Determining Natural Length of a Spring

AI Thread Summary
The discussion revolves around determining the natural length of a spring based on the work required to stretch it. The problem states that 6 J of work is needed to stretch the spring from 10 cm to 12 cm, and another 10 J is needed for the same stretch, indicating a potential typo in the problem. Participants suggest using the formula for spring potential energy, PE = 1/2*k*x², and emphasize the importance of identifying the unstretched length, denoted as L. The conversation highlights the need for a clear understanding of Hooke's Law and the work-energy principle to solve the problem effectively. Overall, the thread seeks guidance on how to approach the calculations needed to find the spring's natural length.
TG3
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Homework Statement


If 6 J of work is needed to stretch a spring from 10 cm to 12 cm, and another 10 J is needed to stretch it from 10 to 12 cm, what is the natural length of the spring?


Homework Equations


W=FD
Hooke's Law

The Attempt at a Solution


Honestly, I stare at this problem and am at a loss as to where to start, and there are no examples in the book like this. Obviously I'm not asking for answers because I know the rules here, we're supposed to show effort; but if someone gave me some starting help it would be much appreciated.
 
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TG3 said:

Homework Statement


If 6 J of work is needed to stretch a spring from 10 cm to 12 cm, and another 10 J is needed to stretch it from 10 to 12 cm, what is the natural length of the spring?

Homework Equations


W=FD
Hooke's Law

The Attempt at a Solution


Honestly, I stare at this problem and am at a loss as to where to start, and there are no examples in the book like this. Obviously I'm not asking for answers because I know the rules here, we're supposed to show effort; but if someone gave me some starting help it would be much appreciated.

Consider

PE = 1/2*k*x2
 
TG3 said:

Homework Statement


If 6 J of work is needed to stretch a spring from 10 cm to 12 cm, and another 10 J is needed to stretch it from 10 to 12 cm, what is the natural length of the spring?
Looks like you have a typo in the problem statement.

Hint: Call the unstretched length of the spring L. How do you determine the work done to stretch a spring? (What's the expression for spring potential energy?)
 

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