One spring is located inside a wider spring. Both ends are welded together and hanged from a tree. both springs are ##30 cm## long when not deformed. The first spring has ##30 g## and ##k=5 g/cm## the second spring has ##60 g## and ##k= 6g/cm##. How deep under the branch will be the bottom weld?
2. Relevant equations
3. The attempt at a solution
My idea was to calculate the deformation of each spring separately. Let’s say that ##s_1## is the deformation of the first one and ##s_2## deformation of the second one.
Of course one will have greater deformation than the other, but when welded together, this means that one of the springs will have to carry some of the mass of the other spring with greater deformation.
For easier writing let’s say that the second spring has greater deformation than the first one. So my idea was to calculate how much mass of the second spring, will the first one have to carry. I think I could do that because I know the difference between the springs deformations.
This would than mean, that the total distance of the bottom weld from the top one is a sum of deformed length of the first spring + additional deformation of spring no. 1 because it has to take some the mass of spring no 2.
Even explaining what I am trying to sounds too complex to me. So, is there an easier way? Or even better, is this even the right way?
I would love to show you my calculations yet the problem is that I have absolutely NO idea how to calculate the deformation of the hanged springs due to gravity. Whatever I do, everything seems do deduct down to zero in the first two steps 🙁