{
"metadata": {
"name": "",
"signature": "sha256:aa8849d14e0b72277789cfe0c1cc3e7e66ca9061ac47dccbae27561c50c68d32"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 1 Motion"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1 Page no 17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"d=180 #Distance of satellite above the surface of earth in km\n",
"t=90 #Time taken to complete one revolution of the earth in minutes\n",
"r=6400 #Radius of the earth in kms\n",
"\n",
"#Calculations\n",
"R=(r+d)*1000\n",
"T=t*60\n",
"v=(2*3.14*R)/T\n",
"a=(v**2/R)\n",
"\n",
"#Output\n",
"print\"Orbital speed is \",round(v,0),\"m/s\" \n",
"print\"Centripetal acceleration is \",round(a,1),\"m/s**2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Orbital speed is 7652.0 m/s\n",
"Centripetal acceleration is 8.9 m/s**2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.2 Page no 17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=0.05 #Mass of the stone in kg\n",
"r=0.4 #Radius of the string in m\n",
"\n",
"#Calculations\n",
"import math\n",
"vh=math.sqrt(9.8*r)\n",
"vl=math.sqrt((2/m)*(((1/2.0)*m*vh**2)+(m*9.8*2*r)))\n",
"\n",
"#Output\n",
"print\"Minimum speed when the stone is at the top of the circle is \",round(vh,2),\"m/s\" \n",
"print\"Minimum speed when the stone is at the bottom of the circle is \",round(vl,2),\"m/s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Minimum speed when the stone is at the top of the circle is 1.98 m/s\n",
"Minimum speed when the stone is at the bottom of the circle is 4.43 m/s\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.3 Page no 17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=0.2 #Mass of the ball in kg\n",
"r=1.5 #Radius of vertical circle in m\n",
"q=35 #Angle made by the ball in degrees\n",
"v=6 #Velocity of the ball in m/s\n",
"\n",
"#Calculations\n",
"import math\n",
"T=(m*((v**2/r)+(9.8*math.cos(q*3.14/180.0))))\n",
"at=9.8*math.sin(q*3.14/180.0)\n",
"ar=(v**2/r)\n",
"a=math.sqrt(at**2+ar**2)\n",
"\n",
"#Output\n",
"print\"Tension in the string is \",round(T,1),\"N\" \n",
"print\"Tangential acceleration is \",round(at,2),\"m/s**2\" \n",
"print\"Radial acceleration is \",ar,\"m/s**2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Tension in the string is 6.4 N\n",
"Tangential acceleration is 5.62 m/s**2\n",
"Radial acceleration is 24.0 m/s**2\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.4 Page no 17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"#A small ball is released from height of 4r measured from the bottom of the loop, where r is the radius of the loop\n",
"\n",
"#Calculations\n",
"import math\n",
"ar=(6*9.8)\n",
"at=(9.8*math.sin(90*3.14/180.0))\n",
"\n",
"#Output\n",
"print\"Radial acceleration is \",ar,\"m/s**2\"\n",
"print\"Tangential acceleration is \",round(at,1),\"m/s**2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Radial acceleration is 58.8 m/s**2\n",
"Tangential acceleration is 9.8 m/s**2\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.5 Page no 18"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"l=0.95 #Length of the strring in m\n",
"m=0.15 #Mass of the bob in kg\n",
"r=0.25 #Radius of the circle in m\n",
"\n",
"#Calculations\n",
"import math\n",
"h=math.sqrt(l**2-r**2)\n",
"t=2*3.14*math.sqrt(h/9.8)\n",
"\n",
"#Output\n",
"print\"The period of rotation is \",round(t,2),\"s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The period of rotation is 1.92 s\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.6 Page no 18"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"N=40.0 #Minimum speed of rotor in rpm\n",
"r=2.5 #Radius of rotor in m\n",
"\n",
"#Calculations\n",
"t=60/N\n",
"u=(9.8*t**2)/(4.0*3.14**2*r)\n",
"\n",
"#Output\n",
"print\"The coefficient of limiting friction between the object and the wall of the rotor is \",round(u,3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The coefficient of limiting friction between the object and the wall of the rotor is 0.224\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.7 Page no 18"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"a=30 #Angle of inclination in degrees\n",
"t=3 #Time in s\n",
"\n",
"#Calculations\n",
