diff options
| author | priyanka | 2015-06-24 15:03:17 +0530 |
|---|---|---|
| committer | priyanka | 2015-06-24 15:03:17 +0530 |
| commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /446/CH2 | |
| download | Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.gz Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.bz2 Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.zip | |
initial commit / add all books
Diffstat (limited to '446/CH2')
34 files changed, 211 insertions, 0 deletions
diff --git a/446/CH2/EX2.1/2_1.sce b/446/CH2/EX2.1/2_1.sce new file mode 100755 index 000000000..5d88cb2ac --- /dev/null +++ b/446/CH2/EX2.1/2_1.sce @@ -0,0 +1,6 @@ +clear
+clc
+disp('Exa-2.1');
+v1=60; v2=40 //Velocities of cars wrt to observer in km/hr
+vr=v1-v2; //relative velocity
+printf('The value of relative velocity is %4.f km/h.',vr);
diff --git a/446/CH2/EX2.1/2_1.txt b/446/CH2/EX2.1/2_1.txt new file mode 100755 index 000000000..fd248222c --- /dev/null +++ b/446/CH2/EX2.1/2_1.txt @@ -0,0 +1,2 @@ + Exa-2.1
+The value of relative velocity is 20 km/h
\ No newline at end of file diff --git a/446/CH2/EX2.10/2_10.sce b/446/CH2/EX2.10/2_10.sce new file mode 100755 index 000000000..dac20e3c4 --- /dev/null +++ b/446/CH2/EX2.10/2_10.sce @@ -0,0 +1,6 @@ +clear
+clc
+disp('Exa-2.10');
+u=0.8*c;L=65;c=3*10^8; //all values are in terms of c
+t=u*L/(c^2*(sqrt(1-((u/c)^2)))); //from the equation 2.31
+printf('The time interval between the events is %e sec which equals %.2f usec.',t,t*10^6);
\ No newline at end of file diff --git a/446/CH2/EX2.10/2_10.txt b/446/CH2/EX2.10/2_10.txt new file mode 100755 index 000000000..269b6213e --- /dev/null +++ b/446/CH2/EX2.10/2_10.txt @@ -0,0 +1,3 @@ +
+ Exa-2.10
+The time interval between the events is 2.888889e-007 sec which equals 0.29 usec.
\ No newline at end of file diff --git a/446/CH2/EX2.11/2_11.sce b/446/CH2/EX2.11/2_11.sce new file mode 100755 index 000000000..d3409f6ba --- /dev/null +++ b/446/CH2/EX2.11/2_11.sce @@ -0,0 +1,9 @@ +clear
+clc
+disp('Exa-2.11');
+m=1.67*10^-27;c= 3*10^8;v=0.86*c; //all the given values and constants
+p=m*v/(sqrt(1-((v/c)^2))); // in terms of Kgm/sec
+printf('The value of momentum was found out to be %.3e Kg-m/sec.\n',p);
+c=938;v=0.86*c;mc2=938 // all the energies in MeV where mc2= value of m*c^2
+pc=(mc2*(v/c))/(sqrt(1-((v/c)^2))); //expressing in terms of Mev
+printf('The value of momentum was found out to be %.2f Mev.',pc);
\ No newline at end of file diff --git a/446/CH2/EX2.11/2_11.txt b/446/CH2/EX2.11/2_11.txt new file mode 100755 index 000000000..8ca8a2f37 --- /dev/null +++ b/446/CH2/EX2.11/2_11.txt @@ -0,0 +1,4 @@ +
+ Exa-2.11
+The value of momentum was found out to be 8.443e-019 Kg-m/sec.
+The value of momentum was found out to be 1580.81 M.
