Deriving the Angle of Release for a Simple Pendulum: Help Needed!

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SUMMARY

The discussion focuses on deriving the angle of release for a simple pendulum using known variables such as mass and velocity at the lowest point. The user applies the principle of conservation of energy, represented by the equation mgh = (mv^2)/2, to find the height. However, the challenge lies in determining the angle without knowing the length of the string, which is essential for calculating the angle of release using trigonometric relationships.

PREREQUISITES
  • Understanding of basic physics concepts, particularly conservation of energy.
  • Familiarity with trigonometry, specifically the relationships in right triangles.
  • Knowledge of pendulum mechanics and motion.
  • Ability to manipulate algebraic equations to isolate variables.
NEXT STEPS
  • Research how to derive the angle of release using the length of the pendulum string.
  • Learn about the geometric relationships in pendulum motion, particularly using sine and cosine functions.
  • Explore the concept of potential and kinetic energy in oscillatory systems.
  • Study the effects of varying string lengths on the dynamics of a simple pendulum.
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Students of physics, educators teaching mechanics, and anyone interested in the mathematical modeling of pendulum motion.

thslacker
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I have looked through the forum here and several other forces. My task is to derive a formula to determine the angle of release of a simple pendulum. I know the mass, velocity at lowest point and I can therefore determine the height or distance it fell mgh=(mv^2)/2. I am not able to locate the geometric/trig brain cells that will let me use this information to determine the angle athough I do know the adjacent side of the similar but smaller triangle. I do not know the length of the string. Could someone point me in the right direction please?
 
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If you don't know the length of the string, I don't see how you can find the angle of release.
 
uh-oh, that does not sound promising. Thanks anyway.
 

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