To find the unit rate for the stretch of a spring in relation to the weight, we start from the principle of proportionality you mentioned: the stretch of the spring (let's call it \( S \), in millimeters) is proportional to the weight (let's call it \( W \), in grams).
This relationship can be expressed as:
\[ S = k \cdot W \]
where \( k \) is the constant of proportionality (the unit rate).
To find the unit rate, we can express \( k \) as follows:
\[ k = \frac{S}{W} \]
This means for each gram of weight attached to the spring, \( k \) millimeters will be the stretch.
If you have specific values for \( S \) and \( W \), you can plug them into the equation to calculate \( k \). If the stretch of the spring is x mm when y grams are applied, then the unit rate \( k \) can be found by calculating \( k = \frac{x \text{ mm}}{y \text{ g}} \).
For example, if a weight of 100 grams causes a stretch of 200 mm, then:
\[ k = \frac{200 \text{ mm}}{100 \text{ g}} = 2 \text{ mm/g} \]
This means that for each gram of weight, the spring stretches 2 millimeters.
If you have specific measurements, please provide those to calculate the exact unit rate.
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