Force constant

Definition

The force constant, also known as the spring constant, quantifies the stiffness of a spring in Hooke's Law. It is denoted by $k$ and measured in Newtons per meter (N/m).

5 Must Know Facts For Your Next Test

1. The force constant $k$ appears in Hooke's Law equation: $F = -kx$, where $F$ is the restoring force and $x$ is the displacement from equilibrium.
2. A higher force constant indicates a stiffer spring that requires more force to compress or extend.
3. The unit of the force constant is Newtons per meter (N/m).
4. In a mass-spring system, the angular frequency of oscillation $\omega$ is given by $\omega = \sqrt{\frac{k}{m}}$, where $m$ is the mass.
5. The potential energy stored in a compressed or stretched spring is given by $U = \frac{1}{2}kx^2$.

Review Questions

• What does the force constant measure in a spring?
• How does a higher force constant affect the stiffness of a spring?
• What is the relationship between angular frequency and the force constant in a mass-spring system?

Related terms

Hooke's Law:

A principle stating that the force exerted by a spring is directly proportional to its displacement: $F = -kx$.

Simple Harmonic Motion:

A type of periodic motion where the restoring force is directly proportional to displacement and acts in the direction opposite to that of displacement.

Potential Energy:

Energy stored due to an object's position; for springs, it is given by $U = \frac{1}{2}kx^2$.