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Force is proportional to distance, and is equal when the distance is multiplied by the spring constant
\[F = kx\]
An additional information; F=kx formula is just for small values of x.
Hooke's law basically tells that, matter can always be thought of as made of springs..
so if you consider a spring.. a stiff spring (easier to make out in a stiff string).. try to stretch or compress it.. you will see, that after a point you are no longer to compress or stretch it any further? why?
is it cause the force that you put on the spring has decreased? no.. the force you are putting maybe more or less the same.. then what has happened.. the only logical conclusion is that, you are feeling an equal and opposite force from the spring.. this is called as the restoring force of the spring.. so now the question is why could you stretch until a point and not beyond.. the answer is, as you keep stretch this restoring force keeps on increasing .. until its lesser than your applied force, you continue to stretch it (cause you win).. but at that one point, both forces are equal (tie).. and no longer stretching
so the spring force F is directly proportional to how much stretch... i.e. the stretch distance (or compress distance for that matter)
|dw:1361700193517:dw|\[F \alpha x\] or \[F = -kx\]
k is called the spring constant.. you can easily see, that if k is high, the restoring force is also high for the same stretch.. hence.. spring constant tells about how STIFF a spring is
- sign tells that the force is always in the opposite direction of the displacement.. (forgot to put that in the drawing.. hope you can make that out)
and as @yunus mentioned.. its only applicable for small distances.. what he means to say is, for every spring.. if you stretch or compress beyond one limit.. it loses its properties.. you can test this easily with a simple spring that comes along with a pen.. stretch it a lot and it will not be a spring anymore.. so we have something called as the "ELASTIC LIMIT".. so we say hooke's law holds good within ELASTIC LIMITS