运动 Prepared by Jiang Xiao

Size: px

Start display at page:

Download "运动 Prepared by Jiang Xiao"

湿康释
7 years ago
Views:

1 顿

2 运动 Prepared by Jiang Xiao

3 运动 Prepared by Jiang Xiao

4 运动运动运动 Aristotle 384BC - 322BC 变运动维运动 Galileo Newton 线运动态变这态

5 顿 - 惯顿线运动态变这态满惯满满转 m/s 2 转 m/s 2 银转动证现实验

6 顿顿获质 F = m a [force] = [M] [L] [T ] 2 N = kg m/s 2 满惯运动远

7 顿顿间总线 = - Hero s engine:

8 顿顿间总线 = - mapple = 0.5 kg F = mg =5N 100 m F 1 2 gt2 = h ) t =4.5 s F M = kg F = M a ) a = 5N kg = m/s a t2 = m

9 对长 (~1/r 2 ) ~ m 电 10-2 长 (~1/r 2 ) m p = kg q p = F gravity = G m pm p r 2 q e = C F EM = 1 q p q p 4 " 0 r N N : n! p + e + e + : p! n + e + + e 1 ~ m

10 (AU/year^2) a / r 2 f = ma = K m r 2 a = r! 2 = r T 2 / r 3 2 T (AU)

11 > Prepared by Jiang Xiao > >1 2 f = G m 1m 2 r 2 with G = m 3 /kg s 2 1 Gravitation pulls the small masses toward the large masses, causing the vertical quartz fiber to twist. The small balls reach a new equilibrium position when the elastic force exerted by the twisted quartz fiber balances the gravitational force between the masses. Quartz fiber Mirror m 1 2 Fg The deflection of the laser beam indicates how far the fiber has twisted. Once the instrument is calibrated, this result gives a value for G. Laser beam m 2 Scale Laser Large mass 1m 2 2 F g Small mass 1m 1 2

12 惯质质 f = G Mm gravity r 2 = m gravity g 顿 f = m inertia a a = g ) m intertia = m gravity

13 f = G m 1m 2 r 2 with G = m 3 /kg s 2

14 Prepared by Jiang Xiao 100 km f = G m 1m 2 r 2 with G = m 3 /kg s 2 卫

15 弹 N f P G 间 F = a r 13 b r 7 变弹 F = kx

16 Mona Lisa Louvre, Paris, France Leonardo da Vinci (1) 积 (2) 质

17 N f P G (1) 动压积 (2) 时动 (3) 值间变视对动趋势 Charles Coulomb 动 f k = µ k N 0 apple f s apple µ s N 动 <

18 (a) n (b) n (c) n (d) n T T T f s f s f k w w w w No applied force, box at rest. No friction: f s 5 0 Weak applied force, box remains at rest. Static friction: f s,m s n Stronger applied force, box just about to slide. Static friction: f s 5m s n Box sliding at constant speed. Kinetic friction: f k 5m k n (e) f 1 f s 2 max f k 0 apple f s apple µ s N 动 f k = µ k N O Box at rest; static friction equals applied force. Box moving; kinetic friction is essentially constant. T

19 f N 块动 f s = µ s mg cos mg a mg sin >f s ) tan >µ s ) >arctan µ s 动 F = ma mg sin µ k mg cos = ma ) a = g sin (1 µ k cot ) =g sin (1 µ k /µ s )

20 对变换 S y O S r R y O v 0 x v r u = dr dt x S :(r,t) and S 0 :(r 0,t 0 ) 变换 r = r 0 + ut t = t 0 a = a 0 F = F 0 a = a 0 m = m 0 F = ma F 0 = m 0 a 0 绝对时观 r = r 0 t = t 0

21 惯惯 a 惯顿惯惯顿惯 a 顿线运动态变这态满惯满满转 m/s 2 转 m/s 2 银转动

22 动惯惯 y S y S 0 a a 0 = a a 0 a O x O a 0 x a 惯 S 惯 S F = ma = ma 0 + ma 0 F 6= ma 0 F 0 = F +( ma 0 )=ma 0 f = ma 0 惯 f *

23 转动惯惯!! 0 =! + v r v r 转动 v = v rˆr + v ˆ, v 0 = v +! r, dv a 6= dt a 0 = dv0 dt dˆr dt =!0ˆ dˆ dt = dv!0ˆr dt = a +! v dv dt = v dˆr rˆr + v ˆ + vr dt + v dˆ dt v r v = v rˆr + v ˆ + r ˆ v 2 r ˆr = a +! v 转动! +!(v rˆ v ˆr)

24 转动惯惯! v r 转动 v = v rˆr + v ˆ, v 0 = v +! r, a = vrˆr + v ˆ 6= dv dt a 0 = dv0 dt dˆr dt =!ˆ dˆ dt = dv!ˆr dt = a +! v a 0 = dv0 dt = dv dt + d! dt r +! dr dt = a +! v +! v 0 = a +! v +! (v +! r) = a +2! v +! (! r) = a 2v!! 2 r

25 转动惯惯! v r 转动 v = v rˆr + v ˆ, v 0 = v +! r, a = vrˆr + v ˆ 6= dv dt a 0 = dv0 dt dˆr dt =!ˆ dˆ dt = dv!ˆr dt = a +! v a 0 = a 2v!! 2 r ma 6= F = F 0 = ma 0 F + f = ma f = m! 2 r +2mv!

26 惯 f = m! 2 r +2mv!

27 f = m! 2 r +2mv!! v f C r v f C

28 现 f = m! 2 r +2mv! 竖边东边较严

29 现 f = m! 2 r +2mv! v z 竖边东边较严东!

30 现 - Prepared by Jiang Xiao

31 现 - 风飓风

32 现 - Prepared by Jiang Xiao

33 现 - Prepared by Jiang Xiao

34 现 - 风 Prepared by Jiang Xiao

35 罗贝 (Rossby Number) f = m! 2 r +2mv! U 2 L U Rossby Number: R 0 = U 2L sin 转纬

36 现 - Prepared by Jiang Xiao

37 业习题 2.2, 2.9, 2.16, 2.20, 习题课

动 Prepared by Jiang Xiao

动 Prepared by Jiang Xiao 动处运动动 (-khz) 说颜乐风帜简谐动! (t) =!t + x(t) =x cos(!t + ) x(t) x 频! = 频 T = f F = kx ) mẍ = kx ) ẍ + k m x = 悬弹频 x(t) =x cos(! t + ) with! = r k m 弹谐动 E k = 1 mv = 1 mẋ = 1 mx! sin (! t + ) 势 E