Calculators

Physics

This calculator finds the missing variable in the physics equation for Hooke's Law F_s = -kx, when two of the variables are known.

Hooke's Law states that the force needed to extend or compress a spring is directly proportional to the distance the spring is stretched or compressed.

This means that there is a linear relationship between the force required to stretch a spring, and the length the spring is stretched.

Hooke's Law Equation

The Hooke's Law Calculator uses the formula F_s = -kx where F is the restoring force exerted by the spring, k is the spring constant and x is the displacement, or distance the spring is being stretched.

Variables in Hooke's Law Equation

• F_s = spring force
• k = a spring constant
• x = displacement

The equation can also be stated:

\[ F = kx \]

Where F is the force exerted on the spring, k is the spring constant and x is the displacement.

You might see this equation in the case where the problem is in determining what is the force pulling on or compressing the spring.

 

Hooke's Law in terms of Acceleration

To use Hooke's Law to calculate acceleration, we need to combine it with Newton's Second Law, the force equation, F = ma.

With the knowledge that force equals mass times acceleration we can take Hooke's Law Equation:

\[ F = -kx \]

and rewrite it as

\[ ma = -kx \]

dividing both sides of the equation by mass m we get

\[ a = \dfrac{-kx}{m} \]

This equation states that the acceleration of a spring-mass system is directly proportional to the displacement x and inversely proportional to the mass m where k is the spring constant.