1: Elasticity

Example number 1.1, Page number 30

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=3;     #length of wire(m)
A=6.25*10**-5;     #cross sectional area(m**2)
delta_L=3*10**-3;   #increase in length(m)
F=1.2*10**3;        #force(N)

#Calculation
Y=F*L/(A*delta_L);      #young's modulus(N/m**2)

#Result
print "young's modulus is ",Y/10**10,"*10**10 N/m**2"

young's modulus is  1.92 *10**10 N/m**2

Example number 1.2, Page number 30

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
Y=2*10**11;       #young's modulus(N/m**2)
L=2.75;     #length of wire(m)
d=1*10**-3;       #diameter(m)
M=1;      #applied load(kg)
g=9.8;     #acceleration due to gravity(N)

#Calculation
T=M*g;    #tension(N)
delta_L=T*L/(math.pi*(d/2)**2*Y);    #increase in length of wire(m)

#Result
print "increase in length of wire is",round(delta_L*10**4,5),"*10**-4 m"

increase in length of wire is 1.71569 *10**-4 m

Example number 1.3, Page number 31

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
F=0.3;        #force(N)
d=5*10**-3;     #displacement(m)
L=6*10**-2;     #length of solid(m)
B=6*10**-2;     #breadth of solid(m)
h=2*10**-2;     #height of solid(m)

#Calculation
s=F/(L*B);      #shear stress(N/m**2)
theta=d/h;      #shear strain
rm=s/theta;     #rigidity modulus(N/m**2)

#Result
print "shear stress is",round(s,2),"N/m**2"
print "shear strain is",theta
print "rigidity modulus is",round(rm,2),"N/m**2"

shear stress is 83.33 N/m**2
shear strain is 0.25
rigidity modulus is 333.33 N/m**2

Example number 1.4, Page number 32

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
n=2.5*10**10;     #rigidity modulus(N/m**2)
L=30*10**-2;      #thickness(m)
A=12*10**-4;      #surface area(m**2)
delta_L=1.5*10**-2;     #displacement(m)

#Calculation
F=n*A*delta_L/L;      #shearing force(N)

#Result
print "shearing force is",F/10**6,"*10**6 N"

shearing force is 1.5 *10**6 N

Example number 1.6, Page number 33

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
Y=7.25*10**10;       #young's modulus of silver(N/m**2)
K=11*10**10;         #bulk modulus of silver(N/m**2)

#Calculation
sigma=(3*K-Y)/(6*K);    #poisson's ratio

#Result
print "poisson's ratio is",round(sigma,2)

poisson's ratio is 0.39

Example number 1.7, Page number 34

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=3;     #length of Cu wire(m)
Y=12.5*10**10;    #young's modulus(N/m**2)
r=5*10**-4;       #radius of wire(m)
sigma=0.26;       #poisson's ratio
m=10;             #load(kg)
g=9.8;            #acceleration due to gravity(N)

#Calculation
delta_L=m*g*L/(math.pi*r**2*Y);    #extension produced(m)
ls=sigma*delta_L/3;                #lateral strain
dd=ls*r*2;                         #decrease in diameter(m) 

#Result
print "extension produced is",round(delta_L*10**3,2),"*10**-3 m"
print "lateral compression produced is",round(dd*10**7,3),"*10**-7 m"

extension produced is 2.99 *10**-3 m
lateral compression produced is 2.595 *10**-7 m

Example number 1.8, Page number 35

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=1;      #length of wire(m)
d=1*10**-3;     #diameter of wire(m)
n=2.8*10**10;      #rigidity modulus of wire(N/m**2)
theta=math.pi/2;        #angle of twisting(radian)

#Calculation
C=math.pi**2*n*(d/2)**4/(4*L);      #couple to be applied(Nm)

#Result
print "couple to be applied is",round(C*10**3,5),"*10**-3 Nm"

couple to be applied is 4.31795 *10**-3 Nm

Example number 1.9, Page number 35

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=0.82*10**-3;       #diameter of wire(m)
delta_L=1*10**-3;       #length of elongation produced(m)
m=0.33;             #load(kg)
g=9.8;           #acceleration due to gravity(N)
n=2.2529*10**9;    #rigidity modulus of wire(N/m**2)

#Calculation
Y=m*g/(math.pi*(d/2)**2*delta_L);     #young's modulus(N/m**2)
sigma=(Y/(2*n))-1;       #poisson's ratio

#Result
print "poisson's ratio is",round(sigma,3)

poisson's ratio is 0.359

Example number 1.10, Page number 36

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
p1=1.01*10**5;         #atmospheric pressure(N/m**2)
K=16*10**10;          #bulk modulus(N/m**2)
p2=10**2;           #increased pressure(N/m**2)

#Calculation
dP=p1-p2;       #change in pressure(N/m**2)
dV=dP/K;       #fractional change of volume

#Result
print "change in volume of steel bar is",round(dV*10**7,1),"*10**-7 V m**3"

change in volume of steel bar is 6.3 *10**-7 V m**3

Example number 1.11, Page number 37

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
Y=1.013*10**10;       #young's modulus of bar(N/m**2)
b=2*10**-2;       #breadth of bar(m)
l=1;       #length of bar(m)
d=1*10**-2;    #depth of bar(m)
m=2;       #load(kg)
g=9.8;           #acceleration due to gravity(N)

#Calculation
y=m*g*l**3/(4*Y*b*d**3);    #depression produced in bar(m)

#Result
print "depression produced in bar is",round(y,6),"m"

depression produced in bar is 0.024186 m

Example number 1.12, Page number 37

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
r=1.2*10**-2;         #radius of cantilever(m)
l=1.5;        #length of cantilever(m)
Y=19.5*10**10;      #young's modulus(N/m**2)
m=2;       #load(kg)
g=9.8;           #acceleration due to gravity(N)

#Calculation
y=4*m*g*l**3/(3*Y*math.pi*(r**4));    #depression produced in cantilever(m)

#Result
print "depression produced in cantilever is",round(y*10**3,3),"*10**-3 m"

depression produced in cantilever is 6.943 *10**-3 m