{
"metadata": {
"name": "",
"signature": "sha256:be338ef971644a9f5f4678fb763a92b7fd97bf3ce5a24c5818759072b8dab2d8"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"1: Elasticity"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.1, Page number 30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"L=3; #length of wire(m)\n",
"A=6.25*10**-5; #cross sectional area(m**2)\n",
"delta_L=3*10**-3; #increase in length(m)\n",
"F=1.2*10**3; #force(N)\n",
"\n",
"#Calculation\n",
"Y=F*L/(A*delta_L); #young's modulus(N/m**2)\n",
"\n",
"#Result\n",
"print \"young's modulus is \",Y/10**10,\"*10**10 N/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"young's modulus is 1.92 *10**10 N/m**2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.2, Page number 30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Y=2*10**11; #young's modulus(N/m**2)\n",
"L=2.75; #length of wire(m)\n",
"d=1*10**-3; #diameter(m)\n",
"M=1; #applied load(kg)\n",
"g=9.8; #acceleration due to gravity(N)\n",
"\n",
"#Calculation\n",
"T=M*g; #tension(N)\n",
"delta_L=T*L/(math.pi*(d/2)**2*Y); #increase in length of wire(m)\n",
"\n",
"#Result\n",
"print \"increase in length of wire is\",round(delta_L*10**4,5),\"*10**-4 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"increase in length of wire is 1.71569 *10**-4 m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.3, Page number 31"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"F=0.3; #force(N)\n",
"d=5*10**-3; #displacement(m)\n",
"L=6*10**-2; #length of solid(m)\n",
"B=6*10**-2; #breadth of solid(m)\n",
"h=2*10**-2; #height of solid(m)\n",
"\n",
"#Calculation\n",
"s=F/(L*B); #shear stress(N/m**2)\n",
"theta=d/h; #shear strain\n",
"rm=s/theta; #rigidity modulus(N/m**2)\n",
"\n",
"#Result\n",
"print \"shear stress is\",round(s,2),\"N/m**2\"\n",
"print \"shear strain is\",theta\n",
"print \"rigidity modulus is\",round(rm,2),\"N/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"shear stress is 83.33 N/m**2\n",
"shear strain is 0.25\n",
"rigidity modulus is 333.33 N/m**2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.4, Page number 32"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=2.5*10**10; #rigidity modulus(N/m**2)\n",
"L=30*10**-2; #thickness(m)\n",
"A=12*10**-4; #surface area(m**2)\n",
"delta_L=1.5*10**-2; #displacement(m)\n",
"\n",
"#Calculation\n",
"F=n*A*delta_L/L; #shearing force(N)\n",
"\n",
"#Result\n",
"print \"shearing force is\",F/10**6,\"*10**6 N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"shearing force is 1.5 *10**6 N\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.6, Page number 33"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Y=7.25*10**10; #young's modulus of silver(N/m**2)\n",
"K=11*10**10; #bulk modulus of silver(N/m**2)\n",
"\n",
"#Calculation\n",
"sigma=(3*K-Y)/(6*K); #poisson's ratio\n",
"\n",
"#Result\n",
"print \"poisson's ratio is\",round(sigma,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"poisson's ratio is 0.39\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.7, Page number 34"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"L=3; #length of Cu wire(m)\n",
"Y=12.5*10**10; #young's modulus(N/m**2)\n",
"r=5*10**-4; #radius of wire(m)\n",
"sigma=0.26; #poisson's ratio\n",
"m=10; #load(kg)\n",
"g=9.8; #acceleration due to gravity(N)\n",
"\n",
"#Calculation\n",
"delta_L=m*g*L/(math.pi*r**2*Y); #extension produced(m)\n",
"ls=sigma*delta_L/3; #lateral strain\n",
"dd=ls*r*2; #decrease in diameter(m) \n",
"\n",
"#Result\n",
"print \"extension produced is\",round(delta_L*10**3,2),\"*10**-3 m\"\n",
"print \"lateral compression produced is\",round(dd*10**7,3),\"*10**-7 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"extension produced is 2.99 *10**-3 m\n",
"lateral compression produced is 2.595 *10**-7 m\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.8, Page number 35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"L=1; #length of wire(m)\n",
"d=1*10**-3; #diameter of wire(m)\n",
"n=2.8*10**10; #rigidity modulus of wire(N/m**2)\n",
"theta=math.pi/2; #angle of twisting(radian)\n",
"\n",
"#Calculation\n",
"C=math.pi**2*n*(d/2)**4/(4*L); #couple to be applied(Nm)\n",
"\n",
"#Result\n",
"print \"couple to be applied is\",round(C*10**3,5),\"*10**-3 Nm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"couple to be applied is 4.31795 *10**-3 Nm\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.9, Page number 35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=0.82*10**-3; #diameter of wire(m)\n",
"delta_L=1*10**-3; #length of elongation produced(m)\n",
"m=0.33; #load(kg)\n",
"g=9.8; #acceleration due to gravity(N)\n",
"n=2.2529*10**9; #rigidity modulus of wire(N/m**2)\n",
"\n",
"#Calculation\n",
"Y=m*g/(math.pi*(d/2)**2*delta_L); #young's modulus(N/m**2)\n",
"sigma=(Y/(2*n))-1; #poisson's ratio\n",
"\n",
"#Result\n",
"print \"poisson's ratio is\",round(sigma,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"poisson's ratio is 0.359\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.10, Page number 36"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"p1=1.01*10**5; #atmospheric pressure(N/m**2)\n",
"K=16*10**10; #bulk modulus(N/m**2)\n",
"p2=10**2; #increased pressure(N/m**2)\n",
"\n",
"#Calculation\n",
"dP=p1-p2; #change in pressure(N/m**2)\n",
"dV=dP/K; #fractional change of volume\n",
"\n",
"#Result\n",
"print \"change in volume of steel bar is\",round(dV*10**7,1),\"*10**-7 V m**3\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"change in volume of steel bar is 6.3 *10**-7 V m**3\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.11, Page number 37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Y=1.013*10**10; #young's modulus of bar(N/m**2)\n",
"b=2*10**-2; #breadth of bar(m)\n",
"l=1; #length of bar(m)\n",
"d=1*10**-2; #depth of bar(m)\n",
"m=2; #load(kg)\n",
"g=9.8; #acceleration due to gravity(N)\n",
"\n",
"#Calculation\n",
"y=m*g*l**3/(4*Y*b*d**3); #depression produced in bar(m)\n",
"\n",
"#Result\n",
"print \"depression produced in bar is\",round(y,6),\"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depression produced in bar is 0.024186 m\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.12, Page number 37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"r=1.2*10**-2; #radius of cantilever(m)\n",
"l=1.5; #length of cantilever(m)\n",
"Y=19.5*10**10; #young's modulus(N/m**2)\n",
"m=2; #load(kg)\n",
"g=9.8; #acceleration due to gravity(N)\n",
"\n",
"#Calculation\n",
"y=4*m*g*l**3/(3*Y*math.pi*(r**4)); #depression produced in cantilever(m)\n",
"\n",
"#Result\n",
"print \"depression produced in cantilever is\",round(y*10**3,3),\"*10**-3 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depression produced in cantilever is 6.943 *10**-3 m\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}