Optimizing Pendulum Release Height for Maximum Tension and Circular Motion

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SUMMARY

The discussion focuses on optimizing the release height of a pendulum bob to ensure maximum tension and maintain circular motion. Key equations include the conservation of energy represented by ½ mv² = mgh and the centripetal force equation T + mg = mv²/r. The velocity at the top of the swing is determined to be 1.4 m/s, and it is emphasized that the mass of the bob is necessary to calculate the gravitational force accurately. The tension in the string must be non-negative (T ≥ 0) to keep it taut during the swing.

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  • Understanding of basic physics concepts such as energy conservation and centripetal force.
  • Familiarity with the equations of motion, specifically ½ mv² = mgh.
  • Knowledge of forces acting on objects in circular motion.
  • Ability to manipulate algebraic equations to solve for unknown variables.
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  • Study the principles of pendulum motion and energy conservation in physics.
  • Learn about centripetal force calculations and their applications in circular motion.
  • Explore the relationship between height and velocity in pendulum dynamics.
  • Investigate the effects of mass on gravitational force and tension in pendulum systems.
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reganw
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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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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