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# Hooke's Law

Introduction: In our everyday lives, we are surrounded by elastic springs - from spring mattresses to diving boards. Hooke's Law describes the relationship between the force acting on a spring and its displacement from its equilibrium position. The equation for Hooke's Law is as follows:

$F_s=-kx$, where $F_s$=spring force, k=spring constant, and
x=displacement from equilibrium

The spring force is directly proportional to a spring's displacement from its equilibrium position. However, at equilibrium, the spring force will equal zero. The spring constant refers to the stiffness of the spring and is an important consideration when looking at mattresses. Generally, stiffer springs have higher spring constants. It is also worth noting that the spring force is directly proportional to the spring constant. Generally, as the value of the spring constant increases, the stiffness of the spring is greater and the magnitude of the spring force also increases.

Aside from considerations of spring force and spring stiffness, it is also important to consider the directions of the displacement of the spring and the spring force. The force exerted by the spring is always in the direction opposite that of the spring's displacement from the equilibrium position. The spring force, in this way, acts to return a spring to its position of rest.

Outside of the variables involved in Hooke's Law, one must also consider speed and acceleration. At the equilibrium position, the speed of the spring reaches a maximum. On the other hand, at maximum displacement, the acceleration of the spring reaches a maximum.

Directions for This Lesson: In this lesson, you will learn about Hooke's Law. First, try the practice questions to determine what you already know about Hooke's Law. Then, watch the video lesson to learn more about Hooke's Law.

1. Required Video

2. Activity