Question on Springs

[ieatshrimp24]

So I missed two questions in TPRH SW when dealing with displacement of springs. When do you choose between F = -kx and PE = 1/2kx^2?

One question explanation about a vertical spring at rest chose F = -kx while another question explanation on work done by a spring chose the PE equation. I used the opposite equation for both questions.

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[Cawolf]

@ieatshrimp24

It depends on if you want the potential energy of the spring or the force exerted by it.

For example:

I have this mass = m sitting and clamped down on a vertical spring that is compressed a distance = x with spring constant k. What is the max velocity the mass will reach when I release the spring?

Well then we use the work-energy theorem.

PE = KE

PE = 0.5kx^2

PE = KE = 0.5kx^2 = 0.5mv^2 (then solve)

v = sqrt [(kx^2)/m]

But say I wanted to know the acceleration that the mass will get from the spring, then I would find it more useful to use the force equation.

F = -kx (we will use the magnitude and just know the force will be opposite the direction of compression, or upwards)

F = kx = ma

a = kx/m

Then if you wanted the total acceleration you would take gravity into account.

a = (kx/m) - mg

There are many ways to use the formulas, you just have to know what they are telling you.