Two massless springs of spring constants K 1 and K 2 are connected one after the other forming a single chain, suspended vertically and a certain mass is attached to the free end. If x 1 and x 2

Question

Two massless springs of spring constants K 1 ​ and K 2 ​ are connected one after the other forming a single chain, suspended vertically and a certain mass is attached to the free end. If x 1 ​ and x 2 ​ are their respective extensions and 'F' is their stretching force, the total extension produced is

TestHub · Accepted Answer

When springs are connected in series, the same stretching force $F$ acts on each spring.

The extension in the first spring is $x_{1} = \frac{F}{K _{1}}$

The extension in the second spring is $x_{2} = \frac{F}{K _{2}}$

The total extension produced is $x = x_{1} + x_{2}$

$x = \frac{F}{K _{1}} + \frac{F}{K _{2}} = F (\frac{1}{K _{1}} + \frac{1}{K _{2}})$

Answer: $F (1/ K_{1} + 1/ K_{2})$

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