What is Proportionality: Definition and 82 Discussions
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).
I found this quote online:
“Multiplication is the mathematical manifestation of the fundamental physical phenomenon of proportionality (as addition is to combination).”
Question 1: How are multiplication and proportion linked? How can and WHY DOES multiplication model proportion? (My...
Hi all,
I'm a little confused about something.
Force-extension graphs and stress-strain graphs are always both straight lines up until the limit of proportionality, implying both the spring constant and the Young modulus are constant up until then.
For a force-extension graph, Hooke's Law...
So i have this question. If a projectile is fired from a spring loaded system and when it goes pass a chronograph, reads 300FPS and has a mass of 0.12grams. Is there any way to use the proportionality theorem (1/3=x/6 example) to approximate how fast a mass of 0.25grams is when fired from same...
Do not understand the statement:
Ben’s method requires that the voltage output be directly proportional to the intensity, which it is not.
https://www.asi.edu.au/wp-content/uploads/2015/03/2010_Physiscs_solutions.pdf
My thoughts are that by I= Io cos(theta)^2
We can relate voltage to theta...
According to Basic proportionalit theorem
if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides proportionaly.
I can't figure a way out how to prove it.
Here is an attempt.
we know that AE/EB = AD/DC.
Using the fact that
Pa ∝ |α|^2 and Pb ∝ |β|^2, we get:
Pa = k|α|^2 and Pb = k|β|^2
Since the probability of measuring the two states must add up to 1, we have Pa + Pb = 1 => k = 1/(|α|^2 + |β|^2). Substituting this in Pa and Pb, we get:
Pa = |α|^2/(|α|^2 + |β|^2)
and Pb = |β|^2/(|α|^2 + |β|^2)...
I am doing a project, but am struggling to find relationships of proportionality or formulae between my dependent variables (angular velocity, displacement, acceleration of the disc and kinetic energy of the system) and my independent variables (falling masses and then the number of winds) or...
Homework Statement
Its a series of problems essentially basically asking questions about solving proportionality
. For example
"Hooke's Law of a spring can be described by the equation F = -kx, where F is the force exerted by a spring, K us the spring constant, and X is the amount of distance...
If I'm standing on a cliff-top, according to Newton's Law of Gravity I exert less force than I would at sea-level. However, it seems I've increased my Gravitational Potential Energy. So, is the reduction in force equal and opposite to the increase in energy?
Homework Statement
Scientist want to put a satellite into an orbit where the gravitational field of Earth is half its value at Earth's surface. The altitude of this orbit above the Earth's surface will be
A.3R B. √2R-R C. 4R D.√2R
Homework Equations
Fg∝1/r^2
The Attempt at a Solution
I know...
Homework Statement
An astronaut on the moon throws a stone horizontally with a speed V0. If the acceleration due to gravity on the moon is 1⁄6 that of the Earth, by what factor will the horizontal distance traveled by the stone, d, change?
Answer Options:
2
2.44
1.20
36
6Homework...
Good day all,
Sorry if this has been posted a lot before but I've been fiddling with the formulas for the redshift and I came up with a question regarding the proportionality of it. I'm new at this so please bear with me. For the sake of argument, I'm talking about redshift in an expansion with...
Homework Statement
A chart has values of Fc (dependant): 10, 15, 20, 25, 30, respectively. The independant variable, F, has values 0.98, 1.07, 1.16, 1.32, 1.50, respectively. These values form a root graph.
Fc is proportional to 4√F, this is the proportionality statement allowing me to make...
in particular f=Gm1m2/r^2?sorry if my question sounds very irrelevant.if f is proportional to m1m2 it implies f=some constant times m1m2.okay.at the same time f is inversely proportional to r^2 .so force = some other constant times 1/r^2.okay.but in most places i see that what is done is they...
Homework Statement
In an astronomy problem, I am given ##P^2 \propto \frac {a^3}{M_s}## and I must solve for M. How do I use an equation like this? Is this not the same as ##P^2 = \frac {a^3}{M_s}##
Homework Equations
N/A
The Attempt at a Solution
My attempt is to treat the given equation...
