deviation di x i x standard deviation s

[偏差](deviation) di = x i - x [標準差](standard deviation) s = (Sidi 2 /n)1/2 但次數n不大時, 誤差較大, 修正為 s = [Sidi 2 /(n-1)]1/2 (不準度uncertainty/準確度accuracy) x = x s or x = x s/x (%) (例) L = L s = 21. 9 0. 2 mm 或 21. 93 0. 16 mm = 21. 93 mm 0. 73% [平均標準差](standard deviation of the mean) 如果作 N組n個測量, 有N個平均值, 總平均值之標準差(平均標準差) 但如N = 1, 平均標準差為 s(x) = s/ n = {Sidi 2 /[n(n-1)]}1/2 x = x s(x)/x (% or ppm/part per million) (例) 如 N=1, n=16 L = L s(L) = 21. 93 0. 04 mm = 21. 93 mm 0. 18 % (例) 電子質量 me = 9. 1093897 x 10 -31 kg (uncertainty 0. 59 ppm) (例) 光速 c = 2. 99792548 x 108 m/s (exact by definition)(1983) [計算時通常只取三位] (1 -4)

錄影帶A: 基本力(Fundamental Forces) (The Mechanical Universe…and Beyond)(10) F = ma, F? 1. 強原子核力(strong nuclear force) -- 強交互作用 短程(short range), 原子核中核子間強吸引力(strong attractive force) 漸進自由性(asymptotic freedom) -- 距離極近時, 交互作用~0 [2004諾貝爾物理獎—Gross, Politzer, Wilczeck] 2. 弱原子核力(weak nuclear force) -- 弱交互作用 短程(short range) 原子核衰變(decay)之弱力(weak force)(~強力 10 -14, <電磁力) 3. 靜電力(electrostatic force) -- 電磁交互作用 長程(long range 1/r 2), 吸引/排斥力(attractive/repulsive force) Fe = Keq 1 q 2 r/r 2 = q 1 q 2 r/4 pe 0 r 2 (r r/r unit vector) [e 0 = 8. 85 x 10 -12 C 2/Nm 2 = 1/(4 px 10 -7. c 2) permittivity constant] 4. 重力(gravitational force) -- 重力交互作用 長程(long range), 極弱吸引力 Fg = - Gm 1 m 2 r/r 2 (r r/r) [G = 6. 67 x 10 -11 Nm 2/kg 2 gravitational constant]