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Волгоградский государственный технический университет

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РавнВала(1)

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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.

Кирсанов М.Н. Решебник. Теоретическая механика с. 94.

Вариант 1 C19.

F = 0.4N, T1 = 50,

= 29

= 34

P2 = 20, P3 = 28,

= 10,

= 25,

6 ~

α = 45◦, R1 = 24,

= 10

= 12

T~1

a = 24, b = 25,

= 27

, d

Вариант 2 C19.

	z 6									A
	z 6						3	B			pb
		F~					3		pb

T~1	α	~	6			q		Q		b
T~1		N
		-		q	1
		2	-	q				a

			~2
			Tx
		-
		q

*y		F = 0.4N, T1 = 50,
		T2	, P1	,
			= 96	= 44
	d	P2 = 30, P3 = 38,
		P2 = 30, P3 = 38,
		Q = 22, G = 25,

c
c		α = 60◦, R1 = 26,

R2 = 12, R3 = 14, a = 24, b = 28,

c = 31, d = 27.

Вариант 3 C19.

F = 0.3N, T1 = 40,

= 30, P3

= 38,

, P1

= 78

= 46

T~1 α

= 14,

= 20,

◦

α = 60 , R1 = 30,

-q

c = 29, d = 28.

R2 = 12, R3 = 14,

a = 24, b = 26,

Вариант 4 C19.

	z 6									A
	z 6						3	B			pb
		F~					3		pb

T~1	α	~	6			q		Q		b
T~1		N
		-		q	1
		2	-	q				a

			~2
			Tx
		-
		q

*y		F = 0.3N, T1 = 50,
		T2	, P1	,
			= 96	= 46
	d	P2 = 30, P3 = 38,
		P2 = 30, P3 = 38,
		Q = 22, G = 25,

c
c		α = 60◦, R1 = 30,

R2 = 12, R3 = 14, a = 24, b = 28,

c = 31, d = 28.

Вариант 5 C19.

T~2

F = 0.4N, T1 = 60,

= 20, P3

= 28,

, P1

= 117

= 32

= 18

= 30

, G

= 45◦, R1

= 20,

?T~1a

a = 24, b = 27,

= 10

= 12

, d

= 29

= 26

Вариант 6 C19.

F = 0.4N, T1 = 60,

T2 = 118, P1 = 30,

P2 = 20, P3 = 28,

, R1

Q = 14,

G = 30,

?T~1 b

R2 = 10, R3 = 12,

= 45◦

= 16

a = 24, b = 26,

= 28

= 25

Вариант 7 C19.

F = 0.3N, T1 = 40,

T2 = 77,

P1 = 22,

2 = 10,

3 = 18,

Q = 18, G = 20,

◦

α H A

R2 = 8, R3 = 10,

= 24,

= 27,

= 30

, R1 = 18,

-q

c = 28, d = 26.

x ?T~1

Вариант 8 C19.

F = 0.1N, T1 = 30,

= 58,

P1 = 18,

2 = 10,

3 = 14,

α H-

α = 30 , R1 = 18,

T~2

= 14,

= 15,

◦

R2 = 8, R3 = 9,

a = 22, b = 24,

?T~1 a

, d .

= 25

= 24

Вариант 9 C19.

F = 0.2N, T1 = 60,

T2 = 117, P1 = 16,

P2 = 10, P3 = 14,

, R1

Q = 18,

G = 30,

?T~1 b

R2 = 8, R3 = 9,

= 30◦

= 14

a = 22, b = 25,

= 26

= 23

Вариант 10 C19.

F = 0.4N, T1 = 30,

T2 = 19, P1 = 46,

2 = 30,

3 = 38,

T~1 α

Q = 10, G = 15,

= 60◦

= 30

, R1

-T~2

R2 = 12, R3 = 14,

a = 24, b = 25,

-q

c = 28, d = 28.

Вариант 11 C19.

