Chapter 12.8, Problem 11OE

To determine

To Describe: Translate the statement into formula:

The centrifugal force, $F$ , of an object moving in a circular path is directly proportional to the square of its velocity , $V$ , and inversely proportional to the diameter, $d$ of its path.

Answer to Problem 11OE

The formula of the statement is $F=K\frac{V^2}{d}$ .

Explanation of Solution

Given information:

Translate statement to formula:

The centrifugal force, $F$ , of an object moving in a circular path is directly proportional to the square of its velocity , $V$ , and inversely proportional to the diameter, $d$ of its path.

Use $K$ as constant.

Consider the statement,

The centrifugal force, $F$ , of an object moving in a circular path is directly proportional to the square of its velocity , $V$ , and inversely proportional to the diameter, $d$ of its path.

Here if a variable varies directly as he product of two or more other variables the resulting relationship is a joint variation.

As , $F$ ,varies directly to the square of $V$ and inversely to the diameter $d$ .

  $F$ is directly as the square of $V$ .

  $F\alpha V^2$ .

Then $F$ is inversely as its diameter $d$ .

  $F\alpha \frac{1}{d}$

From both of the equations:

  $\begin{array}{c}F\alpha V^2\\ F\alpha \frac{1}{d}\\ F\alpha \frac{V^2}{d}\end{array}$

Same as above,

Here,

  $F\alpha \frac{V^2}{d}$

For replacing $\alpha$ apply constant $K$ .

  $\begin{array}{l}F\alpha \frac{V^2}{d}\\ F=K\frac{V^2}{d}\end{array}$

Thus, the formula is: $F=K\frac{V^2}{d}$ .