What is the unit for measuring the spring constant?

The spring constant measures the stiffness of a spring, indicating how much force is required to stretch or compress the spring by a unit distance. In terms of its definition, the spring constant (often represented by the symbol ( k )) is derived from Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position. This relationship can be expressed mathematically as:

[ F = k \cdot x ]

where ( F ) is the force applied to the spring in newtons (N), ( x ) is the displacement in meters (m), and ( k ) is the spring constant in newtons per meter (N/m).

In this context, the units of force (newtons) divided by the units of displacement (meters) gives us the unit for the spring constant:

[ \text{Units of } k = \frac{\text{N}}{\text{m}} = \text{N/m} ]

Thus, the spring constant is measured in newtons per meter, making this the correct and appropriate unit for quantifying spring behavior under applied forces.