~1 α

F = 0.4N, T1 = 60,

P2 = 30, P3 = 38,

, P1

= 116

= 46

= 22,

= 30,

◦

= 60

1 = 30,

, R

a = 24, b = 28,

-T~2

= 12,

= 14,

d .

= 31

= 28

Вариант 12 C19.

F = 0.1N, T1 = 50,

T2 = 26, P1 = 16,

2 = 10,

3 = 14,

Q d

Q = 10, G = 25,

α = 30◦, R1 = 14,

R2 = 8, R3 = 9,

= 22,

= 23,

= 24

= 23

, d

~ x

Вариант 13 C19.

F = 0.2N, T1 = 30,

= 58,

P1 = 26,

2 = 20,

3 = 24,

α H-

α = 45 , R1 = 16,

T~2

= 14,

= 15,

◦

R2 = 10, R3 = 11,

a = 22, b = 24,

?T~1 a

, d .

= 26

= 23

Вариант 14 C19.

T~2

F = 0.3N, T1 = 60,

= 30, P3

= 38,

= 33

= 42

= 26

= 30

, G

= 60◦, R1

= 22,

?T~1a

a = 24, b = 29,

F ?

= 12

= 14

, d

= 32

= 26

Вариант 15 C19.

F = 0.3N, T1 = 60,

= 30, P3

= 38,

= 33

= 44

= 10,

= 30,

◦

6 T~1 α

= 60

1 = 26,

, R

R2 = 12, R3 = 14,

d .

a = 24, b = 25,

= 28

= 27

Вариант 16 C19.

F = 0.3N, T1 = 50,

T2 = 96, P1 = 30,

2 = 20,

3 = 28,

Q d

Q = 22, G = 25,

α = 45◦, R1 = 16,

R2 = 10, R3 = 12,

= 24,

= 28,

= 30

= 25

, d

~ x

Вариант 17 C19.

F = 0.3N, T1 = 30,

= 57,

= 26,

◦

2 = 10, 3

= 18,

Q = 18, G = 15,

-b

R2 = 8, R3 = 10,

= 30

, R1

= 26

a = 24, b = 27,

-q

c = 28, d = 28.

Вариант 18 C19.

			~				~
			~			1
						~	N		y
						?
						F		*
	6		α H			B q		*
	6		α H			B q		c
z			T2		2	pb				d
z			HY		2	pb				d
							b
			A	q		?T~1 a	b
		3	pb

	q		Qx
			-

F = 0.1N, T1 = 70, T2 = 36, P1 = 36, P2 = 30, P3 = 34, Q = 10, G = 35,

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

c = 26, d = 23.

Вариант 19 C19.

F = 0.2N, T1 = 50,

T2 = 27, P1 = 32,

2 = 20,

3 = 24,

Q = 26, G = 25,

= 45◦

, R1

= 28

F ?

= 10

= 11

T~1

a = 22, b = 27,

= 29

= 26

Вариант 20 C19.

α H-

T~2

?T~1

F = 0.1N, T1 = 40, T2 = 77, P1 = 26, P2 = 20, P3 = 24, Q = 18, G = 20,

α = 45◦, R1 = 16, R2 = 10, R3 = 11, a = 22, b = 25,

c = 27, d = 23.

Вариант 21 C19.

F = 0.3N, T1 = 60,

= 26,

= 117, P1

= 30◦

= 26

= 10,

3 = 18,

, R1

-T~2

Q = 18,

= 30,

= 8

= 10

d .

a = 24,

= 27,

= 28

Вариант 22 C19.

F = 0.1N, T1 = 40,

T2 = 21,

P1 = 18,

◦

2 = 10,

3 = 14,

α H A

Q = 26, G = 20,

R2 = 8, R3 = 9,

= 22,

= 27,

= 30

, R1 = 18,

-q

c = 28, d = 24.

x ?T~1

Вариант 23 C19.

α H2

F = 0.1N, T1 = 70, T2 = 137, P1 = 16, P2 = 10, P3 = 14, Q = 18, G = 35,

α = 30◦, R1 = 14, R2 = 8, R3 = 9,

a = 22, b = 25, c = 26, d = 23.

