Understanding the Problem
* Forces are vectors: They have both magnitude (size) and direction.
* Resultant force: The single force that has the same effect as the two original forces combined.
Solution
1. Visualize: Imagine a right triangle where:
* The 6.0 N force is the vertical side.
* The 3 N force is the horizontal side.
* The resultant force is the hypotenuse.
2. Pythagorean Theorem: We can use the Pythagorean theorem to find the magnitude of the resultant force:
* Resultant Force² = Vertical Force² + Horizontal Force²
* Resultant Force² = 6.0² + 3²
* Resultant Force² = 36 + 9 = 45
* Resultant Force = √45 ≈ 6.7 N
3. Direction: To find the direction, we need the angle between the resultant force and the horizontal axis. We can use trigonometry:
* tan(θ) = (Vertical Force) / (Horizontal Force)
* tan(θ) = 6.0 / 3 = 2
* θ = arctan(2) ≈ 63.4°
Answer:
The resultant force is approximately 6.7 N at an angle of approximately 63.4° above the horizontal.