Hi, not a homework problem as such, but I am studying introductory quantum physics and having some trouble understanding how applying the rising or lowering operator for angular momentum implies:
L+/-|l,m> ∝ |l, m+/-1>
Basically, my question is the same as the first part (Q1) as described in...
Homework Statement
For part d), how to show that they are inversely proportional to each other ? The mark scheme states:
"Correct calculation to check inverse proportionality. √h x cosϑ = k. Sensible comments relating to calculations to within 20% or their own value and suggested...
Homework Statement
Homework Equations
Please see below.
3. The Attempt at a Solution
The idea is to find Bmin. We know: $$
\tau \frac{eB}{m}\gg 1 \\ \\
\rightarrow \frac{eB}{m}\gg \tau$$
Points:
[1] We are given $$\tau \propto \frac{1}{T^{2}}$$ .
[2] We are also given a conversion...
I wanted to ask how are the values of proportionality constants in physical relations determined. How do we come to know their exact values ? An explanation with an example please...
Homework Statement
A mass-spring system consisting of a mass of 2.9 kg attached to a spring is subject to a frictional force which is both proportional and opposite to the velocity. The mass is displaced from rest and oscillates back and forth with an ever decreasing amplitude. It is found that...
Hello.
Is anyone able to explain the 3 proportionality relationships present in Mersenne's Law, specifically in a conceptual sense? Mathematically they are easier to understand however it is difficult to understand them conceptually relating to strings. Any help would be appreciated.
:)
Homework Statement
A ball starts from rest and rolls down a hill with uniform acceleration, traveling 130m during the second 6.0s of its motion.
How far did it roll during the first 6.0s of motion?Homework Equations
I guess:
v=v(0)+at
v^2=v(0)^2+2ay
x=x(0)+v(0)t+0.5at^2The Attempt at a...
if x is direct, indirect or exponentially propotional to A and as well as B
can we write x=kAB ? if we write the equation seperately, we have x=k1A, x=k2B when combined, x2=(k1k2)1/2 (AB)2 then x=k3(AB)1/2
to see the real complicate example
EX.1 trypsinogen is converted to trypsin in...
Homework Statement
A person running in a race has to pick up a mass equal to her own mass. Assuming she can still do the same
amount of work, her speed will be changed by a factor of
a. 0.25
b. 0.50
c. 0.71
d. 1
e. 2
Homework Equations
E=1/2mv2
The Attempt at a Solution
Since m is...
Supposed you have a beam supported by 2 columns at the beam ends. At the middle of the beam, let's say there is a point load, the weight shared by the 2 columns is 1/2 each. How about if the point load is in the 3/4 portion of the beam, what is the corresponding share of each column of the...
Homework Statement
So, this isn't a homework problem as such just something that I'm after confusing myself about. Pressure is proportional to Temperature. So, a rise in pressure leads to an increase in temperature and vice versa, right? However, an increase in pressure leads to an increase in...
Homework Statement
For main sequence stars, the mass–luminosity relation can be approximated by L\proptoM^{3.5}
f) If luminosity and mass are both measured in solar units, what is the constant of
proportionality? {2}
I know that the luminosity value of the sun is 4x10^{26}W and
M =...
Hi All!
I've been doing some research in an attempt to uncover the proportionality between usable traction, which is defined as the the product of coefficient of static friction and the normal force, and the wheel slip. Given the nature of the the equation for usable traction, I expected that...
Homework Statement
Find the diameter of one atom of argon given that Dp = 2 where D is diffusion and p is pressure.
The Attempt at a Solution
molar mass of argon is 40g/mol
using that for one atom can find mass in kgs.
but that's its!
im not given V, T or p. can put V in terms...
Hi,
We know that if x=2, and y=4 for example, i.e that x is directly proportional to y.
What i am wondering about is when to say that x is proportional to lny? As in the case of Entropy in Statistical Physics where S proportional to lnW?
Homework Statement
F=kx
What does k represent?
Homework Equations
The Attempt at a Solution
k is the proportionality constant of restoring force over displacement. Or with respect to displacement?
