Spring Constant and Spring Series

[Meadow_Lark]

I have a question about the spring constant of springs in series. Basically why is it less than the springs involved in the series? I know that when in series the spring constant is the sum of the inverse of each spring involved, but why?

thanks.

 

[PhanthomJay]

I have a question about the spring constant of springs in series. Basically why is it less than the springs involved in the series? I know that when in series the spring constant is the sum of the inverse of each spring involved, but why?

thanks.

For springs in series, the effective spring constant is the inverse of the sum of the inverses of each spring constant, which with some algebraic manipulation works out to $k_1k_2/(k_1 + k_2)$. Essentially, the force in each spring is the same as the applied force, from equilibrium considerations and free body diagrams. Google springs in series. The total extension of the system of 2 springs will be larger than if just one spring used due to the reduced effective stiffness of the longer relaxed length.

 

[Integral]

Can you derive the result? Start with Hook's Law. Assume massless springs so the force is the same on both, the deflection of the total must be the same as the sum of the extensions of the individual springs.