The minimum number of coplanar forces of equal magnitude whose vector sum can be zero is three.
Explanation:
- Coplanar forces: These are forces that act in the same plane.
- Equal magnitude: This means all the forces have the same strength.
- Vector sum: This refers to the overall effect of the forces, taking into account their directions.
To achieve a zero vector sum, the forces must balance each other out. This can be visualized as a triangle where each side represents a force. If the forces are equal in magnitude and arranged to form a closed triangle, their vector sum will be zero.
Example:
Imagine three forces of equal magnitude, each acting at 120 degrees to the other. If you place these forces at the corners of an equilateral triangle, they will cancel each other out, resulting in a zero vector sum.
Conclusion:
Therefore, the minimum number of coplanar forces of equal magnitude required for their vector sum to be zero is three. This is because three forces can be arranged to form a closed triangle, ensuring their vectors cancel each other out.
