B Why doesn't the Spring Force change on splitting?

navneet9431

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Suppose a spring of spring constant=K and Length=L is split into two parts L1 and L2, with spring constants K1 and K2 respectively.

Then,why is it such that the spring force F=K1*L1=K2*L2=K*L?

Please give an intuitive explanation of why the spring force doesn't change?

I will be thankful for help!
 

Delta2

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If I understand correctly, you asking why all those forces are equal in the case we have two springs connected in series.

Lets focus on spring with constant ##K_2##. To this spring are connected the spring with constant ##K_1## and the block (whose displacement is ##L=L_1+L_2## from the equilibrium position)
We can view the spring with constant ##K_1## as another hypothetical block connected to spring ##K_2##. Hence the force that the spring ##K_2## applies to this hypothetical block is by hook's law equal to $$F_{21}=K_2L_2 (1)$$.
By Newton's 3rd law the hypothetical block applies to the spring ##K_2## a force opposite and equal $$F_{12}=F_{21} (2)$$.

Now we focus on spring ##K_1##. To this spring is connected the spring ##K_2## which also can be viewed as a hypothetical block connected to spring ##K_1##. The force applied from spring ##K_1## to this hypothetical block is essentially the force ##F_{12}## and by hook's law it is equal $$F_{12}=K_1L_1 (3)$$
By combining (1) (2) and (3) we get that ##K_1L_1=K_2L_2##.

Maybe my explanation is not very intuitive but I don't see any other way how we can prove it, without viewing the springs as hypothetical blocks and also have to use Newtons 3rd Law.
 

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