Optimizing Pendulum Release Height for Maximum Tension and Circular Motion

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Homework Help Overview

The discussion revolves around optimizing the release height of a pendulum bob to ensure it maintains tension in the string while completing a circular motion. The problem involves concepts from mechanics, specifically energy conservation and centripetal force.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between potential energy and kinetic energy using the equation ½mv² = mgh. Questions arise regarding the necessary height for release and the implications of centripetal force on the system.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the relationships between variables such as velocity, mass, and forces acting on the pendulum bob. Some guidance has been offered regarding the forces at play, but there is no clear consensus on the next steps or the specific height required for optimal performance.

Contextual Notes

Participants note the lack of certain information, such as the mass of the bob, which complicates the calculations. There is also a recognition that the height 'h' is not predetermined, which adds to the complexity of the problem.

reganw
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pendulum.jpg

The pendulum bob in the above figure must circle the rod interrupting its swing, and the string must remain taut at the top of the swing. How far up must the bob be raised before releasing it to accomplish these goals?

I don't know where to begin with this because I don't quite understand what I'm supposed to find.. I've tried finding Ep and Ek using 1/2mv2=mgh but i don't seem to have enough info.

Thank you in advance for any suggestions.
 
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Well from ½ mv2 = mgh, what would v2 be equal to?

Since the distance of the rod to the bottom of the swing is 10 cm, what is the centripetal force required? (in term of 'm')

At the top of the swing what are the forces acting and in what directions are they acting? (The resultant of these two will be the same as the centripetal force required)
 
rock.freak667 said:
Well from ½ mv2 = mgh, what would v2 be equal to?

Since the distance of the rod to the bottom of the swing is 10 cm, what is the centripetal force required? (in term of 'm')

At the top of the swing what are the forces acting and in what directions are they acting? (The resultant of these two will be the same as the centripetal force required)


the velocity is equal to 1.4m/s and the force acting upon the bob is gravity... but don't i need to know the mass of the bob in order to figure out the force of gravity? still not sure where to go with it..
 
reganw said:
the velocity is equal to 1.4m/s and the force acting upon the bob is gravity... but don't i need to know the mass of the bob in order to figure out the force of gravity? still not sure where to go with it..

At the top you will have both tension and gravity acting the same direction.

So T + mg = mv2/r or T = mv2/r - mg.

For the string to be taut T≥ 0.

Also in v2 = 2gh, 'h' is not necessarily 10 cm since that would mean you've already found 'h' when you're in fact trying to find 'h'.
 
I'm really not understanding this at all, thanks though! I guess i'll just leave it.
 

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