- #1
stunner5000pt
- 1,461
- 2
Ok have a look at the diagram below
A bob of mass m is on the inside of a funnel. The funnel is rotating with an angular velocity omega. The walls of the funnel has a friction coefficient of mu
The question is Show that there is an angle theta = theta max for which the bob cannot slide upwards if theta > theta max no matter how large the omega is. Determine theta max
So far here's what i have
force equation in the X direction (masses cancel out)
[tex] \omega^2 r cos \theta = \mu g cos \theta + \mu \omega^2 r sin \theta + g sin \theta [/tex]
teh answer is [tex] \frac{1}{\mu} = tan \theta _{max} [/tex]
seems to be derived by taking some limit as omega approaches a large number then the g sin theta nad the g cos theta part becomes negligbile. But i want to understand why this is being done. Any help would be greatly appreciated!
A bob of mass m is on the inside of a funnel. The funnel is rotating with an angular velocity omega. The walls of the funnel has a friction coefficient of mu
The question is Show that there is an angle theta = theta max for which the bob cannot slide upwards if theta > theta max no matter how large the omega is. Determine theta max
So far here's what i have
force equation in the X direction (masses cancel out)
[tex] \omega^2 r cos \theta = \mu g cos \theta + \mu \omega^2 r sin \theta + g sin \theta [/tex]
teh answer is [tex] \frac{1}{\mu} = tan \theta _{max} [/tex]
seems to be derived by taking some limit as omega approaches a large number then the g sin theta nad the g cos theta part becomes negligbile. But i want to understand why this is being done. Any help would be greatly appreciated!