83.618	-38.356	70.305
18	25.128	21.356	2.943	-46.818	75.204
19	80.000	-82.895	6.952	61.395	83.723
20	16.000	-55.759	65.013	-71.882	60.587
21	10.000	-8.312	-306.924	26.812	424.561
22	135.000	136.935	842.636	-90.883	-592.636
23	263.000	5.458	204.401	39.227	213.214
24	59.231	-80.579	11.576	-62.633	100.501
25	33.182	-9.828	107.318	14.646	4.228
26	121.250	41.535	110.021	18.175	181.894
27	20.556	-113.107	162.673	175.690	-71.895
28	67.667	-223.239	469.635	166.471	-285.968
29	152.143	30.408	45.144	-52.406	202.786
30	83.214	-26.895	107.292	-6.747	69.638

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