Proportionality Definition and 82 Threads

In mathematics, two varying quantities are said to be in a relation of proportionality,
multiplicatively connected to a constant; that is, when either their ratio or their product yields a constant. The value of this constant is called the coefficient of proportionality or proportionality constant.

If the ratio (y/x) of two variables (x and y) is equal to a constant (k = y/x), then the variable in the numerator of the ratio (y) can be product of the other variable and the constant (y = k ⋅ x). In this case y is said to be directly proportional to x with proportionality constant k. Equivalently one may write x = 1/k ⋅ y; that is, x is directly proportional to y with proportionality constant 1/k (= x/y). If the term proportional is connected to two variables without further qualification, generally direct proportionality can be assumed.
If the product of two variables (x ⋅ y) is equal to a constant (k = x ⋅ y), then the two are said to be inversely proportional to each other with the proportionality constant k. Equivalently, both variables are directly proportional to the reciprocal of the respective other with proportionality constant k (x = k ⋅ 1/y and y = k ⋅ 1/x).If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., a/b = x/y = ... = k (for details see Ratio).

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  1. S

    Uniform circular motion proportionality question

    Homework Statement David spins a sling in a horizontal circle above his head. What would happen to the period of rotation if he applied the same force and the length was a) doubled, b) halved Homework Equations ac = (4π2r) / T2 The Attempt at a Solution Just not sure what to do in...
  2. M

    Magnetic Field Strength: Inverse Proportionality to Square or Cube?

    I have read a number of journal article that state that magnetic field strength diminishes inversely proportional to the square of the distance. BUT more than one has stated that the field strength is inversely proportional to the cube of the distance from the surface of the magnet. Which one...
  3. A

    Understanding AWG Gages & Inverse Proportionality of Diameter to Area

    In AWG Gages, how diameter is inversely proportional to the cross-sectional area of the conductor?
  4. Q

    Combining Proportionality Statements

    Homework Statement Combine the proportionality statements for R and d and R and l to form one statement relating R, d, and l. Homework Equations I already know that R∝(1/d squared) and R∝l The Attempt at a Solution I thought it was R∝ (l/d squared), but that seems too easy lol. Please...
  5. D

    Proportionality of triangles problem

    Homework Statement Is any formulas similar to that of proportionality of the triangles to proportionality of the given figure? Homework Equations The Attempt at a Solution
  6. G

    Is Acceleration Directly Proportional to the Square of Time in Kinematics?

    Homework Statement The acceleration of a particle is directly proportional to the square of the time t... Homework Equations C = constant The Attempt at a Solution I'm just having a little difficutly with the wording. In this case could I write: a = C / t^2 ?
  7. H

    Proportionality between Frequency and Mass

    Homework Statement There was an investigation on how mass affected frequency and we had to plot this relationship. Homework Equations None The Attempt at a Solution I plotted frequency as the y-axis and mass as the x-axis. I got this weird parabolic shape opening upwards and...
  8. M

    How Does Graphing Reveal the Relationship Between F and r?

    Homework Statement In the following table of results, determine the relationship between F and r, using graphical techniques. r : 1 , 1.2 ,1.8 , 2.4 , 3.0 F : 10 , 6.9 , 3.1 , 1.7 , 1.1 Homework Equations y is proportional to 1/xn The Attempt at a Solution I graphed the data...
  9. S

    Velocity-Friction proportionality.

    1. A 1000kg boat is traveling across a lake when its engine is shut off. The magnitude of the frictional force between the water and the boat is proportional to the boat's speed (proportionality constant is 70) . Find the time it takes the boat to slow to one half its speed when the engine was...
  10. N

    Current Proportionality and Thevenin Equivalence

    Homework Statement For the linear circuit shown, given that the current I in the 0.9 K\Omega is 10mA when Vs = 100V: (a) Predict I using the proportionality property for: Vs = 25V, -12V, and 145 V respectively. (b) Use Thevenin’s theorem across terminals a and b. Find I in terms of Vs and...
  11. P

    Understanding Proportional Components in Equations

    Homework Statement Looking at a set of equations -how exactly do you work out if one component is proportional to another. Homework Equations In the example given s = ut + 1/2 at^2, I am told that s is not proporional to t unless acceleration is zero, because u is a constant...
  12. E

    Solving for exponents in proportionality

    In an experiment I am performing, I observed the following: Result is directly proportional to A Result is inversely proportional to B So, I assume two constants, alpha and beta such that: Result = (A^alpha)/(B^beta) Now, if I know I want to solve for alpha and beta but is this the...
  13. A

    What is the fact of constant of proportionality?

    Its so confusing for me... in Ohm's law V=IR here V is independent variable and I is dependent variable (i,e increasing V, I also increases) here we place R (proportionality constant) with I (dependent variable). On the other hand.. in electrostatic force F=k(Qq/r^2 ) here K is constant...
  14. A

    Is P Inversely Proportional to R Squared?

    Homework Statement If P is proportional to q^2 and q is inversely proportional to r Show that p is proportional to r^2 Homework Equations p = kq^2 q = c/r where k and c are proportional constants The Attempt at a Solution I'd say this is impossible. This is all the...
  15. P

    Why do we call the constant of proportionality in hook's law as Young's Modulus?

