why do we need a constant while removing proportional sign and putting equal's sign in scientific equation
Answers
Answered by
11
We do it because that is what it means.
I imagine you came across it in a context such as this:
Force exerted by a spring is proportional to its elongation. If FF is the force and xx is the elongation,
Fα−xFα−x
and the proportionality constant is kksuch that
F=−kxF=−kx
When we say to quantities are proportional to each other, what we mean is that the variables maintain a constant ratio to each other.
As an example, we can say that the circumference of a circle is proportional to its radius, since the circumference is 2π2π times its radius.
But the area of a square is NOT proportional to its side, but rather to the square of the side.
As=sAs=s
The ratio of area and side depends on the side and large squares have larger ratios.
However, it is always true that
As2=1As2=1
The Wikipedia Page does a decent job of explaining it. You should probably go through it too.
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OTHER ANSWERS

Prabha Mohan M Baliga, Aircraft Performance Instructor at Go Airlines (2015-present)
Answered Sep 10 2015
Mathematically, the word proportional means just that. If I were to say that 'A' is directly proportional to 'B', it means 'A' increases when 'B' increases and 'A' reduces when 'B' reduces. That is, in such a way that the value of A/B is a constant.
If 'A' is inversely proportional to 'B', it means 'A' increases when 'B' reduces and 'A' reduces when 'B' increases. That means, the product A*B is a constant.
1.2k Views · 4 Upvotes

Kanishk P.S
Answered May 18
First we find a relationship between quantities but we were not fully satisfied as proportionality doesn't gives us values that we can check directly so we developed a system to get a value.
For example :
Force on a body is proportional to acceleration
F αα a
But it also depends on mass of a body. As mass doesn't change for a body of fixed mass, it is a constant.
Next we developed a system. Let's say 1 Newton is the force on a body of mass 1kg accelerated at 1m/s².
Then, we find the ‘equal to' relationship. By finding force for different sets of values of acceleration we calculate the constant called mass here.

Now with this relationship we can get exact values
F = m*a (y=m*x + c, straight line graph)
F = 0.201*a
So what is the force when acceleration is 2m/s²?
F = 0.201*2 (1kg*m/s² = 1newton)
F = 0.402 N
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Sriram Krishna, Master of Science majoring in Physics
Answered May 16
We don’t do that always. We only do that when we are confident that we know all the factors that might affect the final quantity. We think we have already incorporated all such factors into our equations or at least controlled for them.
Suppose you find a new force, and this force happens to be proportional to the charge of the object. Then you can write:
F∝QF∝Q
But if you don’t know how it varies with position, orientation, velocity etc. you wouldn’t just go ahead and write this as:
F=kQF=kQ
That would be done only if all affecting quantities are already in the equation or can be controlled.
209 Views · 4 Upvotes · Answer requested byTanishq Rajput

Prajakta Bedekar
Correct me if I'm wrong, but as we can never make sure that we have indeed accounted for all poss...

Ebaad Chowdhry
Answered Sep 13 2015
It's very simple as u mentioned in ur question that its a PROPORTIONAL SIGN this means that it indicates a relation not a certainity for example in the statement "1+1=2" the "=" sign is a assignment operator that means that the inherent values of the quantities written on both sides won't change their value based on circumstances. That means that if 1 represents single unit today won't represent double units tommorrow. And see this statement "Gravitational force is directly proportional to the masses of the bodies" the proportional sign represented by the Greek letter alpha represents dependency which is that if a RHS of a equation changes this leads to change in the LHS also since it's a dependency the calculator or any other analytical software requires a constant to replace Alpha in order to get u a correct answer rather than to retrieve another dependency
I imagine you came across it in a context such as this:
Force exerted by a spring is proportional to its elongation. If FF is the force and xx is the elongation,
Fα−xFα−x
and the proportionality constant is kksuch that
F=−kxF=−kx
When we say to quantities are proportional to each other, what we mean is that the variables maintain a constant ratio to each other.
As an example, we can say that the circumference of a circle is proportional to its radius, since the circumference is 2π2π times its radius.
But the area of a square is NOT proportional to its side, but rather to the square of the side.
As=sAs=s
The ratio of area and side depends on the side and large squares have larger ratios.
However, it is always true that
As2=1As2=1
The Wikipedia Page does a decent job of explaining it. You should probably go through it too.
646 Views · Answer requested by Tanishq Rajput
By
Quora for Business
Have an educational or career focused company?
Quora Ads can promote your business alongside career or school advice.
Learn more
MORE ANSWERS BELOW. RELATED QUESTIONS
Why do we exactly put a constant after removing sign of proportionality, while deriving scientific equations and formula's?
2,621 Views
Why is k used as constant of proportionality?
2,459 Views
What is proportionality constant?
919 Views
In chemistry, what is the proportionality constant? How is it used?
1,194 Views
Why is the constant of proportionality in the equation "F=ma" one?
7,657 Views
OTHER ANSWERS

