Understanding the Relationship
* Force Constant (k): A measure of the stiffness of a spring. It represents the force required to stretch or compress the spring by a unit length.
* Force (F): Measured in Newtons (N) or kg m/s²
* Displacement (x): Measured in meters (m)
Hooke's Law
Hooke's Law describes the relationship between force, displacement, and the force constant:
* F = -kx
Dimensional Analysis
1. Solve for k: k = -F/x
2. Substitute dimensions:
* [k] = [F] / [x]
* [k] = (kg m/s²) / (m)
* [k] = kg/s²
Therefore, the dimensional formula of the force constant (k) is M L⁻¹ T⁻²
Where:
* M represents mass
* L represents length
* T represents time
