Chapter 6 : Friction

Example 6.1 Page No : 115

In [3]:
import math 
			
# Variables
W = 100. 			#lb
Frictioncoefficient = 0.65
			
# Calculations
A1 = math.degrees(math.atan(Frictioncoefficient))
			
# Results
print  'Maximum Incliantion = %.f degrees'%(A1)

Maximum Incliantion = 33 degrees

Example 6.2 Page No : 115

In [2]:
import math 
			
# Variables
W = 100.     			#lb
Frictioncoefficient = 0.40
x = 3.
y = 4.
			
# Calculations
Fmax = (W*y/(math.sqrt(x**2+y**2)))+Frictioncoefficient*W*x/(math.sqrt(x**2+y**2))
Fmin =(W*y/(math.sqrt(x**2+y**2)))-Frictioncoefficient*W*x/(math.sqrt(x**2+y**2))
 			
# Results
print  'Fmin = %.f lb'%(Fmin)
print  'Fmax =%.f lb'%(Fmax)

Fmin = 56 lb
Fmax =104 lb

Example 6.3 Page No : 116

In [3]:
import math 
from numpy import linalg
			
# Variables
mus = 0.25
d = 0.5 			#in
h = 3.   			#in
			
# Calculations
A = [[1, -1],[mus, mus]]
b = [0,1]
c = linalg.solve(A,b)
Na = c[0]
Nb = c[1]
d = -d*mus*Na+h*Na
			
# Results
print  'minimu distance = %.2f in'%(d)

minimu distance = 5.75 in

Example 6.4 Page No : 118

In [9]:
import math 
			
# Variables
Ft = 1000. 			#lb
a1 = 5. 			#degrees
mu = 0.30
			
# Calculations
R1 = Ft/math.cos(a1+math.tan(mu))
F = R1*math.sin(a1)+math.tan(mu)+math.tan(mu)/math.sin(90-math.tan(mu))
			
# Results
print  'Forec required to start wedge = %.f lb'%(F)

Forec required to start wedge = -1705 lb

Example 6.5 Page No : 120

In [10]:
			
import math 

# Variables
W = 100. 			#lb
n1 = 1/2.
n2 = 3/2.
mus = 0.40
			
# Calculations
Ts1 = W/(math.exp(mus*n1*2*math.pi))
Ts2 =  W/(math.exp(mus*n2*2*math.pi)) 
			
# Results
print  'Ts1 = %.2f lb'%(Ts1)
print  'Ts2 =%.2f lb'%(Ts2)

Ts1 = 28.46 lb
Ts2 =2.31 lb

Example 6.6 Page No : 121

In [5]:
import math 
from numpy import linalg
			
# Variables
F = 20.			#lb
L1 = 6. 			#in
L2 = 12. 			#in
L3 = 24. 			#in
mus = 0.60
			
# Calculations
A =[[1,-math.exp(mus*math.pi)],[(L1+L2),(L1)]]
b =[0,F*(L1+L2+L3)]
c = linalg.solve(A,b)
TL = c[0]
Ts = c[1]
			
# Results
print  'TL = %.2f lb'%(TL)
print  'Ts = %.2f lb'%(Ts)

# note : answers are slightly different because of rounding off errors.

TL = 44.42 lb
Ts = 6.74 lb

Example 6.7 Page No : 123

In [12]:
import math 
			
# Variables
d = 24. 			#in
mu = 0.05
W = 2000. 			#lb
			
# Calculations
F = W*mu*2/d
			
# Results
print  'F = %.2f lb'%(F)

F = 8.33 lb

Example 6.8 Page No : 124

In [13]:
import math 
			
# Variables
F = 800. 			#lb
muk = 0.10
Do = 5. 			#in
Di = 3. 			#in
			
# Calculations
M = 2*muk*F*((Do/2)**3-(Di/2)**3)/(3*((Do/2)**2-(Di/2)**2))
			
# Results
print  'M = %.f lb in'%(M)

M = 163 lb in