MHB Mechanics-Conical pendulum, circular motion

[dragonoid122]

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

 

[I like Serena]

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! :)

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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.