Hooke's Law: Two springs in series

[xxx7r1s7axxx]

[SOLVED] Hooke's Law: Two springs in series

can someone explain and prove to me why the equation for two springs in series is
K= [(1/k1)+(1/k2)]^-1 ?

this is how far i got
F= -k ∆x
F= -k (x1+x2)

 

[rock.freak667]

Wikipedia has a derivation that seems simple to understand...

http://en.wikipedia.org/wiki/Hooke's_law#Multiple_springs

 

[xxx7r1s7axxx]

thanks
i looked at it but i don't understand this part

"Meanwhile, the force on the point between the two springs is
Fs = -k1x1+k2(x2-x1)"

 

[Doc Al]

The proof on that website is rather obscure. Instead, try this: What's the force exerted by each spring and by both springs?

F = k1x1 = k2x2 = k(x1 + x2)

Play around with this and you should be able to figure out k in terms of k1 and k2.

 

[xxx7r1s7axxx]

thanks doc al
this might be a stupid question
but k1x1 = k2x2 is it because the tension of both spring are equal?

 

[rock.freak667]

Because the force is the same,yes

 

[xxx7r1s7axxx]

kk i think i got it
thanks for helping me =]