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{
"metadata": {
"name": "",
"signature": "sha256:754c71c2e29646e743d2602122b6349e57c8b539ae4803d803ea41cdce275af3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3 Potential energy"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.1 page no 35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=0.04 #Mass of stone in kg\n",
"vi=25 #Initial velocity in m/s\n",
"vf=0 #Final velocity in m/s\n",
"yi=0 #Initial height in m\n",
"\n",
"#Calculations\n",
"import math\n",
"Ui=(m*9.81*yi)\n",
"Ki=(1/2.0)*m*vi**2\n",
"Etotal=(Ui+Ki)\n",
"h=(Etotal/(m*9.8))\n",
"#when the stone is at (2/3)h, total energy is again same\n",
"v=math.sqrt((Etotal-(m*9.8*(2/3.0)*h))/((1/2.0)*m))\n",
"\n",
"#Output\n",
"print\"Maximum height it will reach is \",round(h,1),\"m\" \n",
"print\"velocity when it is at the two-third of its maximum height is \",round(v,2),\"m/s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum height it will reach is 31.9 m\n",
"velocity when it is at the two-third of its maximum height is 14.43 m/s\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.2 page no 36"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=0.5 #Mass of the sphere in kg\n",
"vi=100 #Initial velocity in m/s\n",
"vf=20 #Final velocity in m/s\n",
"\n",
"#Calculations\n",
"h=(vi**2-vf**2)/(2.0*9.8)\n",
"PE=(m*9.8*h)\n",
"\n",
"#Calculations\n",
"print\"Potential energy of the sphere is \",PE,\"J\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Potential energy of the sphere is 2400.0 J\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.3 page no 36"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=0.5 #Mass of the block in kg\n",
"x=0.05 #Distance to which block is pulled in m\n",
"k=300 #Force constant of the spring in N/m\n",
"\n",
"#Calculations\n",
"import math\n",
"U=(1/2.0)*k*x**2\n",
"v=x*math.sqrt(k/m)\n",
"\n",
"#Output\n",
"print\"Potential energy of the block when spring is in stretched position is \",U,\"J\" \n",
"print\"Velocity of the block when it passes through the equilibrium position is \",round(v,2),\" m/s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Potential energy of the block when spring is in stretched position is 0.375 J\n",
"Velocity of the block when it passes through the equilibrium position is 1.22 m/s\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.4 page no 37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"l=0.8 #Length of a simple pendulum in m\n",
"q=30 #Angle with the vertical through which the bob is released in degrees\n",
"q1=10 #Required angle in degrees\n",
"\n",
"#Calculations\n",
"import math\n",
"v=math.sqrt(2*9.8*l*(math.cos(q1*3.14/180.0)-math.cos(q*3.14/180.0)))\n",
"\n",
"#Output\n",
"print\"Speed when the bob is at the angle of \",q1,\"degrees with the vertical is \",round(v,2),\"m/s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Speed when the bob is at the angle of 10 degrees with the vertical is 1.36 m/s\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.5 page no 37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=(9.1*10**-31) #Mass of the electron in kg\n",
"v=(3*10**8) #Velocity of light in m/s\n",
"c=(1.6*10**-19) #Charge of the electron in coloumbs\n",
"\n",
"#Calculations\n",
"import math\n",
"Re=(m*v**2)/(c*10**6)\n",
"E=(Re/math.sqrt(1-0.9**2))\n",
"\n",
"#Output\n",
"print\"Rest energy of the electron is \",round(Re,3),\"MeV\" \n",
"print\"Total energy is \",round(E,2),\"MeV\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rest energy of the electron is 0.512 MeV\n",
"Total energy is 1.17 MeV\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}
|
