{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 1:Relativity"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1,Page no:9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Varible declaration\n",
"t0= 3600 # time interval on Earth, seconds\n",
"t= 3601.0 #time interval for spacecraft as measured from Earth, seconds\n",
"\n",
"#Calculation\n",
"c= 2.998 *(10**8) #speed of light, m/s\n",
"v=c*math.sqrt((1-((t0/t)**2))) #relative velocity of spacecraft, m/s\n",
"\n",
"#Result\n",
"print\"The speed of the Spacecraft relative to Earth is:%.2g \"%v,\"m/s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The speed of the Spacecraft relative to Earth is:7.1e+06 m/s\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.2,Page no:13"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Varible declaration\t\n",
"fg= 5.6*(10**14) #frequency of green color, Hz\n",
"fr= 4.8*(10**14) #frequency of red color, Hz\n",
"c= 3.0*(10**8) #velocity of light, m/s\n",
"\n",
"#Calculation\n",
"v= c*((fg**2 - fr**2)/(fg**2 + fr**2)) #longitudinal speed of observer, m/s\n",
"v= v*3.6 #convert to km/h\n",
"R= 1.0 #rate at which fine is to be imposed per km/h, $\n",
"l= 80.0 #speed limit upto which no fine is to be imposed, km/h\n",
"fine= v-l # fine to be imposed, $\n",
"\n",
"#Result\n",
"print\"The fine imposed is:\",fine,\"$\\n\"\n",
"\n",
"print\"NOTE:Approx value of v is taken in book as 1.65*10^8,which is very less precise.\\nTherefore,chnge in final answer\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The fine imposed is: 165176390.588 $\n",
"\n",
"NOTE:Approx value of v is taken in book as 1.65*10^8,which is very less precise.\n",
"Therefore,chnge in final answer\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.3,Page no:14"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Varible declaration\n",
"v= 6.12*(10**7) #receding velocity with respect to Earth, m/s\n",
"c= 3.0*(10**8) #velocity of light, m/s\n",
"L0= 500.0 #initial wavelength of spectral line, nm\n",
"\n",
"#Calculation\n",
"L= L0*math.sqrt(((1+(v/c))/(1-(v/c)))) #final wavelength of spectral light, nm\n",
"Ls= L-L0 #shift in wavelength, nm\n",
"\n",
"#Varible declaration\n",
"print\"Shift in Green spectral line is: \",round(Ls),\"nm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Shift in Green spectral line is: 115.0 nm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.4,Page no:19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Varible declaration\n",
"StartingAge= 20 #starting age for both Dick and Jane\n",
"c= 3*(10**8) #velocity of light, m/s\n",
"v= 0.8*c #rate of separation of Dick and Jane, m/s\n",
"t0= 1 #interval for emission of signals, yr\n",
"\n",
"#Calculation\n",
"t1= t0*((1+v/c)/(1-v/c)) #interval for reception of signals on outward journey, yr\n",
"t1= t0*(math.sqrt((1+v/c)/(1-v/c))) #interval for reception of signals on outward journey, yr\n",
"t2= t0*(math.sqrt((1-v/c)/(1+v/c))) #interval for reception of signals on return trip, yr\n",
"#Dick's frame of reference\n",
"Tout1= 15 #duration of outward trip, yr\n",
"Tin1= 15 #duration of return trip, yr\n",
"JaneAge= StartingAge+(Tout1/t1)+(Tin1/t2) #Jane's age according to Dick\n",
"#Jane's frame of reference\n",
"Tout2= 25 #duration of outward trip, yr\n",
"d= 20 #delay in transmission of signal to Jane, caused by distance of the star, yr\n",
"Tin2= 5 #duration of return trip\n",
"DickAge= StartingAge+((Tout2+d)/t1)+(Tin2/t2) #Dick's age according to JAne\n",
"\n",
"#Result\n",
"print\"According to Dick, age of Jane is:\",JaneAge,\"years\"\n",
"print\"According to Jane, age of Dick is:\",DickAge,\"years\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"According to Dick, age of Jane is: 70.0 years\n",
"According to Jane, age of Dick is: 50.0 years\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.6,Page no:27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Varible declaration\n",
"mf= 1 #mass of each entity, kg\n",
"c= 3*(10**8) #velocity of light, m/s\n",
"v= 0.6*c #velocity of fragments relative to original body, m/s\n",
"\n",
"#Calculation\n",
"E0= 2*((mf*(c**2))/math.sqrt(1-((v/c)**2))) #Total energy of fragments\n",
"m= E0/(c**2) #mass of original body, kg\n",
"\n",
"#Result\n",
"print\"The total mass of the stationary body is: \",m,\"kg\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total mass of the stationary body is: 2.5 kg\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.7,Page no:28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Varible declaration\n",
"r=1.4 # Rate of arrival of Solar Energy at erath, kW per square meter\n",
"R=1.5*(10**11) #Radius of Earth, m\n",
"\n",
"#Calculation\n",
"P=r*(4*math.pi*(R**2)) #Total power recieved by Earth, kW\n",
"P= P*(10**3) #W\n",
"C= 3*(10**8) #Velocity of light, m/s\n",
"E=P #Energy lost by Sun, J\n",
"m= E/(C**2) #Mass of Sun lost per second as energy, kg\n",
"\n",
"#Result\n",
"print\"Mass lost by sun per second, is:%.2g\"%m,\"kg\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mass lost by sun per second, is:4.4e+09 kg\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.8,Page no:32"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Varible declaration\n",
"c= 3*(10**8) #Velocity of light, m/s\n",
"me= 0.511/(c**2) #mass of electron, MeV\n",
"mp=0 #mass of proton, MeV\n",
"p= 2.000/c #momenta for both particles, MeV\n",
" \n",
"#Calculation \n",
"##Using Eq. 1.24 and 1.25, Page 31 \n",
"Ee=math.sqrt(((me**2)*(c**4))+((p**2)*(c**2))) #Total energy of electron, MeV\n",
"Ep= p*c #Total energy of proton, MeV\n",
"\n",
"#Result\n",
"print\"Total energy of Electron is: \",round(Ee,3),\"MeV\"\n",
"print\"Total energy of Photon is: \",Ep,\"MeV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total energy of Electron is: 2.064 MeV\n",
"Total energy of Photon is: 2.0 MeV\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.11,Page no:44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Varible declaration \n",
"c=3*(10**8) #velocity of light, m/s\n",
"VaE= 0.90*c #velocity of spacecraft alpha w.r.t Earth, m/s\n",
"VbA= 0.50*c #velocity of spacecraft beta w.r.t. Alpha, m/s\n",
"\n",
"#Calculation\n",
"VbE= (VaE+VbA)/(1+((VaE*VbA)/(c**2))) #velocity of beta w.r.t Earth, m/s\n",
"VbE=VbE/c #Converting to percent of c\n",
"\n",
"#Result\n",
"print\"The required velocity of spacecraft Beta w.r.t. Earth is:\",round(VbE,2),\"c\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required velocity of spacecraft Beta w.r.t. Earth is: 0.97 c\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}