Finding Spring Constants After Cutting a Spring

[stpmmaths]

Homework Statement

A spring with spring constant 8 N m^-1 is cut into 2 equal parts. Find the spring constant of each part?

Homework Equations

The Attempt at a Solution

Spring constant of each part = 16 N m^-1
Above is the answer given.
1. Why should we times 2?
2. If the spring is cut into a ratio of 1:2:3, then what should be the spring constant of each parts?

 

[rl.bhat]

Force constant is force required to produce unit extension.
In the spring for a given load, extension is proportional to the length of the spring. So when the length reduces, extension reduces and k increases.

 

[inhere]

Hello. Consider the spring to be like two capacitors. 1/keq = 1/k + 1/k'. So in this case we consider the entire spring with keq to be the sum of two individual spring halves that have some other spring constant k where k = k' for this problem. Doing a bit of algebra shows that k = 2*keq.[

 

[stpmmaths]

Thanks a lot.