Constant of proportionality

In summary, the constant of proportionality, K1, is used in the equation Q=K1*M to represent the direct relationship between net charge and molecular weight of aggregates. This means that as the molar mass of the aggregates increases, the net charge also increases, and this relationship is linear. Similarly, the concept of proportionality is used when describing the relationship between two variables, such as y and x, where y=k*x. Inversely proportional means that y is equal to k divided by x, and the relationship is not linear. The constant of proportionality is important in understanding relationships between variables, such as in Newton's law of gravitation.
  • #1
dranseth
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0

Homework Statement


Can anyone translate what k would be? I have never had to deal with a constant of proportionality before, and am not quite sure how to deal with it..

The resulting aggregates therefore
each have a net charge Q that is directly proportional to their molecular weight M:
Q= K1 M
where K1 (and in subsequent steps of this derivation K ) is a constant of proportionality.
 
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  • #2
You've dealt with them, you just didn't know what they were called

When I say y is directly proportional to x, what I mean is that if I double x, I double y. If I halve x, I halve y. If I square root x, I square root y, etc.

so y=x? No, I said if I double x it doubles y, but I didn't say they're the SAME number! So if y and x are proportional you'd say y=k*x (or whatever letter) so all those things I said are true, if you double x, for that equation to still be equal you must double y

For a counterexample what if they AREN'T directly proportional? So say y=k*x^2, if I double x, for the equation to hold, I have to quadruple y!

You'll note that y=k*x results in the graph of a line with slope k, so you'll also hear that y and x are linearly related, which means the same thing as directly proportional

You'll also commonly hear "inversely proportional", which means y=k/x, so if I double x, I take half of y, if I triple x, a third of y

Counterexample again when it's NOT inversely proportional, y=k/x^2, if I double x, I take a fourth of y!

ADDENDUM: The constant of proportionality that you're likely most familiar with is probably pi!

What is pi exactly?(3! Wait no...) A bajillion years ago(1 jigga year)some ancient Greeks or Carthaginians or whoever were looking at circles and thinking "hey the circumference and diameter are directly proportional!" Meaning if you took a circle with diameter of 1 m(well ancient greeks so like...1 hand?), it would have some circumference. If you took a circle with diameter 2(same unit), well the circumference is twice as much as before!

So C=k*d they figured. So what was k? They had to take an actual circle that they could measure the circumference and diameter of, and find the ratio(so if C=k*d, then k=C/d) and they found it was a little more than 3. About .14 more than 3. And they called it pi since they were Greeks and the latin letter k probably didn't exist then >_>

That's how Newton figured out his law of gravitation. He figured that the net force(which he had already figured out was directly proportional to acceleration, with that particular constant of proportionality being the mass)was directly proportional to the product of the two masses involved, and inversely proportional to the distance squared(so if you double either mass, you double the force, but if you double the distance between them you cut the force by a FOURTH)

And that's the meat of the law, the part that really matters. The constant of proportionality (G, so F=G*m1*m2/d^2) is just some fundamental constant which he didn't have the tools to measure at the time

So for the equation in your question, if you're not given K1, you're not really expected to care then. The POINT is that charge is directly proportional to M, so you understand the relationship between the two. As the molar mass of the aggregates increases, Q increases, and the nature of their relationship is linear
 
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  • #3


I can explain that the constant of proportionality, denoted as K1 and potentially changing in future steps, is a numerical value that relates the net charge (Q) of the aggregates to their molecular weight (M). In other words, for every increase in molecular weight, there is a corresponding increase in net charge, and the value of K1 helps us determine the exact relationship between the two. This constant is commonly used in mathematical models and equations to describe the relationship between two variables. In this case, it helps us understand the behavior of the aggregates and their net charge based on their molecular weight.
 

What is the constant of proportionality?

The constant of proportionality is a value that relates two variables in a proportional relationship. It determines the rate at which the two variables change in relation to each other.

How is the constant of proportionality calculated?

The constant of proportionality can be calculated by dividing the two variables in a proportional relationship. For example, if y is proportional to x, then the constant of proportionality is equal to y/x.

What is the difference between the constant of proportionality and the slope?

The constant of proportionality and the slope are related concepts, but they are not the same. The constant of proportionality is a specific value that represents the rate of change between two variables in a proportional relationship. The slope, on the other hand, is a general measure of the steepness of a line on a graph.

What is an example of a proportional relationship?

A common example of a proportional relationship is distance and time. As the distance traveled increases, the time it takes to travel that distance also increases, and the constant of proportionality between them is the speed of travel.

Why is the constant of proportionality important in science?

The constant of proportionality is important in science because it helps us understand and predict the relationship between two variables in a proportional relationship. It allows us to make accurate measurements and calculations, and it is a fundamental concept in many scientific fields, such as physics and chemistry.

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