Question

In analyzing the general case of forces in a plane, one must ensure:

• A. Only horizontal forces are considered for equilibrium
• B. Forces are resolved into their scalar components
• C. Forces are represented as vectors and resolved into vertical and horizontal components
• D. Only vertical forces are analyzed for system stability

Hint:

Always resolve forces into horizontal and vertical vector components when dealing with equilibrium in a plane. This ensures all force effects are accounted for correctly.

Answer 1

The Correct Option is C

Step 1: In two-dimensional force analysis, the general method involves treating forces as vectors and resolving them into two perpendicular directions—typically horizontal (x-axis) and vertical (y-axis).
Step 2: Each force acting on a body is broken down into components using trigonometric relations. The system is in equilibrium when the sum of forces in each direction is zero: \[ \sum F_x = 0 \quad \text{and} \quad \sum F_y = 0 \] Step 3: This approach allows for a complete and accurate analysis of the system’s equilibrium by considering all directions simultaneously.
Why the other options are incorrect:

• (A) Considering only horizontal forces gives an incomplete analysis.
• (B) Scalar resolution doesn't preserve direction and thus is insufficient for vector equilibrium analysis.
• (D) Vertical forces alone cannot determine system stability unless all other directional forces are zero or negligible.