# Find Max Velocity of Object From Spring Force Equation

• deesal
In summary, the object was asked to move at a maximum velocity where the force did not exceed 12lbs and it was not possible to find x from the equation that would give the velocity. It seems that an integral may be needed to find the work done to move the object at the desired velocity.
deesal
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

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

## What is the spring force equation?

The spring force equation is F = -kx, where F is the force applied by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

## How do you find the maximum velocity of an object from the spring force equation?

To find the maximum velocity of an object, we can use the equation v = sqrt((2*k*x)/m), where v is the maximum velocity, k is the spring constant, x is the displacement, and m is the mass of the object.

## What factors affect the maximum velocity of an object in a spring system?

The maximum velocity of an object in a spring system is affected by the spring constant, the mass of the object, and the displacement from the equilibrium position. A higher spring constant and a greater displacement will result in a higher maximum velocity, while a greater mass will result in a lower maximum velocity.

## How does changing the spring constant impact the maximum velocity in a spring system?

Increasing the spring constant will result in a higher maximum velocity, as the force applied by the spring will be greater. On the other hand, decreasing the spring constant will result in a lower maximum velocity.

## Can the maximum velocity of an object in a spring system be greater than the initial velocity?

Yes, the maximum velocity of an object in a spring system can be greater than the initial velocity. This is because the spring force can provide additional acceleration to the object, increasing its velocity beyond the initial velocity.

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