{
"metadata": {
"name": "chapter 1 som.ipynb"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 1:Centre Of Gravity\n"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 1.1,Page No.8"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of Variables\n",
"\n",
"#Rectangle-1\n",
"a_1=37.5 #cm**2 \n",
"y_1=26.25 #cm \n",
"\n",
"#Rectangle-2\n",
"a_2=50 #cm**2 \n",
"y_2=15 #cm \n",
"\n",
"#Rectangle-3\n",
"a_3=150 #cm**2 \n",
"y_3=2.5 #cm \n",
"\n",
"\n",
"#Calculation\n",
"\n",
"\n",
"Y_bar=(a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1 #cm \n",
"\n",
"#Result\n",
"print\"The centroid of the section is\",round(Y_bar,2),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centroid of the section is 8.88 cm\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 1.2,Page No.9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"#Area-1\n",
"a_1=6 #cm**2 \n",
"x_1=3 #cm\n",
"y_1=0.5 #cm\n",
"\n",
"#Area-2\n",
"a_2=6 #cm**2\n",
"x_2=2.671 #cm\n",
"y_2=3 #cm\n",
"\n",
"#Area-3\n",
"a_3=16 #cm**2\n",
"x_3=1 #cm\n",
"y_3=5 #cm\n",
"\n",
"\n",
"#Calculation\n",
"\n",
"\n",
"X_bar=(a_1*x_1+a_2*x_2+a_3*x_3)*(a_1+a_2+a_3)**-1 #cm\n",
"Y_bar=(a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1 #cm\n",
"\n",
"\n",
"#Result\n",
"print\"The centre of gravity of section is\",round(X_bar,2),\"cm\"\n",
"print\"The centre of gravity of section is\",round(Y_bar,2),\"cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centre of gravity of section is 1.79 cm\n",
"The centre of gravity of section is 3.61 cm\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 1.3,Page no.10"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"#Area-1\n",
"a_1=93.75 #cm**2 \n",
"y_1=6.25 #cm\n",
"\n",
"#Area-2\n",
"a_2=93.75 #cm**2 \n",
"y_2=6.25 #cm\n",
"\n",
"#Area-3\n",
"a_3=375 #cm**2 \n",
"y_3=9.375 #cm\n",
"\n",
"#Area-4\n",
"a_4=353.43 #cm**2\n",
"y_4=6.366 #cm\n",
"\n",
"\n",
"#Calculation\n",
"\n",
"Y_bar=(a_1*y_1+a_2*y_2+a_3*y_3-a_4*y_4)*(a_1+a_2+a_3-a_4)**-1 #cm\n",
"\n",
"\n",
"#Result\n",
"print\"The centre of gravity lies at a distance of \",round(Y_bar,2),\"cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centre of gravity lies at a distance of 11.66 cm\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 1.4,Page no.10\n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"\n",
"a_1=36*pi #cm**2 #Area of Quadrant of a circle\n",
"x_1=16/pi #cm \n",
"y_1=16*pi**-1 #cm\n",
"\n",
"\n",
"a_2=18*pi #cm**2 #Area of the semicircle\n",
"x_2=6 #cm\n",
"y_2=8*pi**-1 #cm\n",
"\n",
"\n",
"#Calculation-1\n",
"\n",
"X_bar=(a_1*x_1-a_2*x_2)*(a_1-a_2)**-1 #cm\n",
"\n",
"#Calculation-2\n",
"#To calculate Y_bar,taking AB as the Reference line\n",
"\n",
"Y_bar=(a_1*y_1-a_2*y_2)*(a_1-a_2)**-1 #cm\n",
"\n",
"#Result\n",
"\n",
"print\"The centre of gravity is \",round(X_bar,2),\"cm\"\n",
"print\"The centre of gravity is\",round(Y_bar,2),\"cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centre of gravity is 4.19 cm\n",
"The centre of gravity is 7.64 cm\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 1.5,Page no.11"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"#Circle-1 \n",
"a_1=100*pi #cm**2\n",
"x_1=10 #cm\n",
" \n",
"#Square-2 \n",
"a_2=50 #cm**2\n",
"x_2=15 #cm\n",
" \n",
"#Calculation\n",
"\n",
"X_bar=(a_1*x_1-a_2*x_2)*(a_1-a_2)**-1 #cm\n",
"\n",
"\n",
"#Result\n",
"print\"The centre of gravity is\",round(X_bar,2),\"cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centre of gravity is 9.05 cm\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 1.6,Page no.12\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#intilization of variables \n",
"\n",
"#Rectangle-1\n",
"a_1=51200 #mm**2 \n",
"x_1=160 #mm\n",
"y_1=80 #mm\n",
"\n",
"#Triangle-2\n",
"a_2=6400 #mm**2\n",
"x_2=80*3**-1 #mm\n",
"y_2=320*3**-1 #mm\n",
"\n",
"#Semicircle-3\n",
"a_3=1250*pi #mm**2\n",
"x_3=210 #mm\n",
"y_3=(160-(4*50-(3*pi)**-1)) #mm\n",
"\n",
"\n",
"#Calculation\n",
"\n",
"X_bar=(a_1*x_1-a_2*x_2-a_3*x_3)*(a_1-a_2-a_3)**-1 #mm\n",
"Y_bar=(a_1*y_1-a_2*y_2-a_3*y_3)*(a_1-a_2-a_3)**-1 #mm\n",
"\n",
"#Result\n",
"print\"The centroid of the given area is\",round(X_bar,2),\"mm\"\n",
"print\"The centroid of the given area is\",round(Y_bar,2),\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centroid of the given area is 176.07 mm\n",
"The centroid of the given area is 87.34 mm\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 1.8,Page no.12"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"\n",
"alpha=pi/2 #degree #In case of semicircle\n",
"\n",
"#Semicircle-1\n",
"r_1=20 #cm #radius of semicircle \n",
"y_1=4*r_1*(3*pi)**-1 #cm #distance from the base\n",
"a_1=(pi*r_1**2)*2**-1 #cm**2 #area of semicircle\n",
"\n",
"#Semicircle-2\n",
"r_2=16 #cm #radius of semicircle\n",
"y_2=4*r_2*(3*pi)**-1 #cm #distance from the base\n",
"a_2=(pi*r_2**2)*2**-1 #cm**2 #area of semicircle\n",
"\n",
"#Calculations\n",
"\n",
"\n",
"Y_bar=(a_1*y_1-a_2*y_2)*(a_1-a_2)**-1 #cm #centroid\n",
"\n",
"\n",
"#Result\n",
"print\"The centroid of the area is \",round(Y_bar,2),\"cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centroid of the area is 11.51 cm\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem no1.12,Page no.16"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"#Right Circular Cyclinder\n",
"#m_1=(16*pi*h*rho_1) #gm \n",
"#y_1=4+h*2**-1 #cm\n",
"\n",
"#Hemisphere\n",
"#m_2=256*pi*rho_1 #gm \n",
"y_2=2.5 #cm \n",
"\n",
"Y_bar=4 #cm\n",
"r=4 #cm\n",
"\n",
"#Calculation\n",
"\n",
"#Y_bar=(m_1*y_1+m_2*y_2)*(m_1+m_2)**-1 #cm #Centroid\n",
"h=(402.114*25.132**-1)**0.5\n",
"\n",
"#Result\n",
"print\"The value of h is\",round(h,2),\"cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of h is 4.0 cm\n"
]
}
],
"prompt_number": 2
}
],
"metadata": {}
}
]
}