7.0.0. MATHEMATICS ASPECT OF PHYSICS

7.0.0.  MATHEMATICS ASPECT OF PHYSICS:
The mathematics aspect of physics are the direct proportion or variation and the inverse proportion or variation. We are going to look into them one after the other.

DIRECT PROPORTION:
In a direct proportion, one quantity increases as the other quantity increases or one quantity decreases as the other quantity decreases. The increase or decrease may be by the same amount or size.

Explanation:
For example if we say the quantity A is directly proportional to quantity B, it means that quantity A increases as quantity B increases or quantity A decreases as quantity B decreases.

MATHEMATICAL FORMULA OF DIRECT PROPORTION
Example:
Given that A is directly proportional to B, what is the relation between A and B?

Solution:
          A & B ,  A = K x B ,  k = A/B where k is the constant of proportionality.
If there is any change in A or B , there will be a corresponding change in B or A.
Therefore we will have ,
 A1 / B1 = A2 / B2

Worked Example:
The amount of heat generated by a body is directly proportional to the mass of the body. If 10kg mass produced 25J of heat, what is the quantity of heat that 15kg will produce?

Solution:
From the question, it is a direct proportion.
Then, amount of heat is directly proportional to mass of body
That is,  H is directly proportional to M
Mathematically,
H = K x M .     k = H ÷ M
M1 = 10kg,  H1 = 25J,   M2 = 15kg while H2 = ?
Since