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# Working with springs of different force constants

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Springs A and B are identical except that A is stiffer than B, that is the force constant Ka is greater than the force constant Kb. On which spring is more work expended if,

(a) They are stretched by the same amount?
(b) They are stretched by the same force?

https://brainmass.com/physics/work/working-springs-different-force-constants-7476

## SOLUTION This solution is FREE courtesy of BrainMass!

a) Let x be the extension in each spring.

The work done Wa = (1/2) Ka x^2

and Wb = (1/2) Kb x^2

Since Ka > Kb, Wa > Wb

b) If the stretching force on each side is F,

The extension in A Xa = F/Ka and

The extension in B is Xb = F/Kb

Wa = (1/2) Ka (Xa)^2 = (1/2) Ka (F/Ka)^2 = (1/2) F^2/Ka

And Wb = (1/2) F^2/Kb

Since Ka > Kb,

Wa < Wb

Where Wa and Wb are the work done on spring A and B respectively.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!