Question

大帥哥

這題有沒有可能只用反函數就可以解出來⋯
為啥算不出答案，ㄚ。

Assignment (part I)
(page 50)
*2-8. Two forces are applied at the end of a screw eye in order to remove the post.
Determine the angle 0 (0° ≤ 0 ≤ 90°) and the magnitude of force F so that the
resultant force acting on the post is directed vertically upward and has a
magnitude of 750 N.
30°
500 N
2025/2/25
CHIANG Yu-Chou
33

工程力學

Answer 1

✨ ベストアンサー ✨

qn

水平：500sinθ = F/2
鉛直：500cosθ + (√3/2)F = 750

⇒ 500cosθ + √3 (500sinθ) = 750
⇒ (1/2)cosθ + (√3/2) sinθ = 3/4
⇒ sin(θ+30°) = 3/4
範圍：30° ≤ θ + 30° ≤ 120°
其中 90° < θ+30° ≤ 120° 無解
可以確定 θ+30° = sin⁻¹(3/4)
⇒ θ = sin⁻¹(3/4) - 30°

F = 1000 sinθ = 1000 sin(sin⁻¹(3/4) - 30°)
= 1000 [sin(sin⁻¹(3/4)) cos30° - cos(sin⁻¹(3/4)) sin30°]
= 1000 [ (3/4)(√3/2) - (√7/4)(1/2) ]
= 1000 [ 3√3 / 8 - √7 / 8 ]
= 375√3 - 125√7

大帥哥

娃所以這題沒有實數解嗎？
這題可以用拉密定理嗎，我餘弦也用了
就是求不出角度

qn

是
（嚴格來說他還是實數，只是不能用常見運算來表達）

然後拉密定理要有3個力