Don't Forget that Energy

Classical Mechanics Level 3

A disk of mass $m$ and radius $r$ is pushed up on an inclined plane of angle $\theta$ with initial speed $v$ . If $g=10[\frac{m}{s}]$ and the coefficient of friction is such that the disk can roll without slipping, the maximum height reached by the disk can be expressed as $\frac{a}{b}v^2$ . Find $a+b$ .

The answer is 43.

1 solution

Hjalmar Orellana Soto
Jul 3, 2016

At first we have kinetic energy and rotational kinetic energy of a disc, so we have: $E_{0}=\frac{mv^2}{2}+\frac{I\omega^2}{2}=\frac{mv^2}{2}+\frac{mr^2v^2}{2\cdot 2r^2}=\frac{3}{4}mv^2$ At maximum height we have: $E_{f}=mgh$ As energy conservates: $E_{f}=E_{0}$ $mgh=\frac{3}{4}mv^2$ $h=\frac{3}{4g}v^2=\frac{3}{40}v^2$

Don't Forget that Energy

The answer is 43.

1 solution

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