The stretch of a spring in millimeters in proportional to the weight in grams attached to the end of the spring. Find the unit rate
The unit rate in this situation can be found by determining how much the spring stretches for every gram of weight added.
Let's assume that for every gram of weight added to the spring, it stretches by 1 millimeter.
Therefore, the unit rate would be 1 millimeter per gram.
To find the unit rate, we need to determine the relationship between the stretch of the spring and the weight attached to it. Let's assume that the stretch of the spring (in millimeters) is directly proportional to the weight (in grams).
Let's say that the stretch of the spring is "s" millimeters and the weight attached to the end of the spring is "w" grams. According to the given information, we can express the relationship as:
s ∝ w
To find the unit rate, we need to determine the constant of proportionality. In this case, the constant of proportionality represents how many millimeters the spring stretches per gram of weight attached to it.
We can write this relationship as:
s = k * w
where "k" is the constant of proportionality (unit rate).
To find the value of "k" (unit rate), we need some data points. Let's consider two scenarios:
Scenario 1:
s = 10 mm (stretch of the spring)
w = 100 g (weight attached)
Scenario 2:
s = 20 mm
w = 200 g
Now we can find the value of "k" by setting up a ratio:
k = (s2 - s1) / (w2 - w1)
= (20 - 10) mm / (200 - 100) g
= 10 mm / 100 g
= 0.1 mm/g
Therefore, the unit rate is 0.1 mm/g. This means that for every gram of weight attached to the spring, it stretches by 0.1 millimeters.
To find the unit rate, we need to determine how much the spring stretches for each gram of weight added to it.
Let's consider an example where the spring stretches by 5 millimeters when a weight of 10 grams is attached.
To find the unit rate, we divide the change in the stretching of the spring by the change in the weight. In this case, the change in stretching is 5 millimeters, and the change in weight is 10 grams. Thus, the unit rate would be:
5 millimeters / 10 grams = 0.5 millimeters/gram
So, the unit rate for this spring is 0.5 millimeters per gram. This means that for every gram added to the spring, it would stretch by 0.5 millimeters.