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

In summary, the question is asking for the mathematical condition that must be met for the string to remain taut when a rock is swung in a circular path in a vertical plane. The equation that may define this condition is [F[/c] = m[v][/2] / r, but to fully answer the question, a free body diagram is needed, as well as an interpretation of Newton's 2nd law, and an equation based on that interpretation.
  • #1
Student4Life
1
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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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  • #2
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:

1. What factors affect the speed of a swinging rock on a string in a vertical circle?

The speed of a swinging rock on a string in a vertical circle is affected by the length of the string, the mass of the rock, and the gravitational force acting on the rock.

2. How does the angle of the string affect the motion of the rock?

The angle of the string affects the motion of the rock by changing the direction of the gravitational force acting on the rock. As the string is pulled closer to the vertical position, the gravitational force becomes more horizontal, causing the rock to move faster. As the string is pulled further from the vertical position, the gravitational force becomes more vertical, causing the rock to move slower.

3. What is the relationship between the speed and the tension of the string?

The speed of the swinging rock is directly proportional to the tension of the string. As the speed of the rock increases, the tension in the string also increases. This is because the tension in the string is what provides the centripetal force necessary for circular motion.

4. How does the mass of the rock affect the motion in a vertical circle?

The mass of the rock affects the motion in a vertical circle by changing the amount of force and energy required for the rock to complete the circular motion. A heavier rock will require more force to move at the same speed as a lighter rock, but it will also have more inertia and will resist changes in its motion more than a lighter rock.

5. What is the difference between circular motion and simple harmonic motion?

Circular motion involves a constant radius and changing velocity, while simple harmonic motion involves a constant velocity and changing radius. In circular motion, the force acting on the object is always directed towards the center of the circle, while in simple harmonic motion, the force is directly proportional to the displacement from the equilibrium position.

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