Springs in Series Combination

In physics and mechanics, springs can be connected to each other in a variety of combinations. Mainly they are spring in a series and spring for a combination of springs in parallel. Springs are said to be in a series combination when they are connected to each other via point to point or end to end.

Spring for a combination of springs in parallel is when it is connected to the other spring, side by side. There are two important concepts to understand when we are studying the springs in series. One is the spring constant, or how stiff the spring is and how much it will compress or stretch. It is dependent on the material used to make the given spring, tightness of the spring, number of coils present in the spring, etc. The other factor is Hooke’s law. It gives the relation between the force produced by the spring and how far the spring can be stretched, the relation being proportional to each other. 

When the given spring for a combination of springs in parallel has to be evaluated for total force, the forces add up together. When the strain of the ensemble is their common strain, and the stress is the sum of stresses. 

Springs in a series combination, on the other hand, would still obey Hooke’s law, as two forces are acting on the vertical series, which is pulling the top of the spring. They are the force of gravity and the restoring forces. As these two forces are acting on both the upper and lower springs in a vertical series combination, the spring system in series will overall stretch more than expected. 

When spring is in series, any external force applied to the entire ensemble shall be applied to each spring with the same magnitude, and the deformation or the amount of strain in the entire series setting will be equal to the sum of strains of the individual springs present in the series combination. 

Now that we have understood the just of spring in series, let us understand the equation when we add two springs in series.

Let us assume we have two springs with force constants, namely k1 and k2, which are connected in series. These springs in vertical series combinations are supporting a load, F= mg.

We shall represent the force constant of the combination with k

Now,

F=kx (where x is the total stretch)

And so, x = F/k 

Now, for each spring, the bottom will support F= mg and will stretch by x1.

So, F = k1x1 or x1=F/k1

For top spring,

F=k2x2 or x2 = F/k2

Thus, the total stretch x,

x = x1+x2 or F/k= F/k1 + F/k2

Conclusion

Thus, to conclude, we talked about springs in series. When we add two springs in a series combination, they are connected to each other end to end. We also talked about spring as a combination of spring in parallel. We talked about the derivation of the spring constant for springs in a series. We also talked about the forces which are present for springs in series.