# Spring Fall Lab Report

1345 Words
6 Pages

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)

The slope is what was left of the equation: (g sinθ)/k. g and sinθ 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 sinθ)/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 sinθ)/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 sinθ)/∆x

Predicted Graph Mass vs Change in

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 sinθ)/k. g and sinθ 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 sinθ)/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 sinθ)/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 sinθ)/∆x

Predicted Graph Mass vs Change in