"import math\n",
"a=(9.8*math.sin(a*3.14/180.0))\n",
"v=(0+a*t)\n",
"\n",
"#Output\n",
"print\"Speed of the block after \",t,\"s is \",round(v,1),\"m/s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Speed of the block after 3 s is 14.7 m/s\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.8 Page no 19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=10.0 #Mass of the block in kg\n",
"F1=40 #Horizontal force to start moving in N\n",
"F2=32 #Horizontal force to move with constant velocity in N\n",
"\n",
"#Calculations\n",
"u1=(F1/(m*9.8))\n",
"u2=(F2/(m*9.8))\n",
"\n",
"#Output\n",
"print\"Coefficient of static friction is \",round(u1,3)\n",
"print\"Coefficient of kinetic friction is \",round(u2,4)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Coefficient of static friction is 0.408\n",
"Coefficient of kinetic friction is 0.3265\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.9 Page no 19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=(3,12) #Masses of the blocks in kg\n",
"q=50 #Angle made by the string in degrees\n",
"a=3 #Acceleration of 12kg block in m/s^2\n",
"\n",
"#Calculations\n",
"import math\n",
"T=m[0]*(9.8+a)\n",
"u=(m[1]*(9.8*math.sin(q*3.14/180.0)-a)-T)/(m[1]*9.8*math.cos(q*3.14/180.0))\n",
"\n",
"#Output\n",
"print\"Tension in the string is \",T,\"N\" \n",
"print\"The coefficient of kinetic friction is \",round(u,3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Tension in the string is 38.4 N\n",
"The coefficient of kinetic friction is 0.207\n"
]
}
],
"prompt_number": 54
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.e.1 Page no 9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"w=50 #Weight in N\n",
"a=(40,50) #Angles made by two cables in degrees\n",
"\n",
"#Calculations\n",
"#Solving two equations obtained from fig. 1.10 on page no.10\n",
"#-T1cos40+T2cos50=0\n",
"#T1sin40+T2sin50=50\n",
"import math\n",
"A = array([[math.cos(a[1]*3.14/180.0),-math.cos(a[0]*3.14/180.0)], \n",
" [math.sin(a[0]*3.14/180.0),math.sin(a[1]*3.14/180.0)]])\n",
"b = array([0,50])\n",
"X = solve(A, b)\n",
"T2=X[1]\n",
"print \"T2=\",round(T2,1),\"N\"\n",
"T1=(math.cos(a[1]*3.14/180.0)/math.cos(a[0]*3.14/180.0))*T2\n",
"print \"T1\",round(T1,1),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"T2= 32.7 N\n",
"T1 27.4 N\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.e.5 Page no 13"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=100.0 #Mass of block in kg\n",
"F=500 #Force in N\n",
"q=30 #Angle made with the horizontal in degrees\n",
"u=0.4 #Coefficient of sliding friction\n",
"\n",
"#Calculations\n",
"R=m*9.8\n",
"f=(u*R)\n",
"a=(F*math.cos(q*3.14/180.0)-f)/m\n",
"\n",
"#Output\n",
"print\"The acceleration of the block is \",round(a,2),\"m/s**2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The acceleration of the block is 0.41 m/s**2\n"
]
}
],
"prompt_number": 56
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.e.6 Page no 14"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=(20.0,80.0) #Masses of blocks in kg\n",
"F=1000 #Force with which 20kg block is pulled in N\n",
"\n",
"#Calculations\n",
"a=F/(m[0]+m[1])\n",
"T=F-(m[0]*a)\n",
"\n",
"#Output\n",
"print\"The acceleration produced is \",a,\"m/s^2\" \n",
"print\"The tension in the string connecting the blocks is \",T,\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The acceleration produced is 10.0 m/s^2\n",
"The tension in the string connecting the blocks is 800.0 N\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.e.8 Page no 15"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"w=588 #Weight of the person in N\n",
"a=3 #Acceleration in m/s^2\n",
"b=180\n",
"\n",
"#Calculations\n",
"m=(w/9.8)\n",
"P=(w+(m*a))\n",
"p=w-b\n",
"\n",
"#Output\n",
"print\"Weight of the person when the elevator is accelerated upwards is \",P,\"N\"\n",
"print\"Weight of the person when the elevator is accelerated upwards is \",p,\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Weight of the person when the elevator is accelerated upwards is 768.0 N\n",
"Weight of the person when the elevator is accelerated upwards is 408 N\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}