Potential Energy and Conservation of energy

AI Thread Summary
The work required to stretch a spring is not linear but quadratic, as described by the formula for potential energy (P.E.) of a spring, P.E. = 1/2 kx^2. Stretching a spring 2 cm requires four times the work compared to stretching it 1 cm, due to the square relationship with the extension. This principle is derived from integrating Hooke's Law over the distance moved. Therefore, the assumption that stretching a spring 2 cm requires twice the work is incorrect. Understanding this relationship is crucial for solving problems related to spring mechanics and energy conservation.
msattar07
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Homework Statement


How does the work required to stretch a spring 2cm compare with the work required to stretch a spring 1 cm?


Homework Equations


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The Attempt at a Solution



i think its twice the work
 
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Assuming that the two springs are the same and Hookean, you are wrong.
 
P.E. of a spring is 1/2kx^2 , which is directly proportional to the square of extension from the natural length
 
you can derive the expression for the potential energy of the spring by integrating the hooke law over the distance moved.
 
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