1 3 8 1 S 8

sini = n. ( 1` ) sinr

n = c υ sini = n sinr 1 3 n 1 υ1 υ =, n1 =. υ υ 1 υ1 c / υ n 1 n1 = = = =. υ c / υ n n 1 1 1

sini n = n 1 =, sinr n1 60 n = 3

sin90 1 = =, sinc sinc n sin C = 1. n

3

CO A B = OF B F. 1 1 1 AB A B = BO B O. 1 1 1 OF BO B F = B O. 1 1 f u υ f = υ. 1 1 1 + +. u υ f 1 1 1 u υ f u m A B 1 = 1. AB A1B1 υ 15 AB u υ m. u

7 1 + 1 1 u υ f

1 4 f L d f =. 4L 1 u L + 1 1 υ u v u υ f

1 1 + 1 u υ f 1 1 1 5 u υ f

F = F F F F cos180 θ 1 1 F F F F cosθ. 1 1

F = F + F + F F cos θ. ( 1) 1 1 1 CD tgφ = = OD CD = OA + AD F F sinθ. ( ) + F cosθ 1

FF + F + F F cos θ, 1 1

υ = s t. υ = s υ = s t t = tg s t s t 10 - t 5 = 5 s = 10.0-.5 = 7.5 = 1.5 t s 5 υ t υ 1. / t = 5 t = 6 5 6 1 υ = 1.1

υ.6-.5 / 0.1 = 1.0 /

1 60 30 / 45 /

( 17 0) / = 85 / 0. (50-0) / = 5 10 4 / 0.005 υt υ a = 0. t υ t υ 0 t 5

υ t υ 0 t υ t υ 0 ( / 0 50

a = υ υ t 0 t + 1 AR RP = υ t + 1 at 0 1 s = υ 0 t + at. ( ) υ υ = as. ( 3) t 0

1 s = υ0t + ( υ t υ0) t 1 = ( υ0 + υ t) t. ( 4) s t = = 5. + υ t υ0 υ s / t 4 1 υ = ( υ0 + υt).

s υ s υ t υ t 1 1 υ υ υ s υt a υ t 1 s at s t

s t 1 1 s s3 = = = t t 3

aae υ

t 1 t s υ0t at υ = s t 1 s gt t - 1 1 s g( t 1) 1 s s

s = 1 at a1 F1 = a F a F

a1 = m 1 a a m m 1

F a, m

s υ = t υ = s t υt υ / a = 0 t a = F m = 14 = 14 / = / 7 7 υ t = at = / 5 = 10 / a = F m = 14 7 / = / υ t = at = 5 / = 10 /

υ υ = as t 0 υ υ0 s = = = 4 0 a g 9. 8 = 90

t = = = 4 1 υ υ 0 0 a g 9.8 = 4.3 υ t = as = gs = 98. 90 / = 4 / υ t = = = 4 t υ t a g 98. = 4.3

s A B s t

s = 1 at s = s s = t + 1 at υ υ 1 0

xt υ 0 1 y = gt

1 y = gt t t = y g xυ tυ 0 0 y g h = 1 gt l = υ t g υ = l h 0

H 3 υ 0 H 3 A υ gt 0 B υ gt Cυ Dυ t + ( gt) 0 + 3( gt ) 1

υ0 υ 1 υ

a = Fcos θ - f 1 m = Fcos θ - µ N m Fcos θ µ ( Fsin θ + mg) = 3 m 1 s = at = 0.08 s t + 1 at υ 0 ( s υ 0t) a = 1 t f mg sinθ ma gsinθ a µ =. N mgcosθ gcosθ

0. 91 / a = 0.13 /. 7. 0 m = F a - m = 895 1-3400 = 3500 0.13

F f f a m + m 1 1

F a 1 M + m m 1 f F M + m

mg NmgtgαT cosα

lm F cos30 M G l sin30 11

l M1M Flcos30 G sin30 0 F cos30 G 34.6 sin30

'

m m = υ υ υ υ.

mυ m1υ1 υ = m m. 1

π a = cosa = 0W = 0

π a cosa 0 W 0 10 π a F π a cosα 0 W 0 π a a =

W p t W Fs P = Fs s = υ t t υ m = P f

υ υ as s υ υ / a 1 1 υ υ1 Fs = ma a 1 1 = mυ m υ1 ( 1 ) 1 F mυ 1 mυ E k E k = 1 m υ 1 1 E k mυ Ek1 mυ1

1 E k = m Fs fs υ Fs fs = 1 m υ mυ F = + f s mυ = kmg s

1 1 W G = mυ mυ 1 1 W = 1 G m 1 υ mυ 1. ( 1) 1 1 mυm υ1 = mgh 1mgh 1 1 mυmgh = mυ 1 mgh1 3

1 u E p = 0 E k = m E = Ep υ + E k = 1 m υ 1 m υ = mgh υ = gh = 9.8 1 / = 4.4 / 1 1 mυ E p = 0 E = mυ

1 mυ mg llcosθ υ = gl (1- cos θ)

g 4 m h 3 1 A. mgh 3 B. mgh 3 1 C. mgh 3 D mgh

υ s t φ t

π υ = r, ( 1 ) T π T 5 / 16 33 1 45 78 3 3

ω υ 1 r υ Fm. r υ a = 4 r

υ s υ = υ = s. υ r r υ t = s t υ r. υ s t a t t a = υ r υ 4 a = rw a r a = a r r

υ F m r υ u m = G = mg r υ = gr F G G υ = gr υ υ gr m mg F G r u u gr υ m mg F G G r

