A uniform spring whose unstretched length .

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
4 replies · 10K views
Estrex
Messages
2
Reaction score
0
A uniform spring whose unstretched length...

A uniform spring whose unstretched length is L has a spring constant k. the spring is cut into two pieces of unstretched lengths L1 and L2, with L1 = nL2. What are the corresponding spring constants k1 and k2 in terms of n and k?

The answer is k1 = (n+1)k/n and k2 = (n+1)k. I have no idea how they got that. I tried setting up the force equation F = kL and solving for k, k = F/L, but the substitution never worked out.
 
Physics news on Phys.org
Estrex said:
I tried setting up the force equation F = kL and solving for k, k = F/L, but the substitution never worked out.
Stop right there. The restoring force generated in a string is given by F = kΔx, where Δx is the length by which the string is compressed or elongated. F does not depend on L at all.
Well now consider the original spring to be split up into two strings of spring constants k1 and k2, which are connected in series and consider what tiny-tim said. That's pretty much all you need to do here!
 
Ok, I figured it out. I just forgot the formula for springs in series, 1/k = 1/k1 + 1/k2.
Since L1 = nL2, k2 = nk1. 1/k = 1/k1 + 1/nk1. 1/k = n+1/nk1. k = nk1/n+1. k1 = k(n+1)/n. Solving for k2, 1/k = n/k2 + 1/k2. 1/k = n+1/k2. k = k2/n+1. k2 = k(n+1).
 
good job... if u forget something, u can always derive it... works for me most of the time...