Finding Velocity and Pressure of Half-Sphere on Horizontal Plane

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SUMMARY

The discussion focuses on calculating the velocity and pressure exerted by a half-sphere on a horizontal plane after the break of a supporting wire. Participants suggest using Newton's laws rather than Lagrange's equations for this problem, emphasizing the need to analyze vector components and torque. The behavior of the half-sphere is compared to that of a mathematical pendulum for small angles, indicating a specific approach to the dynamics involved.

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  • Basic principles of pendulum motion
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Homework Statement


The half a sphere with a 'm' mass and 'r' radius is equilibrated on a plan absolutely polished horizontal with the side of the AB wire. So the surface of the half a sphere has with the horizontal plan an alpha angle. Find, after the break of the wire, the velocity of the O center and her maximal value too, also the maximal value of the pressure of the half-sphere over the horizontal. Find that for small angles it behaves like a mathematical pendulum.
Illustration:
http://img135.imageshack.us/img135/9526/fiz1rf6.th.jpg

Homework Equations





The Attempt at a Solution



I think that the lagrange's equations can be employed to solve it.
 
Last edited by a moderator:
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Hello.

I think that using Lagrange's methods won't help you. The best you can do is using Newton... use vectors!

Regards.
 
I would use Newton as well but I think it will take some work to draw the components and figure out which contributes to the torque in which way
 

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