\ No newline at end of file diff --git a/446/CH2/EX2.12/2_12.sce b/446/CH2/EX2.12/2_12.sce new file mode 100755 index 000000000..b482f7a0e --- /dev/null +++ b/446/CH2/EX2.12/2_12.sce @@ -0,0 +1,8 @@ +clear
+clc
+disp('Exa-2.12');
+pc=1580; mc2=938;E0=938; // all the energies in MeV mc2=m*c^2 and pc=p*c
+E=sqrt(pc^2+mc2^2);
+printf('The relativistic total energy is %.2f MeV.\n',E); //value of Energy E
+K=E-E0; //value of possible kinetic energy
+printf('The kinetic energy of the proton is %.1f MeV.',K);
diff --git a/446/CH2/EX2.12/2_12.txt b/446/CH2/EX2.12/2_12.txt new file mode 100755 index 000000000..80cfbc643 --- /dev/null +++ b/446/CH2/EX2.12/2_12.txt @@ -0,0 +1,4 @@ +
+ Exa-2.12
+The relativistic total energy is 1837.46 MeV.
+The kinetic energy of the proton is 899.5 MeV.
\ No newline at end of file diff --git a/446/CH2/EX2.13/2_13.sce b/446/CH2/EX2.13/2_13.sce new file mode 100755 index 000000000..d7da6071a --- /dev/null +++ b/446/CH2/EX2.13/2_13.sce @@ -0,0 +1,8 @@ +clear
+clc
+disp('Exa-2.13');
+E=10.51; mc2=0.511; //all the values are in MeV
+p=sqrt(E^2-mc2^2); //momentum of the electron
+printf('The momentum of electron is %.1f MeV/c\n',p);
+v=sqrt(1-(mc2/E)^2); //velocity in terms of c
+printf('The velocity of electron is %.4f c',v);
\ No newline at end of file diff --git a/446/CH2/EX2.13/2_13.txt b/446/CH2/EX2.13/2_13.txt new file mode 100755 index 000000000..78b94cafe --- /dev/null +++ b/446/CH2/EX2.13/2_13.txt @@ -0,0 +1,4 @@ +
+ Exa-2.13
+The momentum of electron is 10.5 MeV/c
+The velocity of electron is 0.9988 c
\ No newline at end of file diff --git a/446/CH2/EX2.14/2_14.sce b/446/CH2/EX2.14/2_14.sce new file mode 100755 index 000000000..2e7af67d0 --- /dev/null +++ b/446/CH2/EX2.14/2_14.sce @@ -0,0 +1,8 @@ +clear
+clc
+disp('Exa-2.14');
+k=50;mc2=0.511*10^-3;c=3*10^8; // all the values of energy are in GeV and c is in SI units
+v=sqrt(1-(1/(1+(k/mc2))^2)); //speed of the electron in terms of c
+k=c-(v*c); //difference in velocities
+printf('Speed of the electron as a fraction of c is %.12f*10^-12.\n',v*10^12); // v=(v*10^12)*10^-12; so as to obtain desired accuracy in the result
+printf('The difference in velocities is %.1f cm/s.',k*10^2);
\ No newline at end of file diff --git a/446/CH2/EX2.14/2_14.txt b/446/CH2/EX2.14/2_14.txt new file mode 100755 index 000000000..c79feae33 --- /dev/null +++ b/446/CH2/EX2.14/2_14.txt @@ -0,0 +1,4 @@ +
+ Exa-2.14
+Speed of the electron as a fraction of c is 999999999947.776860000000*10^-12.
+The difference in velocities is 1.6 cm/s.
\ No newline at end of file diff --git a/446/CH2/EX2.15/2_15.sce b/446/CH2/EX2.15/2_15.sce new file mode 100755 index 000000000..02bef3a87 --- /dev/null +++ b/446/CH2/EX2.15/2_15.sce @@ -0,0 +1,9 @@ +clear
+clc
+disp('Exa-2.15');
+r=1.5*10^11; I=1.4*10^3; //radius and intensity of sun
+s=4*%pi*r^2 //surface area of the sun
+Pr=s*I // Power radiated in J/sec
+c=3*10^8; //velocity of light
+m=Pr/c^2 //rate od decrease of mass
+printf('The rate of decrease in mass of the sun is %.1e kg/sec.',m);
\ No newline at end of file diff --git a/446/CH2/EX2.15/2_15.txt b/446/CH2/EX2.15/2_15.txt new file mode 100755 index 000000000..9d7eced48 --- /dev/null +++ b/446/CH2/EX2.15/2_15.txt @@ -0,0 +1,2 @@ + Exa-2.15
+The rate of decrease in mass of the sun is 4.4e+009 kg/sec.
