Two springs together more elastic?

[ys2050]

Based on the equation: 1/ktot = 1/k1 + 1/k2
Why is it that the reciprocal of the total spring force is equal to the reciprocals of each spring constants??
I know how to derive the equation, but what is the physics behind it??
The total spring constant is much less than those of the two individual springs... smaller k means that the spring is more elastic... why does two combined springs cause the elasticity to increase??
I know I'm asking a lot of questions.. but any help would be appreciated! :)

 

[Kurdt]

The following web page might answer some questions.

http://scienceworld.wolfram.com/physics/SpringsTwoSpringsinSeries.html

 

[Moetasim]

The equation 1/ktot = 1/k1 + 1/k2 is known as the parallel spring equation and it is derived from Hooke's law, which states that the force exerted by a spring is directly proportional to its spring constant and the displacement of the spring from its equilibrium position. In the case of two springs connected in parallel, the total force exerted is the sum of the individual forces exerted by each spring.

Now, let's consider the physical explanation behind this equation. When two springs are connected in parallel, they essentially act as one single spring with a combined spring constant. This is because when one spring is compressed or stretched, the other spring also experiences the same displacement. This results in a larger displacement and thus a larger force being exerted by the combined spring system.

In terms of elasticity, a smaller spring constant (k) means that the spring can be compressed or stretched more easily, making it more elastic. When two springs are connected in parallel, their combined spring constant (ktot) is smaller than the individual spring constants (k1 and k2). This is because the total displacement of the combined spring system is larger than the individual displacements of each spring. Therefore, the combined springs are more elastic compared to the individual springs.

In conclusion, the physics behind the parallel spring equation can be explained by the fact that when two springs are connected in parallel, their displacements add up, resulting in a larger displacement and thus a smaller spring constant. This leads to an overall increase in elasticity of the combined springs. I hope this helps to clarify your questions.