## Related questions with answers

A body of mass $m$ moves in an elliptical path with a constant angular speed $\omega$ (see the figure). It can be shown that the force acting on the body is always directed toward the origin and has magnitude given by

$F=m \omega^2 \sqrt{a^2 \cos ^2 \omega t+b^2 \sin ^2 \omega t} \qquad t \geq 0$

where $a$ and $b$ are constants with $a>b$. Find the points on the path where the force is greatest and where it is smallest. Does your result agree with your intuition?

Solution

VerifiedWe begin by taking $F'$:

$\begin{align*} F' &= \left(\frac{m\omega^2}{2}\right)\frac{(2a^2\cos{\omega t}(-\sin{\omega t})) + 2b^2\sin{\omega t}\cos{\omega t})}{\sqrt{a^2\cos^2{\omega t} + b^2\sin{\omega t}}}\\ &= \left(\frac{m\omega^2}{2}\right)\frac{(\sin{2\omega t})(b^2 - a^2)}{\sqrt{a^2\cos^2{\omega t} + b^2\sin{\omega t}}} \end{align*}$

## Create an account to view solutions

## Create an account to view solutions

## More related questions

1/4

1/7