F = G m m 1 r 4π rm mrω = T G Mm 4 rm = π r T r M = 4 π 3 GT

11 3 4 314. ( 149. 10 ) M = 11 7 6. 67 10 ( 316. 10 ) = 1.9610 30

G Mm mυ r r GM υ r υgm / R GM / R g υgr

υ GM / r

a k x m

f 1 T 1 T f 1 B

F mgsinq sin l x θ x l F x mg l T l g π

π 3 3 4.0 10-10 = 3.010-9 6-5 3 1.8 10 / 3 1 N = -9 3 = 6.0 10 3 0 10

- 1 1.8 10-6 m = 3 1 = 3.010 6.0 10 K = AB ab = R r = 10 6 = 10 5 10-6

5 V -5 3 5 4-3 p p 1 = V. V1

1 73 p p0 p0 = t 73 t p = p0 ( 1 + ). ( 1 ) 73

t 1 73 + t 1 p1 = p0 ( 1 + ) = p 0, 73 73 t 73 + t p = p0 ( 1 + ) = p0. 73 73 p p 1 73 + t = 73 + t p p 1 1, T1 =. ( 3 ) T

p 1. V T p = V p C T. V pv = C 1 T R = p V 0 0. T 0 5 3 3 1013. 10 /. 4 10 / R 73 8.31 / pv p V 1 = 0 0 R T T 0

pv p V n p V 0 0 0 0 = = = nr. T T T 0 pvnrt 0 pv = m M RT. 3

V p1v1 pv = T T p1v1 4. 9 10 30 10 = = 5 T 98. 10 6 3 3 1 1 3 = 15. 10. V V 1 = 30 10-3 1 = 0. = 0% 80% 15. 10 m p V M RT 3 1 1 = 1 m M = 10 / 3 3 p1v1m 30 10 10 m = = 4.9 10 6-1 = 1.18 10 RT 8.31 300 1

p( V1 V) p V1 =. ( 1 ) T T 1 p( V + V) p V = T T. ( ) p V p V 1 1 T = T T 1

1000 3 10

1 1 n 6 0 υ n υ 6 0 1 1 n0υ mυ = n 0mυ 6 3 p = 1 n mυ. 3 0

p B = 100%. p s

t p s t p s t p s t p s 15 1.9 10 3 7.58 10 1.486 10 3 39 6.990 10 3 14.08 10 4 8.13 10.643 10 3 40 7.374 10 3 13.5 10 5 8.7 10 3.809 10 3 41 7.777 10 3 1.44 10 6 9.34 10 4.983 10 3 4 8.198 10 3 11.65 10 7 1.001 10 3 5 3.167 10 3 43 8.638 10 3 10.87 10 8 1.073 10 3 6 3.361 10 3 44 9.099 10 3 9 3.11 10 9 1.148 10 3 7 3.564 10 3 45 9.58 10 3 8 3.35 10 10 1.8 10 3 8 3.779 10 3 50 1.33 10 4 7 3.63 10 11 1.31 10 3 9 4.004 10 3 60 1.991 10 4 6 3.91 10 1 1.40 10 3 30 4.4 10 3 70 3.115 10 4 5 4.1 10 13 1.497 10 3 31 4.99 10 3 80 4.733 10 4 4 4.55 10 14 1.598 10 3 3 4.753 10 3 90 7.009 10 4 3 4.89 10 15 1.705 10 3 33 5.03 10 3 100 1.013 10 5 5.8 10 16 1.817 10 3 34 5.319 10 3 150 4.759 10 5 1 5.68 10 17 1.937 10 3 35 5.63 10 3 00 1.554 10 5 0 6.11 10 18.064 10 3 36 5.940 10 3 50 3.975 10 5 1 6.57 10 19.197 10 3 37 6.74 10 3 300 8.589 10 5 7.05 10 0.338 10 3 38 6.65 10 3 350 1.653 10 5 3 11. 10 B 3 100 = 48. 3 10

h 30.0 10.0 t d 1.5 73.0 43.5.0 41. 3.7 3.0 18.4 10.5 5.0 6.8 3.9 π 1 1 1 d t d d d d 1/d 1/ t 1.5 0.44 73.0.0 0.5 41. 3.0 0.11 18.4 5.0 0.04 6.8 1 1 t t d d 10 t 1 d

sini sinr sini n sin r

1 f = 1 u + 1 υ L d f = A 5 4L f = L d f 4L

υ = s t 1 3 4 5

a = s a = s 4 s1 5 s 1 3T 3T

4 1 5 6 3

s1 3 4 1 3 4 1 3 4

1 y = gt x = υ0t υ0 υ 0

1 m υ = mgh. t 1 3 h3 - h 1 1 1 1 3 4 mυ mυ3 mυ4 1 1 1 m υ = mghm υ3 = mgh 3m υ 4 = mgh4

1 M + m υ = M + m gh υ = gh M + m υ = gh. m υ = M m gh. 3 υ = M gl(1- cos θ). 5 m

l T = π g l g = 4π T.

F F p = p0 ± S S p = p ± F 0 S

F p = p + p0 F S pv T

3 3 υ υ -1 3 3