Energy methods for spring velocity

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Homework Help Overview

The problem involves a collar attached to a spring that rotates around a fixed circular body. The scenario describes the energy transformations as the collar moves from the top of the circle to point A, halfway down the circle, and seeks to determine the collar's velocity at that point using energy methods.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between gravitational potential energy and kinetic energy, questioning how energy conservation applies in this context. There is an exploration of the potential energy calculations for both the spring and gravity, with some participants attempting to clarify how these energies relate to the collar's velocity.

Discussion Status

The discussion is ongoing, with participants raising questions about the conservation of energy principles and how the calculated potential energies contribute to determining the collar's velocity. Some guidance has been offered regarding the relationship between energy forms, but no consensus has been reached on the next steps for solving the problem.

Contextual Notes

Participants are working within the constraints of the problem statement and the provided equations, with some uncertainty about the application of energy conservation in this specific scenario. There is an acknowledgment of the complexity of the problem and the need for further clarification on the energy transformations involved.

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Homework Statement


A spring is attatched to a single position with a 1.2 kg collar at the end. The collar is attatched to a circular fixed body so it can rotate around it. The radius of the circle is 180 mm and the position of where the spring is attatched is 75mm directrly above the center of circle. The springs constant is 300 n/m and its undeformed length is 105mm. It starts out at rest at the top of the circle and is given a slight push to get it moving. It passes through point A on the circle, which is located halfway down on the circle. Using energy methods, find the velocity of collar as it passes through point A.


Homework Equations


Vs=1/2kX^2=potential spring energy, Vg=(distance)x(weight)=gravitational potential energy
T1+V1=T2+V2

The Attempt at a Solution


the distance of point A to the attatched spring is sqrt(75^2+180^2)=195mm
The elongation of the spring is therefore 195-105=90mm then the potential energy would be 1/2kX^2=1/2(300N/m)(.09mm)^2=1.215 J
and the gravitational potential energy would be (.18mm)(1.2 kg)(9.8m/s^2)=2.1
This is where I don't know what to do after calculating the potential energy at point A. How am I supposed to get velocity out of all this mess?

I understand this is a lengthy problem so any help will be GREATLY appreciated.
 
Last edited:
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The gravitational potential energy has decreased.
apart from the spring's energy, what is this converted into?
 
So you're saying that the gravitational potential energy lossed was conserved by the increase in kinetic energy?
 
physicsnewb7 said:
So you're saying that the gravitational potential energy lossed was conserved by the increase in kinetic energy?
+ the springs PE

I don't claim to be the first person to say that:smile:
 

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