Circular Motion: Swinging a rock on a string in a vertical circle....

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SUMMARY

The discussion focuses on the conditions required for a rock swung on a string to maintain a taut string while traveling in a vertical circular path. Specifically, it addresses the mathematical condition for centripetal acceleration at the highest point of the swing. The relevant equation discussed is the centripetal force equation, F[c] = m(v²) / r, which must be analyzed in conjunction with Newton's Second Law. A free body diagram is recommended for a clearer understanding of the forces acting on the rock.

PREREQUISITES
  • Understanding of centripetal force and acceleration
  • Familiarity with Newton's Second Law of Motion
  • Ability to draw and interpret free body diagrams
  • Basic knowledge of circular motion dynamics
NEXT STEPS
  • Study the derivation of the centripetal force equation F[c] = m(v²) / r
  • Learn how to construct and analyze free body diagrams in circular motion scenarios
  • Explore the implications of gravitational force on centripetal acceleration
  • Investigate the effects of varying string lengths on the motion of the rock
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of circular motion and dynamics in a vertical plane.

Student4Life
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Homework Statement

:[/B]
One swings a rock at the end of a string. We wish for the string to remain taut and for the rock to travel in a circulat path, in a vertical plane. What mathematical condition must the centripetal acceleration of the rock satisfy for the string to remain taut when the rock is at its highest point?

Homework Equations

:[/B]
[F[/c] = m[v][/2] / r ?

The Attempt at a Solution


So far I come up with this equation to define what is going on but I am not sure [F[/c] = m[v][/2] / r ?
 
Last edited by a moderator:
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Student4Life said:

Homework Statement

:[/B]
One swings a rock at the end of a string. We wish for the string to remain taut and for the rock to travel in a circulat path, in a vertical plane. What mathematical condition must the centripetal acceleration of the rock satisfy for the string to remain taut when the rock is at its highest point?

Homework Equations

:[/B]
[F[/c] = m[v][/2] / r ?

The Attempt at a Solution


So far I come up with this equation to define what is going on but I am not sure [F[/c] = m[v][/2] / r ?
You need to do better than that. Draw a free body diagram for the rock when it is at the top of the trajectory, interpret it in terms of Newton's 2nd law, then write down the equation.
 
Last edited by a moderator:

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