Mechanics-Conical pendulum, circular motion

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SUMMARY

The discussion focuses on determining the range of angular velocities for a particle of 100 grams attached to two strings of lengths 30 cm and 50 cm, with point A positioned 30 cm vertically below point B. The established range for angular velocity is between 5 and 9.14 radians per second, ensuring both strings remain taut while the particle describes horizontal circles. The analysis incorporates the equilibrium of forces, specifically the vertical component of tension balancing gravitational force and the horizontal component providing the necessary centripetal force.

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  • Familiarity with centripetal force calculations
  • Basic grasp of equilibrium conditions in mechanics
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dragonoid122
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A particle of 100 grams is attached by two strings of lengths 30cm and 50cm respectively to points A and B, where A is 30cm vertically below B. Find the range of angular velocities for which the particle can describe horizontal circles with both strings taut. Take g as 10m/s^2

Answer
Show diagram if possible
5<angular velocity<9.14
 
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dragonoid122 said:
A particle of 100 grams is attached by two strings of lengths 30cm and 50cm respectively to points A and B, where A is 30cm vertically below B. Find the range of angular velocities for which the particle can describe horizontal circles with both strings taut. Take g as 10m/s^2

Answer
Show diagram if possible
5<angular velocity<9.14

Welcome to MHB, dragonoid! :)

What is your question?
Can you show some of your thoughts?

Note that the range is limited by the fact by the boundary condition where either there is just no tension on the upper string, or there is just no tension on the lower string.

We will need:
  1. equilibrium between the vertical component of the tensional force and the force of gravity,
  2. the horizontal component of the tensional force equal to the required centripetal force.
 

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