College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 3 - Section 3.6 - Variation - 3.6 Exercises - Page 365: 6


$f=\frac{mv^2}{r}$ means that f varies directly with m and the square of v and varies inversely with r.

Work Step by Step

The general equation for direct variation is $y=kx$, where k is the constant of the variation. The general equation for inverse variation is $y=\frac{k}{x}$, where k is the constant of the variation. As $m$ and $v^2$ are in the numerator, there will be a direct variation between $f$ and $m$; and $f$ and $v^2$ as $r$ is in the denominator, there will be an inverse variation between $f$ and $r$ Thus, $f=\frac{mv^2}{r}$ means that $f$ varies directly with $m$ and the square of $v$ and varies inversely with $r$. As none of $m$ $v^2$ or $r$ is constant, there isn't any constant in these variations. Therefore we can say that the centripetal force varies directly with the mass of the object and the square of the radius and varies inversely with its velocity.
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