# Spring Fall Lab Report

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Purpose
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)
…show more content…
The slope is what was left of the equation: (g sin⁡θ)/k. g and sin⁡θ are constants which leave us with our unknown quantity, k, which was our goal solve in the procedure. Our mathematical model was as follows:
∆x=(mg sin⁡θ)/k
As explained above, the change in x (∆x) depends on the change in mass, which we can change, therefore:
Independent Variable: mass (m)
Dependent Variable: ∆x
To extract information from our graph, we used the x-value as (m), the y-value as ∆x, and the slope as (g sin⁡θ)/k, as explained in the “slope intercept” form from above. We used what the variables meant above to calculate our unknown quantity, k, in the rearranged equation of our mathematical model below: k=(mg sin⁡θ)/∆x
Predicted Graph Mass vs Change in