int_kurs-podg_-ege_kasatkina-i_l_2012

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Физика для старшеклассников и абитуриентов

Площадь трапеции

S = ab2 h

Площадь сферы радиусом R (диаметром D)

2	2			D
S = 4πR	= πD	,	ãäå R =
				2

Площадь круга радиусом R (диаметром D)

S = πR2 = πD4 2

Длина окружности радиусом R (диаметром D)

l 2SR SD

Объем сферы радиусом R (диаметром D)

V = 34 πR3 = 61 πD3

Объем цилиндра высотой H с радиусом основания R

VSR2H

Объем куба со стороной а

Vа2

Объем конуса высотой H с радиусом основания R

V = 31 πR2H

730

СОДЕРЖАНИЕ
ȼɫɬɭɩɥɟɧɢɟ ....................................................................................	3
ɉɪɨɝɪɚɦɦɚ ɩɨ ɮɢɡɢɤɟ ɞɥɹ ɩɨɞɝɨɬɨɜɤɢ ɤ ȿȽɗ........................	6
Ɋɚɡɞɟɥ 1 ɆȿɏȺɇɂɄȺ ..............................................................	11
Ɍɟɦɚ 1. Ʉɢɧɟɦɚɬɢɤɚ.................................................................	11
Ⱥ. ȼɢɞɵ ɩɪɹɦɨɥɢɧɟɣɧɨɝɨ ɞɜɢɠɟɧɢɹ.................................	13
Ɋɚɜɧɨɦɟɪɧɨɟ ɞɜɢɠɟɧɢɟ ................................................	14
Ɋɚɜɧɨɭɫɤɨɪɟɧɧɨɟ ɞɜɢɠɟɧɢɟ..........................................	14
Ⱦɜɢɠɟɧɢɟ ɫ ɩɟɪɟɦɟɧɧɵɦ ɭɫɤɨɪɟɧɢɟɦ.........................	15
ɉɪɚɜɢɥɨ ɫɥɨɠɟɧɢɹ ɤɥɚɫɫɢɱɟɫɤɢɯ ɫɤɨɪɨɫɬɟɣ...............	15
Ȼ. ɋɜɨɛɨɞɧɨɟ ɩɚɞɟɧɢɟ.........................................................	17
ȼ. Ɉɬɧɨɫɢɬɟɥɶɧɨɫɬɶ ɞɜɢɠɟɧɢɹ ..........................................	20
Ƚ. Ⱦɜɢɠɟɧɢɟ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɫ ɩɨɫɬɨɹɧɧɨɣ
ɩɨ ɦɨɞɭɥɸ ɫɤɨɪɨɫɬɶɸ.........................................................	24
ɉɪɨɛɧɵɣ ɷɤɡɚɦɟɧ ɩɨ ɬɟɦɟ 1. Ʉɢɧɟɦɚɬɢɤɚ.............................	27
ɑɚɫɬɶ 1 .................................................................................	27
ɑɚɫɬɶ 2 .................................................................................	38
ɑɚɫɬɶ 3 .................................................................................	39
Ɉɬɜɟɬɵ ɧɚ ɡɚɞɚɧɢɹ ɩɪɨɛɧɨɝɨ ɷɤɡɚɦɟɧɚ
ɩɨ ɬɟɦɟ 1. Ʉɢɧɟɦɚɬɢɤɚ.............................................................	41
ɑɚɫɬɶ 1 .................................................................................	41
ɑɚɫɬɶ 2 .................................................................................	56
ɑɚɫɬɶ 3 .................................................................................	64
Ɍɟɦɚ 2. Ⱦɢɧɚɦɢɤɚ. ɋɬɚɬɢɤɚ.....................................................	84
Ⱥ. Ɂɚɤɨɧɵ ɇɶɸɬɨɧɚ ............................................................	84
Ȼ. Ɋɚɛɨɬɚ ɢ ɦɨɳɧɨɫɬɶ.
Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɜ ɦɟɯɚɧɢɤɟ..........................................	93
ȼ. ɋɬɚɬɢɤɚ..........................................................................	100
Ƚ. Ƚɢɞɪɨɦɟɯɚɧɢɤɚ ..............................................................	103

