Understanding the Problem
* We have two forces acting at right angles to each other (one vertical, one horizontal).
* We need to find the magnitude of the single force that would produce the same effect as these two forces combined.
Using the Pythagorean Theorem
The resultant force forms the hypotenuse of a right triangle where:
* The vertical force (6.0 N) is one leg.
* The horizontal force (4.0 N) is the other leg.
The Pythagorean theorem states: a² + b² = c²
* a = 4.0 N (horizontal force)
* b = 6.0 N (vertical force)
* c = Resultant force (magnitude we are looking for)
Calculation
1. 4.0² + 6.0² = c²
2. 16 + 36 = c²
3. 52 = c²
4. c = √52 ≈ 7.2 N
Answer
The magnitude of the resultant force is approximately 7.2 N.
