4: Mechanics of Continuous Media

Example number 1, Page number 162

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

#Variable declaration
F=1200*9.8;           #tensile force(N)
A=0.025*10**-4;       #area(m**2)
delta_l=0.003;        #extension(m)
l=3;                  #length(m)

#Calculation
Y=F*l/(A*delta_l);    #youngs modulus(N/m**2)

#Result
print "youngs modulus is",round(Y/10**12,1),"*10**12 N/m**2"

youngs modulus is 4.7 *10**12 N/m**2

Example number 2, Page number 162

In [37]:
#importing modules
import math
from __future__ import division

#Variable declaration
v=3500;              #volume(cm**3)
K=10*10**11;         #bulk modulus(dyne/cm**2)
p=24*76*13.6*980;    #change in pressure(dyne/cm**2)

#Calculation
delta_v=p*v/K;       #volume occupied(cm**3)
V=v-delta_v;         #volume occupied at 25atm(cm**3)

#Result
print "volume occupied at 25atm is",int(V),"cm**3"
print "answer given in the book is wrong"

volume occupied at 25atm is 3499 cm**3
answer given in the book is wrong

Example number 3, Page number 163

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration
eta=1;               #assume
Y=2.5*eta;           #youngs modulus

#Calculation
sigma=Y/(2*eta)-1;   #poissons ratio

#Result
print "poissons ratio is",sigma

poissons ratio is 0.25

Example number 4, Page number 163

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=0.1;           #side of cube(m)
p=10**6;         #static pressure(pa)
delta_v=10**-8;  #change in volume(m**3)

#Calculation
v=l**3;          #volume of cube(m**3)
K=p*v/delta_v;   #bulk modulus(N/m**2)

#Result
print "bulk modulus is",int(K/10**11),"*10**11 N/m**2"

bulk modulus is 1 *10**11 N/m**2

Example number 5, Page number 163

In [38]:
#importing modules
import math
from __future__ import division

#Variable declaration
Y=2*10**11;           #youngs modulus(N/m**2)
eta=8*10**10;         #rigidity modulus(N/m**2)

#Calculation
sigma=Y/(2*eta)-1;    #poissons ratio
K=Y/(3*(1-2*sigma));  #bulk modulus(N/m**2)

#Result
print "poissons ratio is",sigma
print "bulk modulus is",round(K/10**11,2),"*10**11 N/m**2"

poissons ratio is 0.25
bulk modulus is 1.33 *10**11 N/m**2

Example number 6, Page number 163

In [39]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=2;               #length(m)
A=2*10**-6;        #area(m**2)
e=5*10**-3;        #elongation(m)
rho=9000;          #density(Kg/m**3)
C=4200;            #specific heat(J/Kg/K)
F=1000;            #force(N)

#Calculation
v=l*A;             #volume(m**3)
W=F*e*v/(2*A*l);   #work done(J)
m=rho*v;           #mass(kg)
delta_t=W/(m*C);   #increase in temperature(K)

#Result
print "increase in temperature is",round(delta_t,5),"K"

increase in temperature is 0.01653 K

Example number 7, Page number 164

In [40]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=3;                #length(m)
A=2.5*10**-6;       #area(m**2)
e=3*10**-3;         #elongation(m)
F=750;              #force(N)

#Calculation
v=l*A;              #volume(m**3)
E=F*e*v/(2*A*l);    #potential energy(J)

#Result
print "potential energy is",E,"J"
print "answer given in the book is wrong"

potential energy is 1.125 J
answer given in the book is wrong

Example number 8, Page number 164

In [47]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=0.5;          #length(m)
x=0.5;          #depression(m)
y=15*10**-3;    #depression(m)
x1=0.3;         #depression(m)

#Calculation
A=(L*x**2/2)-(x**3/6);            
y1=y*((L*x1**2/2)-(x1**3/6))/A;   #depression of the rod from fixed end(m)

#Result
print "depression of the rod from fixed end is",y1,"m"
print "answer given in the book is wrong"

depression of the rod from fixed end is 0.00648 m
answer given in the book is wrong

Example number 9, Page number 165

In [48]:
#importing modules
import math
from __future__ import division

#Variable declaration
r=0.4;          #radius(cm)
l=100;          #length(cm)
phi=60;         #twisting angle(degree)

#Calculation
theta=r*phi/l       #deformation strain

#Result
print "deformation strain is",theta

deformation strain is 0.24

Example number 10, Page number 165

In [52]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=0.1;       #mass(kg)
g=9.8;       #acceleration due to gravity(m/sec**2)
L=1;         #length(m)
Y=10**10;    #youngs modulus(N/m**2)
r=0.02;      #radius of wire(m)

#Calculation
y1=5*m*g*L**3/(12*Y*math.pi*r**4);       #depression at the mid point(m)

#Result
print "depression at the mid point is",round(y1*10**5,3),"*10**-5 m"
print "answer given in the book is wrong"

depression at the mid point is 8.124 *10**-5 m
answer given in the book is wrong