Find Max Velocity of Object From Spring Force Equation

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To find the maximum velocity of an object from the given spring force equation, F(x) = 3.133x - 4.333x^2 + 5.333x^3 - 2.667x^4 + 0.5333x^5, the approach involves determining the point where the force equals 12 lbs. Since this spring does not follow Hooke's law, the potential energy cannot be expressed as (1/2)kx^2; instead, integration is needed to derive the potential energy function. The work-energy theorem should be applied to find the velocity once the work done in compressing the spring is calculated. Concerns were raised about the nature of the force, as it appears non-restorative, indicating that the equation is not for a traditional spring but for cushioning in packaging. The discussion concluded with the realization that the original force equation was indeed correct for its intended application.
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I'm given the force of a spring in the form F(x) = 3.133x - 4.333x^2 +5.333x^3 - 2.667x^4+.5333x^5 and asked to find the maximum velocity of an object so that the force does not exceed 12 lbs

My approach was to find x from the force equation which was about 2.5 inches and then set the kinetic energy of the object equal to the potential of the spring and solve for velocity but I am not sure how to change the force equation to fit in 1/2 kx^2
could someone tell me if this is the wrong approach or how to change the equation please
 
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deesal said:
but I am not sure how to change the force equation to fit in 1/2 kx^2
The 1/2kx^2 applies to a spring that obeys Hooke's law (F = -kx), which is not the case for this spring. Derive a potential energy function for this spring in a similar manner, using integration to find the work required to stretch the spring.
 
F(x) = 3.133x - 4.333x^2 +5.333x^3 - 2.667x^4+.5333x^5

It seems to me you may have to take an integral to find the work done in compressing the spring to where the force equals 12lbs.

Then solve for velocity using the work-energy theorem. (This spring does not obey Hooke's law, so (1/2)kx^2 is irrelevant.

(Sorry Doc, I was typing before I saw your post).
 
What I don't understand is that the force doesn't seem to be restoring. If the object is at say +1.0, then your function means the force will also be positive. I don't understand how any spring could increase its force directed away from x=0, the farther you are from x=0.
 
DocZaius said:
What I don't understand is that the force doesn't seem to be restoring.
I agree. Looks like there's a minus sign missing.
 
it isn't an actual spring the equation is for package cushioning in a box the equation was right thanks for the help I got it
 

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