How Do You Calculate the Frequency for a Mass to Orbit on a Frictionless Table?

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SUMMARY

The problem involves calculating the frequency required for a 1 kg mass on a frictionless table to maintain equilibrium with a 4 kg hanging mass, given a radius of 75 m. The relevant equations include centripetal acceleration (ac = v2/R), the relationship between velocity and period (v = 2πR/T), and the definition of frequency (T = 1/f). The solution requires applying Newton's second law to both masses and recognizing that the tension in the cord remains constant.

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  • Understanding of Newton's second law
  • Knowledge of centripetal acceleration
  • Familiarity with circular motion equations
  • Basic grasp of frequency and period relationships
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  • Learn how to apply Newton's second law in circular motion scenarios
  • Explore the relationship between tension and mass in pulley systems
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Homework Statement


hi guys i need help solvign the following problem.

A mass 1kg on a frictionless table is attached to a hanging mass 4kg by a cord through a hole in the table. Find the frequency with which 1KG mass must move for 4kg to stay at rest, if the radius of the circle is 75m.



http://img32.imageshack.us/img32/9601/phyp.jpg

Homework Equations



m(v2/R

v = 2piR/T

T = 1/f

ac = 4pi * R/ T2

The Attempt at a Solution




Well i don't really know where to start as there is no angle given so i found the circumference first. which is 4.71 or 471 cm.

I think that is useless because i don't know what to do with it. I know i need to find ac first before i can find the frequency right?

So can someone give me a hit on the first step or where to start?

thanks.
 
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This is more of a force problem than a harmonic motion problem. Try writing out Newton's second law for both the 1 kg mass and the 4 kg mass. Remember that for an object moving in a circle at speed v, acceleration=v^2/r. Also note that the tension in any massless rope is constant throughout the rope.
 

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