    Why do we call the constant of proportionality in hook's law as Young's Modulus and not as Young's coefficient? Is there any difference in Modulus and coefficient in engineering context?
  16. W

    Centripetal Force Proportionality Check

    Homework Statement Write a proportionality statement for F, m, f and r using your three proportionality statements. Homework Equations F = centripetal force f = frequency m = mass r = radius F \propto f^2 r \propto F^2 m \propto F^2 The Attempt at a Solution m \propto...
  17. R

    Kinematics and proportionality.

    Hey, please take a look at this problem, it should be quite straight-forward but I want to know if I've reached the right conclusion. Homework Statement A particle moves in a straight line with displacement s from some fixed point on the line and velocity v. If v is proportional to...
  18. W

    Proportionality calculations (Coulombs Law)

    Two unlike charges attract each other with a force of 5 x 10^-5 when placed 12 cm apart. 1) What is the force between them when they are 4.0cm apart 2)At what distance apart will the force between them be 2.0 x 10^-4 now i have attempted these questions, but i cannot find a...
  19. D

    What Is the Constant of Proportionality in the Equation Q = K1 M?

    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...
  20. O

    Terminal Velocity and Mass Relationship in a Proportionality Argument

    Homework Statement Assume a box is sliding down a ramp with an incline of \theta radians and reaches terminal velocity before arriving at the bottom of the ramp. Assume that the drag force caused by the air is proportional to Sv^2, where S is the cross sectional area perpendicular to the...
  21. M

    Does height affect the constant of proportionality?

    Homework Statement Does height affect the constant of proportionality? 'k' Homework Equations no relevant equations The Attempt at a Solution I don't think it does but I'm not sure why though.
  22. M

    Deriving a Proportionality Statement for Centripetal Force and Frequency

    Hey everyone, I'm new to the forums and this is my second thread started. This is an excellent resource in my opinion. Regardless of the formalities I have a question regarding a proportionality statement. I have here a question asking for a proportionality statement (in words) relating...
  23. G

    Integration with constant of proportionality

    This seems easy enough, but now I'm second guessing myself... Problem: http://www.mcschell.com/probl.gif I solved it as follows: \frac{dN}{ds} = k(250-s) dN = k(250-s) ds \int dN = \int k(250-s) ds N = k\int (250-s) ds N = k(\int 250 ds - \int s ds) N = k(250s - \frac{s^2}{2})...
  24. D

    Magnetism - the proportionality constant question

    Hi! Can anyone please tell me where this equation was derived from? This equation is used to get the magnetic field (B). I is current and r is the distance. And I think I understand the Meu. And yet I have no idea where the 2pi came from. I looked in my textbook, internet and asked friends...
  25. L

    Capacitance proportionality to circuit frequency?

    The way I understand extremely high frequency circuits to work is that in the design consideration it has to be considered capacitance across the traces. This becomes especially true as you increase the frequency. According to this website: http://www.adras.com/Impedance.t647-89-2.html...
  26. D

    Solve Proportionality Problems with Ease: Get Proportionality Help Now!

    proportionality help needed please stuck on a proportionality problem... 1) the pressure exerted by a fluid in a pipe varies inversely as the sixth power of the diameter. what is the multiplicative change (delta X_m) and percentage change (delta X%) in the pressure is the diameter of the pipe...
  27. L

    Heat and Mass Proportionality: Examining the Accuracy

    I NOTICED THAT THE TIME REQUIRED FOR A GIVEN MASS OF A LIQUID IS PROPORTIONAL DIRECTLY TO THE MASS OF THE LIQUID PROVIDED THE HEAT SUPPLY IS CONSTANT,WHICH MAKES t PROPORTIONAL TO m,the heat is constant.now heat is mctheta +ml.which makes t =m^2(l+ctheta).how true is this,is there a fault i...
  28. bayan

    Proportionality of T to R, m1 and m2

    We have done an experimnet latly in which we did an investigation on m1Ug=4Pie^2m(2)r m2/ T^2 We drew the graphs of the values that we found, then we drew the Log values to fing Gradiant to find the power of proportionality. in our experiment gradiant of my Log values were T prop...
  29. M

    Centripetal Force and proportionality

    Hi, can someone please point me in a direction. I need to explain WHY "The centripetal force is proportional to the mass and to the radius and proportional to the square of the frequency." We did the spinning lab, and now I need to do a discussion. Thanks.
  30. S

    Investigating Proportionality of Elastic Band Range to Pull-Back Length

    im doing a lab tomorrow that i must plan soon. if we fire an elastic band, the length we stretch it will affect the range but how do i support my hypothesis that range is proportional to pull back length? do i use hookes law assuming that pull back length is the same as extention? any tips...
  31. D

    KE, v squared and a constant of proportionality

    I was reading about Kinetic Energy and why it is 1/2 mv^2. I couldn't really understand what it was saying, it was mentioning a constant of proportionality being: \frac{kg * m^2/s^2}{m^2/s^2} and then of course you're left with mass. It was very confusing, so basically what I'm asking is for...
  32. M

    Solving for Constant in T=k/L Inverse Proportionality

    I know that the tension of a string is Inversely proportional to the length. obviously this is shown as T=k/L, where t is the tension; k is the constant; and L is the length. My question is; What is the constant? I would also appreciate anything else loosely related to the topic. Thank you.
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