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

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For a rock swung in a vertical circle at the end of a string, the centripetal acceleration must meet specific conditions to keep the string taut at the highest point. The relevant equation involves centripetal force, expressed as F_c = m(v^2)/r, where m is mass, v is velocity, and r is the radius of the circle. A free body diagram should be drawn to analyze forces acting on the rock at the top of its path, applying Newton's second law for clarity. The tension in the string and gravitational force must be considered to ensure the string remains taut. Understanding these dynamics is crucial for solving the problem effectively.
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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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