# Lab Experiment : How Much A Spring Resists Change ( Compression Or Expansion )

The purpose of the lab is to design an experiment to verify the spring constant for an unknown spring, also known as k, how much a spring resists change (compression or expansion). We used a method changing a mass and measured the change in x.

Theory

Free Body Diagram a=0 Legend:

¬¬ a-acceleration Sp-Spring N-Normal S-Surface E-Earth C-Cart G-Gravity y- Y-Component x- X-Component

Mathematical Model

Basic Equations:

Force Equation (used to find the force of any given object):

F=ma

F-Net Force, m-mass, a-acceleration

Summation of Forces on X-Axis:

〖ΣF〗^x=F^(G,x)-F^Sp

〖ΣF〗^x is the sum of the forces on the x-axis, denoted by the superscript x, and the x-axis follows the Free-Body Diagram above. F^(G,x) is the x-component of the Force of Gravity by the Earth on the cart. F^Sp is the Force of Spring on the cart.

Hooke’s Law for Springs:

F^Sp=-k(x-x_0)

Hooke’s Law is an equation used to find the relationship between the force applied to a spring at equilibrium and stretch of a spring. As above, this force is denoted by F^Sp, and is the Force of Spring on the cart. k is the “spring constant:” a constant factor describing the stiffness of the spring. It is negative or positive according to the spring’s restoring force which is opposite of the change in x (displacement). x is the displacement of the spring, x_0 is the original (equilibrium) position of the spring, thus (x-x_0) is the change in x or distance spring is…