Springs in series and in parallel

• Springs in series and in parallel
• Hooke's law and the elastic constant of a spring

This physical paradox was originally developed by Joel E. Cohen, an applied mathematician at Rockefeller University in New York City. The idea for this startling demonstration arose out of Cohen's long-standing interest in mathematical models of biological competition, especially models that produce counterintuitive outcomes.

As a step toward learning whether the same kind of surprising result could occur in a biological system, Cohen started by looking for a mechanical analogue of the traffic paradox, and he came up with the string-spring arrangement.

In fact, it is fairly straightforward to construct a working model of such an apparatus by using strings, rubber bands, and a plastic jug partially filled with water as a weight.

When confronted by the initial spring-and-string configuration, most people are inclined to guess that the weight will go down. Few automatically predict that the weight will go up unless they have already worked out the problem or have seen it before. Only when someone knows the answer does it become "obvious." You can't rely on your intuition unless it already incorporates an understanding of springs in series and parallel arrangements.

In the initial position the two springs are connected in series and each one feels a weight force of mg.

When the springs are connected in parallel we get that the total force F applied to the entire system is split between the two springs into components F1 and F2 that produce the same elongation xp on both springs.

• Steel spring with pointer — 4110.81
• Double side scale, silk screen printed — 2208.20

• What is the main physical property that affects the elastic constant k?
• How is elasticity physically defined?