Andres Heredia, Esteban Martinez
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
$$surface$$
mass (g) | Force (N) |
---|---|
100 | .25 |
200 | .70 |
300 | 1.0 |
400 | 1.35 |
500 | 1.7 |
$$incline$$
mass (g) | Force (N) |
---|---|
100 | .698 |
200 | .897 |
300 | 1.146 |
400 | 1.69 |
500 | 1.943 |
In [21]:
%matplotlib inline
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')
Out[35]:
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.
In [ ]: