It seems like you're describing a situation involving weights and balance, possibly related to a physics problem. To derive an equation based on your description, let's analyze the setup:
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Hanger Model: It seems you have a balance beam or hanger with weights on either side.
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Left Side (Weight at distance): You mentioned "left r r 4," which seems to imply you have a weight of \( r \) at a distance of 4 units from the center.
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Right Side (Weight at distance): The "right 14" likely means you have a different weight or a force acting at a distance of 14 units from the center.
Assuming that the weights on each side of the hanger create a torque about the center (pivot), the condition for balance can be expressed as:
\[ \text{Torque on the left} = \text{Torque on the right} \]
Torque is generally calculated using the formula:
\[ \text{Torque} = \text{Force} \times \text{Distance from pivot} \]
For the left side, if we denote the left distance as 4 and the force (weight) as \( r \):
\[ \text{Torque on the left} = r \times 4 \]
For the right side, assuming that the force is some constant weight \( W \) acting at a distance of 14:
\[ \text{Torque on the right} = W \times 14 \]
Setting these two torques equal (for equilibrium):
\[ r \times 4 = W \times 14 \]
This is the equation that represents your hanger model based on the information you've provided. If \( W \) is a known constant, you can solve for \( r \) or vice versa. If you have more specific details or corrections to the interpretation, please clarify!
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