Understanding the Concepts

* Resultant Force: The single force that produces the same effect as two or more forces acting together.

* Perpendicular Minimum: This refers to the fact that the two forces are arranged in a way that minimizes their combined effect in the direction of the resultant force. This arrangement typically means the forces are perpendicular to each other.

Solving the Problem

1. Visualize: Imagine a right triangle where:

* The hypotenuse represents the resultant force (8 N).

* The two legs represent the two forces acting at the point.

2. Pythagorean Theorem: Since the forces are perpendicular, we can use the Pythagorean theorem:

* Resultant Force² = Force 1² + Force 2²

* 8² = Force 1² + Force 2²

* 64 = Force 1² + Force 2²

3. Equation for the Sum: We also know the sum of the two forces is 16 N:

* Force 1 + Force 2 = 16

4. Solving the System of Equations:

* We can solve for Force 1 in terms of Force 2 (or vice versa) from the second equation:

* Force 1 = 16 - Force 2

* Substitute this value of Force 1 into the first equation:

* 64 = (16 - Force 2)² + Force 2²

* Expand and simplify:

* 64 = 256 - 32 * Force 2 + Force 2² + Force 2²

* 0 = 2 * Force 2² - 32 * Force 2 + 192

* 0 = Force 2² - 16 * Force 2 + 96

* Factor the quadratic equation:

* 0 = (Force 2 - 8)(Force 2 - 12)

* This gives us two possible solutions for Force 2:

* Force 2 = 8 N

* Force 2 = 12 N

5. Finding Force 1:

* If Force 2 = 8 N, then Force 1 = 16 - 8 = 8 N

* If Force 2 = 12 N, then Force 1 = 16 - 12 = 4 N

Conclusion

The two forces acting at the point are either:

* 8 N and 8 N (both forces are equal in magnitude)

* 4 N and 12 N (forces are unequal in magnitude)

Both scenarios satisfy the conditions given in the problem.