The stretch of a spring in millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate. (1 point)
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F = kx
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To find the unit rate, we need to determine how much the spring stretches for a weight of 1 gram attached to the end.
Since the stretch of the spring is proportional to the weight, we can set up the proportion:
Stretched length (in millimeters) / Weight (in grams) = k
where k is the constant of proportionality.
To find the unit rate, we need to find the value of k.
Let's suppose that for a weight of 1 gram, the spring stretches by "x" millimeters.
Using the proportion, we have:
x (mm) / 1 (g) = k
Thus, the unit rate is "k" millimeters per gram.
To find the unit rate in this scenario, we need to determine the amount of stretch in millimeters per gram of weight.
Let's say that when a weight of x grams is attached to the spring, it stretches y millimeters. We can write this relationship as:
y (in millimeters) = kx (in grams)
where k is the constant of proportionality.
To find the unit rate, we need to determine the value of k. We can do this by conducting an experiment where we measure the stretch of the spring for different weights.
1. Take a spring and attach a weight of 1 gram to it. Measure the corresponding stretch in millimeters. Let's say this stretch is a millimeters.
2. Repeat step 1 for several other weights, such as 2 grams, 3 grams, and so on. Measure the corresponding stretches and record them.
3. Once you have enough data points, create a table with the weight in grams and the corresponding stretch in millimeters.
4. Look for a pattern in the data. If the stretch is directly proportional to the weight, then the ratio of the stretch to the weight should remain constant. Calculate this ratio for each data point by dividing the stretch by the weight.
5. Find the average ratio from the data points. This average will be the value of k. Divide the total sum of ratios by the number of data points to get the average.
6. The unit rate is the value of k, which represents the amount of stretch in millimeters per gram of weight.