1. Understand the Problem
* We have two forces acting at an angle.
* We need to find a third force (the balancing force) that will result in a net force of zero.
2. Vector Addition
* Graphical Method: You can represent the two forces as vectors (arrows) on a diagram. Draw them head-to-tail, respecting the angle between them. The resultant force is the vector drawn from the tail of the first vector to the head of the second vector. The balancing force is the vector of the same magnitude as the resultant force but pointing in the opposite direction.
* Analytical Method (using trigonometry):
* Break down the forces into components:
* 10N force:
* x-component: 10N * cos(0°) = 10N
* y-component: 10N * sin(0°) = 0N
* 16N force:
* x-component: 16N * cos(60°) = 8N
* y-component: 16N * sin(60°) = 13.86N (approx.)
* Sum the components:
* Total x-component: 10N + 8N = 18N
* Total y-component: 0N + 13.86N = 13.86N
* Find the magnitude of the resultant force:
* Magnitude = √(18² + 13.86²) ≈ 22.45N
* Find the angle of the resultant force:
* Angle = arctan(13.86/18) ≈ 37.5° (relative to the horizontal axis)
3. The Balancing Force
The balancing force has:
* Magnitude: 22.45N (same as the resultant force)
* Direction: Opposite to the resultant force, meaning 37.5° + 180° = 217.5° (relative to the horizontal axis)
Therefore, a force of approximately 22.45N acting at 217.5° relative to the horizontal axis will balance the two given forces.
