Math Problem Statement

  1. The rectangular components of a force are Fy = +1.3 kN and Fx = +103 N. Calculate the magnitude, inclination with the horizontal axis, and the sense of the resultant force F. Sketch the components forces and the resultant force (realistically) on an XY axis.

Solution

Here is the sketch showing the force components FxF_x, FyF_y, and the resultant force FF on the XY axis. The angle θ\theta between the resultant and the horizontal axis is also indicated.

Let me know if you'd like further details or clarification!

Related Questions:

  1. How does the angle of inclination affect the resultant force direction?
  2. Can the same method be used if one of the force components is negative?
  3. How would the calculation change if FxF_x and FyF_y were in different quadrants?
  4. What would happen if FyF_y was significantly smaller than FxF_x?
  5. How is the direction of the resultant force useful in real-world applications?

Tip:

For any force system, always break forces into components when analyzing motion, as this makes complex problems simpler to handle.

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Math Problem Analysis

Mathematical Concepts

Vector Addition
Trigonometry
Physics (Force Vectors)

Formulas

Magnitude of resultant force: F = √(Fx² + Fy²)
Angle of inclination: θ = tan⁻¹(Fy/Fx)

Theorems

Pythagorean theorem (for magnitude calculation)
Tangent function for angle calculation

Suitable Grade Level

Grades 10-12 (Physics/Trigonometry)