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R = 20.07 kN

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(1)

【解】

(a)平行四邊形定律 合力大小 R

( )( )

2 2

15 10 2 15 10 cos 75 20.07 kN

R =

+ +  =

25°

15kN

R 50°

105°

θ α

(2)

合力方向角 使用正弦定律

sin105 sin

R

15

= θ



15

sin sin105

R

⇒ θ= 

1 15

sin sin105 46.23 20.07

θ=  =

 ,方向角α=50− =θ 3.77

故合力

R = 20.07 kN

3.77 (b)三角形定律

合力大小 R

( )( )

2 2

15 10 2 15 10 cos105 20.07 kN

R

= + −  =

合力方向角 使用正弦定律

sin105 sin

R

15

= θ



15

sin sin105

R

⇒ θ= 

1 15

sin sin105 46.23 20.07

θ=  =

 ,方向角α=50− =θ 3.77

故合力

R = 20.07 kN

3.77

參考文獻

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