To find the tension in each rope supporting the painter and the board, we can start by modeling the situation.
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Identify the total weight:
- Weight of the painter: \(700 , \text{N}\)
- Weight of the board: \(180 , \text{N}\)
- Total weight: \[ W_{\text{total}} = W_{\text{painter}} + W_{\text{board}} = 700 , \text{N} + 180 , \text{N} = 880 , \text{N} \]
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Equilibrium condition: The system is in equilibrium, meaning the total upward forces (tensions in the ropes) must equal the total downward forces (weight). The two ropes are identical, so let the tension in each rope be \(T\).
Therefore, if there are two ropes, we can express this as: \[ 2T = W_{\text{total}} \]
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Solve for the tension: \[ 2T = 880 , \text{N} \implies T = \frac{880 , \text{N}}{2} = 440 , \text{N} \]
Thus, the tension in each rope is \(440 , \text{N}\).
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