Prabha Mohan M Baliga, Aircraft Performance Instructor at Go Airlines (2015-present)
Answered Sep 10 2015
Mathematically, the word proportional means just that. If I were to say that 'A' is directly proportional to 'B', it means 'A' increases when 'B' increases and 'A' reduces when 'B' reduces. That is, in such a way that the value of A/B is a constant.
If 'A' is inversely proportional to 'B', it means 'A' increases when 'B' reduces and 'A' reduces when 'B' increases. That means, the product A*B is a constant.
1.2k Views · 4 Upvotes

Kanishk P.S
Answered May 18
First we find a relationship between quantities but we were not fully satisfied as proportionality doesn't gives us values that we can check directly so we developed a system to get a value.
For example :
Force on a body is proportional to acceleration
F αα a
But it also depends on mass of a body. As mass doesn't change for a body of fixed mass, it is a constant.
Next we developed a system. Let's say 1 Newton is the force on a body of mass 1kg accelerated at 1m/s².
Then, we find the ‘equal to' relationship. By finding force for different sets of values of acceleration we calculate the constant called mass here.

Now with this relationship we can get exact values
F = m*a (y=m*x + c, straight line graph)
F = 0.201*a
So what is the force when acceleration is 2m/s²?
F = 0.201*2 (1kg*m/s² = 1newton)
F = 0.402 N
259 Views · 1 Upvote · Answer requested byTanishq Rajput
Promoted by
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Sriram Krishna, Master of Science majoring in Physics
Answered May 16
We don’t do that always. We only do that when we are confident that we know all the factors that might affect the final quantity. We think we have already incorporated all such factors into our equations or at least controlled for them.
Suppose you find a new force, and this force happens to be proportional to the charge of the object. Then you can write:
F∝QF∝Q
But if you don’t know how it varies with position, orientation, velocity etc. you wouldn’t just go ahead and write this as:
F=kQF=kQ
That would be done only if all affecting quantities are already in the equation or can be controlled.
209 Views · 4 Upvotes · Answer requested byTanishq Rajput

Prajakta Bedekar
Correct me if I'm wrong, but as we can never make sure that we have indeed accounted for all poss...

Ebaad Chowdhry
Answered Sep 13 2015
It's very simple as u mentioned in ur question that its a PROPORTIONAL SIGN this means that it indicates a relation not a certainity for example in the statement "1+1=2" the "=" sign is a assignment operator that means that the inherent values of the quantities written on both sides won't change their value based on circumstances. That means that if 1 represents single unit today won't represent double units tommorrow. And see this statement "Gravitational force is directly proportional to the masses of the bodies" the proportional sign represented by the Greek letter alpha represents dependency which is that if a RHS of a equation changes this leads to change in the LHS also since it's a dependency the calculator or any other analytical software requires a constant to replace Alpha in order to get u a correct answer rather than to retrieve another dependency
Answered by
1
Answer:
We say Velocity = Distance/Time. It could be written as
Velocity varies as the Distance. [Sorry, i cannot include the sign of proportionality, but i hope you understand what i mean!]
So when we change the relation into an equation, we do not know, initially, what all factors affect the relation between Velocity and Distance. So we assume some constant to make the expression as an equation and find out what are the factors involved.
So we write the expression as an equation, as V = xD.
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