731

Физика для старшеклассников и абитуриентов
ɉɪɨɛɧɵɣ ɷɤɡɚɦɟɧ ɩɨ ɬɟɦɟ 2. Ⱦɢɧɚɦɢɤɚ. ɋɬɚɬɢɤɚ...............	110
ɑɚɫɬɶ 1 ...............................................................................	110
ɑɚɫɬɶ 2 ...............................................................................	123
ɑɚɫɬɶ 3 ...............................................................................	125
Ɉɬɜɟɬɵ ɧɚ ɡɚɞɚɧɢɹ ɩɪɨɛɧɨɝɨ ɷɤɡɚɦɟɧɚ
ɩɨ ɬɟɦɟ 2. Ⱦɢɧɚɦɢɤɚ. ɋɬɚɬɢɤɚ..............................................	128
ɑɚɫɬɶ 1 ...............................................................................	128
ɑɚɫɬɶ 2 ...............................................................................	146
ɑɚɫɬɶ 3 ...............................................................................	158
Ɋɚɡɞɟɥ II. ɆɈɅȿɄɍɅəɊɇȺə ɎɂɁɂɄȺ
ɂ ɌȿɊɆɈȾɂɇȺɆɂɄȺ ..........................................................	189
Ɍɟɦɚ 1. Ɇɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ..............................................	195
Ɍɟɦɚ 2. Ɍɟɪɦɨɞɢɧɚɦɢɤɚ.........................................................	210
ɉɪɨɛɧɵɣ ɷɤɡɚɦɟɧ ɩɨ ɪɚɡɞɟɥɭ II. Ɇɨɥɟɤɭɥɹɪɧɚɹ
ɮɢɡɢɤɚ ɢ ɬɟɪɦɨɞɢɧɚɦɢɤɚ ......................................................	217
ɑɚɫɬɶ 1 ...............................................................................	217
ɑɚɫɬɶ 2 ...............................................................................	231
ɑɚɫɬɶ 3 ...............................................................................	234
Ɉɬɜɟɬɵ ɧɚ ɡɚɞɚɧɢɹ ɩɪɨɛɧɨɝɨ ɷɤɡɚɦɟɧɚ
ɩɨ ɪɚɡɞɟɥɭ II. Ɇɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ ɢ ɬɟɪɦɨɞɢɧɚɦɢɤɚ.....	238
ɑɚɫɬɶ 1 ...............................................................................	238
ɑɚɫɬɶ 2 ...............................................................................	260
ɑɚɫɬɶ 3 ...............................................................................	282
Ɋɚɡɞɟɥ III.
ɗɅȿɄɌɊɈɆȺȽɇȿɌɂɁɆ........................................................	312
Ʉɪɚɬɤɚɹ ɬɟɨɪɢɹ ɷɥɟɤɬɪɨɦɚɝɧɟɬɢɡɦɚ.....................................	323
Ɍɟɦɚ 1. ɗɥɟɤɬɪɨɫɬɚɬɢɤɚ.........................................................	323
Ɍɟɦɚ 2. Ɂɚɤɨɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ.........................................	337
Ɍɟɦɚ 3. Ɇɚɝɧɟɬɢɡɦ.................................................................	351
ɉɪɨɛɧɵɣ ɷɤɡɚɦɟɧ
ɩɨ ɪɚɡɞɟɥɭ III. ɗɥɟɤɬɪɨɦɚɝɧɟɬɢɡɦ........................................	361
ɑɚɫɬɶ 1 ...............................................................................	361
ɑɚɫɬɶ 2 ...............................................................................	384

