Determine Tension Forces in Cables AC and AB for Equilibrium

Published on September 24, 2026

Word-Problem

Calculate the forces in cables AC and AB supporting a 20-kg cylinder under a 300 N horizontal load by applying static equilibrium equations in 2D space.

Question

Answer

To determine the forces in cables

and

, we analyze the equilibrium of point

1. Identify the forces acting at point :

The weight of cylinder : (acting downward).
The external horizontal force: (acting to the right).
The tension in cable : .
The tension in cable : .

2. Determine the unit vectors for the cables:
Let point

be the origin

. Based on the dimensions provided:

Point is at . The vector .
The length .
Unit vector .
Point is at . The vector .
The length .
Unit vector .

3. Apply equilibrium equations ( and ):

4. Solve the system of equations:
From the

-equation:

Substitute

into the

-equation:

Now solve for

Final Answer:
The forces in the cables are:

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