Two forces 10N and 20N are inclined at an angle of 60° to each other find the resultant by mathematical method
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To find the resultant of two forces inclined at an angle of 60° to each other, we can use the concept of vector addition.
Step 1: Resolve the forces into their horizontal and vertical components.
Let's assume the 10N force is force F1 and the 20N force is force F2. Since the angle between them is 60°, we can resolve the forces as follows:
F1x = F1 * cos(60°)
F1y = F1 * sin(60°)
F2x = F2 * cos(60°)
F2y = F2 * sin(60°)
Step 2: Add the horizontal and vertical components separately.
The horizontal component of the resultant is given by R_x = F1x + F2x.
The vertical component of the resultant is given by R_y = F1y + F2y.
Step 3: Find the magnitude and direction of the resultant.
To find the magnitude of the resultant, we can use the Pythagorean theorem: R = √(R_x² + R_y²).
To find the direction of the resultant, we can use the inverse tangent function: θ = tan⁻¹(R_y / R_x).
Plugging in the values:
F1 = 10N
F2 = 20N
angle = 60°
F1x = 10N * cos(60°) = 5N
F1y = 10N * sin(60°) = 8.66N
F2x = 20N * cos(60°) = 10N
F2y = 20N * sin(60°) = 17.32N
R_x = F1x + F2x = 5N + 10N = 15N
R_y = F1y + F2y = 8.66N + 17.32N = 25.98N
R = √(15N² + 25.98N²) = √(225N² + 674.22N²) = √(899.22N²) ≈ 29.99N
θ = tan⁻¹(25.98N / 15N) ≈ 58.30°
Therefore, the magnitude of the resultant force is approximately 29.99N, and the angle it makes with the horizontal is approximately 58.30°.