Physics

To find the tension in the rope making a 30° angle with the vertical, we can use the equilibrium conditions for the sign. The vertical forces must balance the weight of the sign.

 

Given:

Weight of the sign () = 120 N

Tension in the first rope () at 30° to the vertical

Tension in the second rope () at 60° to the vertical

 

Step 1: Resolve the tensions into vertical components

The vertical components of the tensions can be expressed as follows:

1. For (30°):

 

2. For (60°):

 

Step 2: Write the equilibrium equation for the vertical forces

The sum of the vertical components must equal the weight of the sign:

Substituting the expressions for and :

 

Step 3: Resolve the horizontal components

Since the system is in equilibrium, the horizontal components must also balance out:

Where:

1. For :

 

2. For :

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