Andres Heredia, Esteban Martinez

Introduction

Our experiment will help us model the relation between mass and static friction. We will see what is the maximum force that can be applied to an object before it moves on a flat surface and on an incline.

Procedure

In order to measure the static friction we hooked a spring scale to a box where we put weights. Then we hooked the scale up to the box and made sure that our scale was set to zero, after which we put varying weights in the box. Finally we pulled on the scale until the box moved and wrote down our findings. For the incline we lifted our surface to a 3° angle and measured the static friction again with the same tools as last time, after which we can formulate a model from our data by using the formula:

$ f_s = f_{sp} - mgsin$θ

$ f_s $ = Static friction
$ f_{sp} $ = Spring scale force

$$Flat$$

$$surface$$

mass (g)	Force (N)
100	.25
200	.70
300	1.0
400	1.35
500	1.7

$$On$$

$$incline$$

mass (g)	Force (N)
100	.698
200	.897
300	1.146
400	1.69
500	1.943



In [21]:

    
%matplotlib inline

Data Analysis



In [35]:

    
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit

mass = [ 100, 200, 300, 400, 500]
force = [ .25, .7, 1.0, 1.35, 1.7]
xx = np.linspace(0,600,10)
def lin_model( x, a, b):
    return a*x + b
a,b = curve_fit(lin_model, mass, force)[0]
print(a,b)
plt.title('Static Friction on a Flat Surface VS an Incline')
plt.ylabel ('Friction (N)')
plt.xlabel ('Mass (g)')
plt.plot(xx, lin_model(xx, a, b))
plt.plot(mass,force,'go')


mass2 = [ 100, 200, 300, 400, 500]
force2 = [.698,.897,1.146,1.691, 1.943]
xx = np.linspace(0,600,10)
def lin_model( x, a, b):
    return a*x + b
a,b = curve_fit(lin_model, mass2, force2)[0]
print(a,b)
plt.plot(xx, lin_model(xx, a, b))
plt.plot(mass2,force2,'go')









    



0.00354999999783 -0.0650000000023
0.00328399999698 0.289800000749






    Out[35]:





[<matplotlib.lines.Line2D at 0x9555438>]

Conclusion

The model that describes the relationship betweem mass and Static friction for a flat surface is $$ 0.00355x - 0.06500 $$ The model that describes the relationship betweem mass and Static friction for an incline is $$ 0.00328x + 0.2898 $$

Looking at the data we can conclude that the realtionship between mass and static friction is linear. If we were given a quantity for mass, we would be able to output a measure for static friction in newtons using these models. We've found that the angle of our incline affects the slope, therefore we'd have to create a model that accounts for the angle variable and works for both a flat surface and incline.



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