F = k x

F = force exerted on the spring (N)

k = spring constant (N/m)

x = displacement of the spring (m)

The animated graph on the right corresponds to a spring constant

k =1.


The same law applies to other elastic materials, like rubber and many others. Even a metal rod presents elastic behaviour, but only for small distortions.


To calculate the force in newtons, the distance must be in meters. If you are given a distance in cm you must convert it to meters first.




Many other physical laws are also described by a simple relationship, like F= kx.

For instance U= RI (Ohm's Law) ,

v = a t (relates velocity, acceleration and time )

and many others.

The behaviour of the systems which obey these laws can also be represented by a straight line, whose slope will reveal important information. But watch out: you won't always get a straight line! For instance, radioactive decay is pictured by a curve called exponential.




Mass and weight

Uniform movement

Accelerated movement

Work / energy

Kinetic energy





Pressure and force

Elastic force (Hooke's Law)

Projectile motion


Some devices that obey Hooke's Law:





Hooke's Law

Hooke's Law simulations:

(a damping effect is present to simulate the disspation of energy caused by friction)

Spring with k= 0.15



Spring with k= 0.03

(a "weaker" spring)


Robert Hooke , born at the Isle of Wight , discovered (in 1676) that when you apply a force on a spring, the force you apply is directly proportional to how far it stretches .

You can represent this variation by a straight line, due to the direct proportionality.

The slope of the graph (example below) will be proportional to the spring constant k : if the spring is tough, the slope will be large and the resulting line will be close to the y axis (vertical). That means that even a small displacement of the spring will require a large force.

if the spring is "soft" the slope will be small; the resulting line will be close to the x axis(horizontal).

The elastic Potential energy stored in a spring which is either compressed or stretched, is:

E =


Demonstration of Hooke's Law for a spring with k=1.


© Ricardo Esplugas. All images in this site can be bought in an enlarged version. Please contact me on ricardochemistry@gmail.com