# 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.

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