A-spring-of-force-constant-k-is-cut-into-two-pieces-such-that-one-piece-is-twice-as-long-as-the-other-Then-the-longer-piece-will-have-a-force-constant-of-

Question Number 18924 by Tinkutara last updated on 01/Aug/17

A spring of force constant k is cut into

two pieces such that one piece is twice

as long as the other . Then the longer

piece will have a force constant of

Answered by ajfour last updated on 01/Aug/17

k \propto \frac{1}{l}

let longer piece has force constant

equal to k_{1}

Then shorter one has force constant

equal to {2 k}_{1} .

their series combination has

force constant k (given)

\frac{1}{k} = \frac{1}{k_{1}} + \frac{1}{{2 k}_{1}}

\Rightarrow \frac{1}{k} = \frac{3}{{2 k}_{1}} \Rightarrow k_{1} = \frac{3 k}{2} .

Commented by Tinkutara last updated on 01/Aug/17

Thank you very much ajfour Sir!