Hooke’s law vs elastic potential energy equation

[nomdeplume1234]

I am having a little trouble with the concept of force required to displace a spring and the potential energy stored by that displacement. I tried solving a problem using Hooke's law but the elastic potential equation was needed instead.

In Hooke’s law, F = - kx.
and if a spring is displaed by x, then Work is F * D = -kx^2.
and if potential energy is change in work, then why is elastic potential equation (1/2)kx^2?

Can someone help me reason through this?
Thank you!

---

Members don't see this ad.

 

[theonlytycrane]

I found this explanation helpful: http://www.studyphysics.ca/30/elastic.pdf

The reason that we can't plug in F = -kx into W = Fd directly is because the force is not constant as d changes. The force is maximum when the spring is displaced the most and smallest when it is first displaced from resting state.

Note: I'm not sure if Hooke's law is tested on the new MCAT. I didn't see it on the AAMC topic list for physics or in my content review book.

 

[nomdeplume1234]

I found this explanation helpful: http://www.studyphysics.ca/30/elastic.pdf

The reason that we can't plug in F = -kx into W = Fd directly is because the force is not constant as d changes. The force is maximum when the spring is displaced the most and smallest when it is first displaced from resting state.

Note: I'm not sure if Hooke's law is tested on the new MCAT. I didn't see it on the AAMC topic list for physics or in my content review book.

Thank you for the pdf. I was wondering if anyone was going to reply. I forget the context of the question but it was in some practice questions for the 2015 mcat.