Conservation of energy of falling chimney

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Homework Help Overview

The problem involves a tall, cylindrical chimney that falls over when its base is ruptured. It requires the application of conservation of energy principles to calculate the angular speed as a function of the angle the chimney makes with the vertical.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conversion of gravitational potential energy into rotational kinetic energy and question the relevant formulas for these energies. There is an emphasis on setting the gravitational potential energy equal to the rotational kinetic energy to isolate the angular speed term.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem and offering guidance on how to relate the energies involved. There is no explicit consensus yet, but some productive directions have been suggested regarding the energy conservation approach.

Contextual Notes

There is a mention of a previous related question, indicating that the original poster may be struggling with similar concepts. The discussion also highlights a potential lack of familiarity with the formulas for rotational kinetic energy and moments of inertia.

James01
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Homework Statement



A tall, cylindrical chimney falls over when its base is ruptured. Assuming that the chimney remains intact before it hits the ground, using conservation of energy, calculate its angular speed [tex]\dot \theta{}[/tex] as a function of [tex]\theta[/tex] , the angle which the chimney makes with the vertical.


Homework Equations



Etotal = Ep+Ek

I posted a question yesterday similar to this one. I really do not understand how to tackle this type of question. Any help would be appreciated.
 
Last edited:
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The gravitational potential energy of the chimney is converted into rotational kinetic energy... have you learned about rotational kinetic energy and moments of inertia?
 
I don't remember the formula for the rotational KE... but I gather the question is asking you to set the gravitational PE equal to rotational KE... then just isolate the angular speed term...
 
SpitfireAce said:
I don't remember the formula for the rotational KE... but I gather the question is asking you to set the gravitational PE equal to rotational KE... then just isolate the angular speed term...

Yes, the difference in gravitational potential energy is the rotational kinetic energy.

Calculate the total energy of the system at the beginning [tex]E_i[/tex] which is all gravitational potential energy initally... then at any angle you know by conservation of energy that

[tex]E_i = E_r + E_g[/tex]. (the quantity on the right is rotational kinetic energy plus gravitational potential energy) You can use that to isolate the angular speed...
 
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