1. Break down forces into components:
* Force 1 (32 N):
* Horizontal component: 32 N * cos(30°) = 27.7 N
* Vertical component: 32 N * sin(30°) = 16 N
* Force 2 (22 N):
* Horizontal component: 22 N * cos(60°) = 11 N
* Vertical component: 22 N * sin(60°) = 19.1 N
2. Calculate net forces in each direction:
* Horizontal: 27.7 N + 11 N = 38.7 N
* Vertical: 16 N + 19.1 N = 35.1 N
3. Find the magnitude and direction of the net force:
* Magnitude: Use the Pythagorean theorem: √(38.7² + 35.1²) ≈ 52.6 N
* Direction: Use the arctangent function: tan⁻¹(35.1 / 38.7) ≈ 42.2°
Therefore, the net force on the ring is approximately 52.6 N at an angle of 42.2° relative to the horizontal.
