what is the resultant of three coplanar forces: 300 N at 0 degree, 400 N at 30 degree and 400 N at 150 degree.?
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Let us assume that the angles are with respect to the positive x direction.
The x component of the resultant force
Fx = 300 * Cos 0⁰ + 400 * Cos 30⁰ + 400 Cos 150⁰
= 300 + 200 √3 - 200 √3 = 300 N
also Fy = 300 * cos 90° + 400 Sin 30° + 400 Sin 30°
= 400 N
F = √(Fx² + Fy²) = 500 N
The angle of the resultant with x axis is
= Tan⁻¹ Fy/Fx = Tan⁻¹ 4/3 = 53.13⁰
The x component of the resultant force
Fx = 300 * Cos 0⁰ + 400 * Cos 30⁰ + 400 Cos 150⁰
= 300 + 200 √3 - 200 √3 = 300 N
also Fy = 300 * cos 90° + 400 Sin 30° + 400 Sin 30°
= 400 N
F = √(Fx² + Fy²) = 500 N
The angle of the resultant with x axis is
= Tan⁻¹ Fy/Fx = Tan⁻¹ 4/3 = 53.13⁰
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