A light spring which has a force constant of 8N/m is cut into two equal parts . What is the force constant for each part ??
isnt that each part has a force constant of 8N/m ??
Hi thereddevils
I think it's better to post your question here :
http://www.physicshelpforum.com
And a little hint for you : the answer is no. Now your job is to find out the reason
$\displaystyle k = 8$ N/m
that means if you apply $\displaystyle 8$ N of force, the spring stretches $\displaystyle 1$ m
cut the spring in half ... attach them with a light non-stretchable string.
apply a force of 8N. Each piece stretches $\displaystyle 0.5$ m
the force in each spring "piece" is 8N
$\displaystyle k_{each \, piece} = \frac{F}{x} = \frac{8}{.5} = 16$ N/m
for two springs in series, the effective force constant of a single spring equivalent to the two is
$\displaystyle k_{eff} = \frac{k_1 \cdot k_2}{k_1 + k_2}$
$\displaystyle k_{eff} = \frac{16 \cdot 16}{16 + 16} = \frac{16^2}{2 \cdot 16} = 8$ N/m