- #1

- 14

- 0

## Homework Statement

A uniform cylinder of radius R, length L and density [tex]\delta[/tex] is rolling without slipping along a horizontal surface with constant centre of mass speed u at A. It then meets a step of height b. We wish to find the conditions under which the cylinder is able to continue past the step and roll along the surface B.

Assuming no energy is lost due to friction or drag, the change in the total kinetic energy before and after must be equal and opposite to the change in gravitational potential energy. Find a requirement on the initial speed u such that the cylinder passes B with positive kinetic energy.

## Homework Equations

As the disc is rolling without slipping it is possible to use [tex]v = \omegaR[/tex].

The total kinetic energy is given by

[tex]\frac{1}{2}I\omega^2 + \frac{1}{2}mx^2 [/tex]

where

[tex]I = \frac{1}{2}MR^2 [/tex]

and gravitational potential is given by [tex]mgh[/tex].

## The Attempt at a Solution

You are told in the question that [tex] \Delta K = -\Delta P[/tex]

The change in kinetic energy will be negative and thus the change in potential will be positive. I want the final kinetic energy to be positive thus

[tex]K > |\Delta K|[/tex].

That's about as far as I have gotten. Any tips on how to get started will be greatly appreciated.

Also, I'm not sure if [tex]\alpha[/tex] is significant or not (the [tex]\alpha[/tex] on the diagram, not the angular acceleration).

NB: Sorry about my equations, I'm still trying to get used to using LaTeX.

Last edited: