Pendulums with Mechanical Energy (conical pendulum?)

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SUMMARY

The discussion focuses on determining the height from which a pendulum bob must be released to ensure it can circle a rod while maintaining a taut string. Key equations include the conversion of gravitational potential energy (mgh) to kinetic energy (1/2mv^2), establishing the relationship mgh = 1/2mv^2. The problem specifically involves a conical pendulum scenario, where the bob must achieve a circular motion with a radius of 10 cm around the rod. The solution requires calculating the necessary height to achieve this motion.

PREREQUISITES
  • Understanding of gravitational potential energy (mgh)
  • Knowledge of kinetic energy (1/2mv^2)
  • Familiarity with the concept of conical pendulums
  • Basic principles of circular motion
NEXT STEPS
  • Study the dynamics of conical pendulums in detail
  • Learn about energy conservation in mechanical systems
  • Explore the mathematical derivation of pendulum motion equations
  • Investigate the effects of varying radius on pendulum height requirements
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators seeking to explain pendulum dynamics and energy transformations.

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Homework Statement



The pendulum bob in Figure 6.11 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?

Screen%20Shot%202011-07-22%20at%207.41.21%20PM.png


Homework Equations



Potential Energy = mgh
Kinetic Energy = 1/2mv^2
mgh = 1/2mv^2

The Attempt at a Solution



I'm still unclear with what the question is asking for or how I'm suppose to solve it; though I'm guessing it deals with the conversion of kinetic energy into gravitational potential energy and maximum height. How the rod play into the question, or what the distance from the rod to the pendulum bob means, I've no idea. This sounds awfully similar to a conical pendulum, which a quick wikipedia search showed as pretty complicated.
So, how do?
 
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When the string hits the rod, it the bob will start circling the rod in a 10 cm radius circle. It won't reach the point 10 cm above the rod unless you release it from high enough. How high is 'high enough'?
 
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