The direction of the force on a spring is consistent with the direction of its deformation due to Hooke's Law, which describes the relationship between the force applied to a spring and the resulting deformation or displacement.
According to Hooke's Law, the force exerted by a spring is directly proportional to the displacement or deformation of the spring from its equilibrium position, as long as the elastic limit of the spring is not exceeded. Mathematically, Hooke's Law is expressed as:
F = -kx
Where: F is the force exerted by the spring, k is the spring constant (a measure of its stiffness), x is the displacement or deformation of the spring from its equilibrium position.
The negative sign in the equation indicates that the force exerted by the spring is opposite in direction to the displacement or deformation. This means that when the spring is compressed or stretched (deformed), it exerts a force in the opposite direction to try to restore itself to its equilibrium position.
For example, if you compress a spring by pushing it inward, the spring exerts a force in the outward direction, opposing the compression and trying to return to its original length. Similarly, if you stretch the spring, it exerts a force inwards, opposing the stretching and attempting to contract.
This consistent directionality of the force with the deformation ensures that the spring behaves as an elastic element, capable of storing and releasing energy in response to external forces or deformations.