Quote from Wikipedia:
I've been told by people that a graph with a straight line on it can be proportional but only if it passes through the origin. I fail to see why that's true. If a translation was applied and it was moved 1 unit to the right then, all of a sudden, x is not proportional to...
Homework Statement
OK so I'm doing a past exam paper as some revision:
The central galaxy in the Perseus cluster has an X-ray spectrum in wavelength units
which is well described by the power law
F_\lambda \propto \lambda^{-2} .
If the spectrum in frequency units is described...
Hello dear Physics Forums members,
My question is about the constant k, in Coulomb's law, which is:
1/4\pi ε0
Can anybody explain me where this constant comes from?
Homework Statement
Homework Equations
L = M^3.5
The Attempt at a Solution
Am I right in saying that this is the correct proportionality for luminosity and mass in a star?
If it is, i am confused. In an example I have it states that when mass is doubled the luminosity...
Homework Statement
Hello,
I have four different, but known, dimensionless values C1, C2, C3 and C4 (they are actually contrasts that can be displayed on a crt monitor).
I have measured the voltages (V1 and V2) required to produce C1 and C2 in isolation, but have had to measure V3 by combining...
A falling object with no initial velocity with mass m is influenced by a gravitational force g and the air resistance which is proportional to the object´s speed. By Newton´s laws this can be written as:
(1) mg-kv=ma or (2) mg-kv^2=ma (for large velocities).
I assume that k is a...
Homework Statement
Dear All,
I currently have a set of data which, when plotted on a scatter diagram, proves an inverse proportionality between two sets of data. (Please see attachment.)
I now need to linearize the graph as to estimate the half-life of the foam.
Homework Equations...
Hey guys, simple question really:
Given the equation v = (Gm/r)1/2
Is it wrong to say v is inversely proportional to r
Or do you have to say v is inverslely proportional to r1/2
First of all sorry if this is the wrong section!
For a physics assignment, I am given a graph of which I am to gather data from.
Graph 1:
In an experiment to investigate how the celcius temperature, T, affects the volume, V, of an enclosed sample of air at a constant pressure, a students...
Is that true ?
Let be \Sigma_{n=1}^{\infty} a_n a series in ℝ .Suppose that \Sigma_{n=1}^{\infty} a_n is absolutely convergent . Suppose that for each Q \in N , \Sigma_{n=1}^{\infty} \frac{a_n}{Q^n} is convergent and \Sigma_{n=1}^{\infty} \frac{a_n}{Q^n} = 0.Then a_n = 0 for all n \in N...
This is not homework. I'm reading a physics for laypeople book and I'm trying to wrap my head around something that other people obviously have little or no trouble understanding.
I understand what it means when someone says that a body's acceleration is directly proportional to the magnitude...
If a ∝ b and a ∝ c, why do you multiply b and c together to find the constant?
I also noticed something, but am not sure of the reason why. If you find the constants individually for each expression and combine them all, you get a the the power of the number of expressions
e.g.
a ∝ b...
If you have two statements, "a ∝ b" and "a ∝ c", you would get: "a = xb" and "a = yc" (where x and y are the constants of proportionality)
But what do you do so that it turns out to be "a = b × c"?
I've been searching for a DETAILED MATHEMATICAL explanation but have failed in finding one...
ok, so i understandthat if i travel near the speed of light for a while and come back on Earth than i would be younger than the rest...but what if i travel x2 c than does it relate to -ve time travel?
since length, mass, time are proportional to motion, how does it relate to traveling more than...
Homework Statement
Homework Equations
First problem:
Second problem:
The Attempt at a Solution
I assume it is acceptable to lump this section into the previous one, as I believe they go hand in hand in this case. My apologies if not.
I am definitely a lot more lost in the second...
Could anyone tell me how to exactly prove that the distance between two objects squared is inversely proportional to the attraction force between them?
Thanks.
Homework Statement
In a lab, we essentially used an apparatus similar to this:
In three experiments with several trials, we varied three things: centripetal force (the mass of the bottom), radius (of the circle by adjusting the alligator clip), and mass (rubber stopper). The trials were...