Page 27 - 機械群機械力學升學寶典

Chapter 2 x̻ࠦɢӻ

表 2-2 二共點力合成之圖解法

Ӊ᜷ ɧԉҖج ̻Б̬ᗙҖج
֛ 1cm = 20Nf ֛ 1cm = 20Nf

B C B C

1 R 40N R
40N
60º 60°
θ θ
O 40N A O 40N A
uu
uu
ur ur ur ur
uu
uu
(1) ਗ਼ OB ̻୅ϓ AC f (1) ί B ᓃʿ A ᓃʱй೥ OA e OB ̻ٙБᇞʹ׵
uu
ur
(2) ஹટ OC уމΥɢ Rf C ᓃf
ur ur
uu
uu
2 (3) ඎ̈ OC Ý 3.5cmd (2) ஹટ OC уމΥɢ Rf
ur
uu
݂ R Ý 3.5 × 20 = 70€Ni (3) ඎ̈ OC Ý 3.5cmd
ඎ̈ θ Ý 30° ݂ R Ý 3.5 × 20 = 70€Ni
ඎ̈ θ Ý 30°
(5) ɚ΍ᓃɢʘΥϓٙ˾ᅰجjྡ 2-3 הͪdF ʿ F މ΍ F 2
2
1
ᓃʘɚɢd˲ɚɢٙѰԉމ θd߰ɚɢٙΥɢމ Rd˙ θ
F 1
Σމφdۆ R = F + F + 2 FF cosθ d
2
2
1 2 12
F sinθ 圖 2-3
φ = tan −1 2
F + F cosθ
1 2
搶分關鍵
1. ͟ R = F + F + 2 FF cosθ ʕ̙ٝ
2
2
1 2 12
຅ θ = 0° ࣛdcosθ = 1d݂Υɢ௰ɽ =F + F
1
2
຅ θ = 90° ࣛdcosθ = 0d݂Υɢ = F + F 2
2
1 2
຅ θ = 180° ࣛdcosθ = –1d݂Υɢ௰ʃ = F – F €৿ண F > F 
2
1
1
2
݂ F – F ≤ R ≤ F + F 2
1
2
1
2. ΥɢٙɽʃᎇɚɢѰԉٙᜊɽϾᜊʃf
3. तًࣿرj຅ F = F dɦ θ = 120°dۆ R = F = F €Υɢၾ΂ɓʱɢ޴ഃf
2
1
1
2
уࣛˢ༰j ˸ʮόجӋ༆ڌ 2-2 הͪɚ΍ᓃɢʘΥɢ
×
R = 40 2 + 40 2 +×24040cos 60 ° = 40 3 Ý 69.28€N
40 sin 60 ° −1 20 3
−1
φ = tan = tan = 30°
40 + 40 cos60 ° 60
17

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