Spring constant

Definition

The spring constant, denoted by $k$, is a measure of the stiffness of a spring. It quantifies the amount of force required to compress or extend the spring by a unit length.

5 Must Know Facts For Your Next Test

1. The spring constant $k$ is defined in Hooke's Law: $F = kx$, where $F$ is the force applied and $x$ is the displacement.
2. The unit of the spring constant in the International System of Units (SI) is Newtons per meter (N/m).
3. A larger value of $k$ indicates a stiffer spring, while a smaller value indicates a more flexible spring.
4. In physical applications, integration can be used to calculate work done by or on a spring: $W = \frac{1}{2}kx^2$.
5. The area under the force vs. displacement graph for a linear spring represents the work done on the spring.

Review Questions

• What does the spring constant represent in Hooke's Law?
• How do you calculate work done on a spring using integration?
• What are the units of the spring constant in SI?

Related terms

Hooke's Law: A principle stating that the force needed to extend or compress a spring by some distance is proportional to that distance: $F = kx$.

Work: In physics, work refers to energy transfer when an object is moved over a distance by an external force: $W = Fd \cos(\theta)$.

Potential Energy: Stored energy due to position or configuration; for springs, it is given by $U = \frac{1}{2}kx^2$.