Chapter 1, Problem 57A

(a)

To determine

The relation between F and R in the equation $F=\frac{m{v}^2}{R}$

Explanation of Solution

Introduction:

A direct relation is one in which one variable increases with the increase in the other and vice versa.

An inverse relation is one in which one variable decreases with the increase in the other and vice versa.

If R increases,F decreases so they are inversely related.

  $F\propto \frac{1}{R}$

Conclusion:

F is inversely proportional to R.

(b)

To determine

The relation between F and m in the equation $F=\frac{m{v}^2}{R}$

Explanation of Solution

Introduction:

A direct relation is one in which one variable increases with the increase in the other and vice versa.

An inverse relation is one in which one variable decreases with the increase in the other and vice versa.

Ifm increases,F increases so relation is directly proportional.

  $F\propto m$

Conclusion:

Fandm are directly related.

(c)

To determine

The relation between F and v in the equation $F=\frac{m{v}^2}{R}$ .

Explanation of Solution

Introduction:

A direct relation is one in which one variable increases with the increase in the other and vice versa.

An inverse relation is one in which one variable decreases with the increase in the other and vice versa.

If v increases, F increases. So, they are directly related.

  $F\propto v$

Conclusion:

Fis directly proportional to v.