Effective Spring Constant of Springs in Series: Deriving & Explaining

[Morass]

Homework Statement

I am trying to derive the effective spring constant of two springs, with different spring constants, in series. I know the equation is everyone online, so the effective spring constant is k1k2/k1+k2.

So the question is, when deriving it, the force exerted on each spring is constant, why is that??

Homework Equations

Hooke's Law -> Fx = kx

The Attempt at a Solution

Is it because of Newton's third law? If so, how does that work?? Force of mass on spring 2 is equal to force of spring 2 on spring 1? So the force acting on each spring is Fg??

 

[tiny-tim]

Hi Morass!

… Is it because of Newton's third law? If so, how does that work?? Force of mass on spring 2 is equal to force of spring 2 on spring 1?

Yes.

 

[kerimek]

I can provide a response to this content by explaining the concept of Newton's third law and how it applies in this situation. Newton's third law states that for every action, there is an equal and opposite reaction. In the case of two springs in series, the force exerted on one spring by the other spring is equal and opposite to the force exerted on the other spring by the first spring. This is because the two springs are connected and any displacement of one spring will result in an equal displacement of the other spring.

When deriving the effective spring constant, we assume that the two springs are connected in a way that they both experience the same displacement. This means that the force exerted on each spring is the same, as stated in Hooke's Law (Fx = kx). This assumption allows us to equate the forces on each spring and solve for the effective spring constant using the equation k1k2/k1+k2.

In other words, the force acting on each spring is not just the force of gravity (Fg), but also the force exerted by the other spring. This is why the force is constant on each spring in this situation. I hope this explanation helps in understanding the concept and derivation of the effective spring constant for springs in series.