732

Приложение

ɑɚɫɬɶ 3 ...............................................................................	390
Ɉɬɜɟɬɵ ɧɚ ɡɚɞɚɧɢɹ ɩɪɨɛɧɨɝɨ ɷɤɡɚɦɟɧɚ
ɩɨ ɪɚɡɞɟɥɭ III. ɗɥɟɤɬɪɨɦɚɝɧɟɬɢɡɦ........................................	397
ɑɚɫɬɶ 1 ...............................................................................	397
ɑɚɫɬɶ 2 ...............................................................................	424
ɑɚɫɬɶ 3 ...............................................................................	470
Ɋɚɡɞɟɥ IV. ɄɈɅȿȻȺɇɂə ɂ ȼɈɅɇɕ.
ɈɉɌɂɄȺ. ɌȿɈɊɂə ɈɌɇɈɋɂɌȿɅɖɇɈɋɌɂ.
ȺɌɈɆɇȺə ɎɂɁɂɄȺ..............................................................	530
Ɍɟɦɚ 1. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɤɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ .........................	530
Ɍɟɦɚ 2. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɤɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ..................	540
Ɍɟɦɚ 3. Ƚɟɨɦɟɬɪɢɱɟɫɤɚɹ ɨɩɬɢɤɚ ...........................................	547
Ɍɟɦɚ 4. ȼɨɥɧɨɜɚɹ ɢ ɤɜɚɧɬɨɜɚɹ ɨɩɬɢɤɚ .................................	562
Ɍɟɦɚ 5. Ɍɟɨɪɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ. Ɏɢɡɢɤɚ ɚɬɨɦɚ................	570
Ⱥ. Ɍɟɨɪɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ .............................................	574
ɉɪɨɛɧɵɣ ɷɤɡɚɦɟɧ ɩɨ ɪɚɡɞɟɥɭ IV. Ʉɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ.
Ɉɩɬɢɤɚ. Ɍɟɨɪɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ. Ⱥɬɨɦɧɚɹ ɮɢɡɢɤɚ...........	582
ɑɚɫɬɶ 1 ...............................................................................	582
ɑɚɫɬɶ 2 ...............................................................................	606
ɑɚɫɬɶ 3 ...............................................................................	609
Ɉɬɜɟɬɵ ɧɚ ɡɚɞɚɧɢɹ ɩɪɨɛɧɨɝɨ ɷɤɡɚɦɟɧɚ
ɩɨ ɪɚɡɞɟɥɭ IV. Ʉɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ. Ɉɩɬɢɤɚ.
Ɍɟɨɪɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ. Ɏɢɡɢɤɚ ɚɬɨɦɚ..............................	615
ɑɚɫɬɶ 1 ...............................................................................	615
ɑɚɫɬɶ 2 ...............................................................................	644
ɑɚɫɬɶ 3 ...............................................................................	668
ɉɪɢɥɨɠɟɧɢɟ...............................................................................	716
ɋɨɤɪɚɳɟɧɢɹ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɣ...........................................	716
Ɏɢɡɢɱɟɫɤɢɟ ɤɨɧɫɬɚɧɬɵ..........................................................	716
ȿɞɢɧɢɰɵ ɋɂ...........................................................................	718
ɇɟɤɨɬɨɪɵɟ ɩɪɢɫɬɚɜɤɢ ɞɥɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
ɜɧɟɫɢɫɬɟɦɧɵɯ ɟɞɢɧɢɰ ɜ ɋɂ..................................................	722
ɉɟɪɟɜɨɞ ɧɟɤɨɬɨɪɵɯ ɟɞɢɧɢɰ ɜ ɋɂ.........................................	723
ɇɟɤɨɬɨɪɵɟ ɫɜɟɞɟɧɢɹ ɢɡ ɦɚɬɟɦɚɬɢɤɢ.....................................	725

733

ɍɱɟɛɧɨɟ ɢɡɞɚɧɢɟ

ɂɪɢɧɚ Ʌɟɨɧɢɞɨɜɧɚ Ʉɚɫɚɬɤɢɧɚ

ɎɂɁɂɄȺ ȾɅə ɋɌȺɊɒȿɄɅȺɋɋɇɂɄɈȼ

ɂ ȺȻɂɌɍɊɂȿɇɌɈȼ. ɂɧɬɟɧɫɢɜɧɵɣ ɤɭɪɫ ɩɨɞɝɨɬɨɜɤɢ ɤ ȿȽɗ

Ɋɭɤɨɜɨɞɢɬɟɥɶ ɩɪɨɟɤɬɚ	Ɏɪɨɥɨɜɚ ɀ.
Ɉɬɜɟɬɫɬɜɟɧɧɵɣ ɪɟɞɚɤɬɨɪ	ɂɧɝɟɪɥɟɣɛ Ɇ.
Ɉɛɥɨɠɤɚ:	Ȼɚɤɭɥɢɧɚ ɇ.
ȼɟɪɫɬɤɚ	Ȼɚɤɭɥɢɧɚ ɇ.
ɂɥɥɸɫɬɪɚɰɢɢ:	Ȼɚɟɜɚ ɗ.
Ʉɨɪɪɟɤɬɭɪɚ:	Ȼɭɬɤɨ ɂ.

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