Final answer:
The x-component of the force F₁ is 3 N, and the y-component is 4 N. Drawing a free-body diagram helps to resolve forces into these components.
Step-by-step explanation:
The question concerns the calculation of force components acting on a particle in the context of Newton's laws of motion and force analysis. To find the x-component and y-component of a given force, one must resolve the force into its horizontal and vertical parts.
Force Component Analysis
For instance, if a force F₁ is represented as F₁ = (3 N)Î + (4 N)Ĵ, the x-component of this force is 3 N, and the y-component is 4 N. Analyzing force components is crucial in physics to understand the behavior of particles under the influence of multiple forces.
When solving problems involving forces, it is recommended to use a free-body diagram to visually represent the forces acting on an object. The forces need to be resolved into their components if not already provided in that form. For a given force vector, such as F₁ = (3î + 4Ĵ) N, the x and y components are simply the values accompanying the unit vectors î (which indicates the x-axis direction) and Ĵ (indicating the y-axis direction).