Hookes Law and Spring Constant: Explaining the Integral

AI Thread Summary
The discussion focuses on understanding the spring constant "k" in relation to Hooke's Law and the energy stored in a spring, expressed as U = 1/2 kx^2. A participant seeks clarification on how the integral leads to the area of a triangle, initially confusing the dimensions of the triangle. After correction, it is acknowledged that the area calculation involves (kx * x)/2, leading to the realization of the squared term in the formula. Additionally, there is a query about the integral of the force function F = kx, confirming that the primitive function is indeed (kx^2)/2, which allows for integral calculations. The conversation emphasizes the relationship between force, energy, and the mathematical representation of springs.
Alec
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Hello, I'm having some problems with the spring constant "k" together with Hookes law. U=1\2kx^2

Could someone please explain how you get that integral?
If you insert it in a diagram and calculate the area as a triangle you would get 1/2kx. Where does the ^2 come from?
 
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No, you don't!
Draw the triangle again.
How long is its base, and how long is its height?
 
Alright, my bad :rolleyes: I missed that it's (kx * x)/2
Now, another question.
The function for F = kx.
The primitiv function for kx = (kx^2)/2 right? Because then you could calculate it as an integral?
 

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