Sat October 27, 2012 By:

sir can u plz explain me what is spring constant and how can we derive its formula of 1/2.k.x.x

Expert Reply
Sat October 27, 2012
Please post one query at a time.
The spring constant, k , is a measure of the stiffness of a spring (large k stiff spring, small k soft spring). To compress a spring by a distance x we must apply a force F ext = kx . By Newton's 3rd law, if we hold a spring in a compressed position, the spring exerts a force Fs = - kx . This is called a linear restoring force because the force is always in the opposite direction from the displacement.
In other words,
the spring constant tells you how much force you need to apply to stretch (or compress a spring) by an amount of 1 meter

so if the spring constant is 100N/m, then you have to apply a force of 100N to stretch it by one meter

the greater the value of k, the more force you need to exert to stretch/compress it.
For a spring
F = -kx
where F is the force exerted by the spring, k is the spring(stiffness) constant and x is the extension of the spring

Work = Force * Distance
For a spring, force is not constant so you use average force * distance =
1/2*Force*Distance =(1/2)Fx
If you substitute F = -kx into 1/2(Fx) (F is negative so energy is gained) as F ,it becomes 1/2(kx)x
Elastic potential energy = 1/2kx2
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