Pendulum find length when it rotates

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Homework Help Overview

The problem involves a pendulum consisting of a string and a sphere, which swings in a vertical plane and is released from a 70-degree angle from vertical. The pendulum interacts with a peg located below the suspension point, and the task is to determine the minimum distance from the peg to the suspension point that allows the sphere to complete a full circular motion around the peg.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss using conservation of energy to analyze the motion of the pendulum and question how to relate the initial conditions to the final motion around the peg. There is also a focus on the implications of the string's length and whether it changes during the motion.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have suggested using energy conservation principles, while others are questioning the assumptions about the string's length and its implications for the setup.

Contextual Notes

There is uncertainty regarding the constancy of the string's length and how it affects the calculations. The original poster has indicated a desire for clarification on these points, and the problem's visual representation is noted as potentially helpful for understanding.

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Homework Statement


A pendulum made of a string and a sphere is able to swing in a vertical plane. The pendulum is released from a position of 70 degree from vertical. The string hits a peg located a distance d below the point of suspension and rotates about the peg. Find the smallest value of d (highest peg position) in order for the sphere to swing in a full circle centered on the peg.

How do i start this?
I understand this is hard without a pic sorry guys.
 
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I would suggest using conservation of energy. If the peg is located at the smallest value of d, the sphere should have just barely enough energy to make it up to the top of its full circle.
 
yeah I thought about that but I could use it at the beginning and the point where the ball barely thouch the floor.
so the equation I use it
mgh=.5mv^2
but that is not going to give me the d. The thing is that the length of the string is 10 m to begin with but I want to find out what is the new length of the string when it rotates around the peg. if you see where I am getting at.
 
Can the length of the string change? Because I don't think you mentioned that in the problem...
 
well the length of the string is changing
so the string is really 10 m right and then there this stick or peg some where at distance d
which causes the rope to rotate. what is the distace d or the rope distance after it rotated both d are the same
 
Sure, the string rotates (or rather, part of it rotates), but that doesn't mean the length of the string changes. I'm fairly confident that the length of the string is supposed to be constant; it seems that you may have been misinterpreting the problem.
 

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