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
The unit rate in this situation would be the amount of stretch per unit weight. In other words, it would be the stretch of the spring in millimeters per gram of weight attached to the spring.
To find the unit rate, we need to determine the amount of stretch in millimeters for a weight of 1 gram.
Let's assume that for a weight of 1 gram, the stretch of the spring is 'x' millimeters.
Since the stretch is proportional to the weight, we can set up the proportion:
Stretch (in millimeters) / Weight (in grams) = x / 1
The unit rate is the amount of stretch for a weight of 1 gram, so the unit rate is 'x' millimeters/gram.
Therefore, the unit rate is 'x' millimeters/gram.
To find the unit rate, we need to determine the ratio of the stretch of the spring to the weight attached to it.
Let's define:
- x as the stretch of the spring in millimeters.
- y as the weight attached to the spring in grams.
Since the stretch of the spring is proportional to the weight, we can write this as an equation:
x ∝ y
Now, we need to find the constant of proportionality. To do this, we can use the information given in the problem.
Let's say when there is a weight of 100 grams attached to the spring, the stretch is 20 millimeters.
So, we have the following equation:
x = ky
where k is the constant of proportionality.
Plugging in the values, we get:
20 = k * 100
To find k, we divide both sides by 100:
k = 20 / 100
k = 0.2
Now we know that the constant of proportionality is 0.2.
Therefore, the unit rate is 0.2 millimeters per gram. This means that for every gram of weight attached to the spring, it stretches by 0.2 millimeters.