Вариант 24 C19.

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

			B-		q
A					2
A				pb				b
				x
		pb

F = 0.4N, T1 = 30, T2 = 19, P1 = 32, P2 = 20, P3 = 28, Q = 26, G = 15,

α = 45◦, R1 = 20, R2 = 10, R3 = 12, a = 24, b = 29,

c = 31, d = 26.

Вариант 25 C19.

F = 0.3N, T1 = 50,

T2 = 28, P1 = 22,

2 = 10,

3 = 18,

Q d

Q = 26, G = 25,

α = 30◦, R1 = 18,

R2 = 8, R3 = 10,

= 24,

= 29,

= 30

= 26

, d

~ x

Вариант 26 C19.

T~2

F~ 6

F = 0.3N, T1 = 70,

= 30, P3 = 38,

, P1

= 137

= 42

= 18

= 35

= 12, R3

= 14,

α H2

α = 60◦, R1 = 22,

?T~1 a

a = 24, b = 27,

d .

= 30

= 26

Вариант 27 C19.


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

F = 0.2N, T1 = 30, T2 = 56, P1 = 22, P2 = 10, P3 = 14, Q = 22, G = 15,

α = 30◦, R1 = 26, R2 = 8, R3 = 9,

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

Вариант 28 C19.

α H2

F = 0.1N, T1 = 70, T2 = 36, P1 = 26, P2 = 20, P3 = 24, Q = 26, G = 35,

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

c = 29, d = 23.

Вариант 29 C19.


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

F = 0.3N, T1 = 40, T2 = 23, P1 = 26, P2 = 10, P3 = 18, Q = 26, G = 20,

α = 30◦, R1 = 26, R2 = 8, R3 = 10, a = 24, b = 29,

c = 30, d = 28.

Вариант 30 C19.

F = 0.2N, T1 = 50,

T2 = 27, P1 = 20,

2 = 10,

3 = 14,

Q = 10, G = 25,

= 30◦

, R1

= 22

F ?

= 8

= 9

T~1

a = 22, b = 23,

= 24

= 25

Ответы

	N	XA	ZA	XB	ZB
1	34.375	52.031	2.436	-102.636	113.584
2	23.462	479.490	-185.826	-642.253	310.442
3	28.889	-59.116	61.439	-82.414	57.894
4	27.111	470.056	-185.594	-636.468	313.461
5	44.250	40.192	36.940	-1.711	50.629
6	64.375	-213.655	-75.470	232.719	148.281
7	21.481	-1.895	124.214	47.097	-41.158
8	54.444	66.467	-150.260	-70.682	216.816
9	105.000	-302.778	-85.280	299.103	153.780
10	22.667	-10.116	40.037	-25.798	106.630
11	30.333	275.874	-256.283	-474.169	380.150
12	201.429	23.036	-185.056	19.624	498.484
13	39.375	44.748	-194.475	-43.111	274.588
14	104.242	-3.127	35.867	50.900	265.797
15	59.487	115.882	-372.686	-182.997	554.173
16	40.833	169.817	-114.638	-142.768	209.506
17	4.615	37.086	-18.459	-113.701	78.094
18	298.889	-4.478	-39.776	52.367	522.488
19	92.143	88.201	7.778	-132.128	176.010
20	107.500	-245.272	292.431	192.219	-209.628
21	35.385	47.165	183.404	-229.549	-143.981
22	214.444	41.864	486.066	-2.233	-154.121
23	267.143	400.209	67.800	-548.706	-0.014
24	52.750	-68.984	-468.933	103.519	659.248
25	80.741	29.212	326.214	19.259	-108.473
26	83.636	-35.154	1.794	20.018	87.470
27	1.923	38.896	-19.834	-111.819	76.468
28	391.250	-102.693	-784.122	167.274	1350.916
29	50.769	-60.443	109.269	32.673	6.859
30	62.273	-125.110	63.293	85.564	34.679