Is the force directly proportional to the direction

General information and resources

theory

In physics, the relationship between two quantities can often be described by a law. A very simple context that plays an important role in early physics lessons is that direct proportionality between two sizes.

Distinguishing features of direct proportionality

a) Determining the proportionality using a measurement table (series of measurements)

Example:

1. Size (x): mass of a product in g
2. Size (y): Price of a product in €
 

Determination:
When to double, triple, quadruple. . . .n times the 1st size double, triple, quadruple. . . . belongs to the 2nd size,
so are the two quantities to each other directly proportional.

The easiest way to recognize this connection is to form the quotient of values ​​that belong together. If this quotient is constant, the two quantities are directly proportional to one another.

They say:

Directly proportional quantities are equal in quotients

The above example results in:

1. Size (x): mass of a product in g
2. Size (y): Price of a product in €
Quotient y / x: Price per mass in € / g

Notation:
If two quantities x and y are directly proportional to each other, we write:

y ~ x (read: y proportional to x)

Because of the equality of quotients, you can also write
\ [\ frac {y} {x} = C \ Leftrightarrow y = C \ cdot x \]

C is referred to as Constant of proportionality.

So if y ~ x (1) holds, then by introducing the proportionality constant C one can immediately obtain the equation y = C × x (2). (2) has the advantage over (1) that an equation is present. You (hopefully) have mastered the use of equations.