\ No newline at end of file diff --git a/446/CH2/EX2.16/2_16.sce b/446/CH2/EX2.16/2_16.sce new file mode 100755 index 000000000..06aede701 --- /dev/null +++ b/446/CH2/EX2.16/2_16.sce @@ -0,0 +1,15 @@ +clear
+clc
+disp('Exa-2.16');
+K=325; mkc2=498; //kinetic energy and rest mass energy of kaons
+mpic=140; //given value
+Ek=K+mkc2;
+pkc=sqrt(Ek^2-mkc2^2);
+//consider the law of conservation of energy which yields Ek=sqrt(p1c^2+mpic^2)+sqrt(p2c^2+mpic^2)
+// The above equations (4th degree,hence no direct methods)can be solved by assuming the value of p2c=0.
+p1c=sqrt(Ek^2-(2*mpic*Ek));
+//consider the law of conservation of momentum. which gives p1c+p2c=pkc implies
+p2c=pkc-p1c;
+k1=(sqrt(p1c^2+(mpic^2))-mpic); //corresponding kinetic energies
+k2=(sqrt((p2c^2)+(mpic^2))-mpic);
+printf('The corresponding kinetic energies of the pions are %.0f MeV and %.1f MeV.',k1,k2);
\ No newline at end of file diff --git a/446/CH2/EX2.16/2_16.txt b/446/CH2/EX2.16/2_16.txt new file mode 100755 index 000000000..09e2b9214 --- /dev/null +++ b/446/CH2/EX2.16/2_16.txt @@ -0,0 +1,2 @@ + Exa-2.16
+The corresponding kinetic energies of the pions are 543 MeV and 0.6 MeV.
diff --git a/446/CH2/EX2.17/2_17.sce b/446/CH2/EX2.17/2_17.sce new file mode 100755 index 000000000..f5250bdb4 --- /dev/null +++ b/446/CH2/EX2.17/2_17.sce @@ -0,0 +1,11 @@ +clear
+clc
+disp('Ex-2.17');
+mpc2=938;c=3*10^8; //mpc2=mp*c^2,mp=mass of proton
+Et=4*mpc2; //final total energy
+E1=Et/2;E2=E1; //applying conservation of momentum and energy
+v2=c*sqrt(1-(mpc2/E1)^2); //lorentz transformation
+u=v2;v=(v2+u)/(1+(u*v2/c^2));
+E=mpc2/(sqrt(1-(v/c)^2));
+K=E-mpc2;
+printf('The threshold kinetic energy is %.3f Gev',K/10^3);
diff --git a/446/CH2/EX2.17/2_17.txt b/446/CH2/EX2.17/2_17.txt new file mode 100755 index 000000000..d9b930489 --- /dev/null +++ b/446/CH2/EX2.17/2_17.txt @@ -0,0 +1,3 @@ +
+ Ex-2.17
+The threshold kinetic energy is 5.628 Gev
\ No newline at end of file diff --git a/446/CH2/EX2.2/2_2.sce b/446/CH2/EX2.2/2_2.sce new file mode 100755 index 000000000..df3ebd3d2 --- /dev/null +++ b/446/CH2/EX2.2/2_2.sce @@ -0,0 +1,8 @@ +clear
+clc
+disp('Exa-2.2');
+Va_w=[320 0]; Vw_g=[0 65]; //Vp/q=[X Y]=>velocity of object p wrt q along X(east) and Y(north) directions.
+Va_g=Va_w + Vw_g; //net velocity
+k=norm(Va_g); //magnitude
+s=atan(Va_g(1,2)/Va_g(1,1))*180/%pi; //angle in rad*180/pi for conversion to degrees
+printf('The magnitude of velocity Va/g(airplane wrt ground) is %.3f Km/h at %.3f degrees north of east.',k,s);
diff --git a/446/CH2/EX2.2/2_2.txt b/446/CH2/EX2.2/2_2.txt new file mode 100755 index 000000000..7f6d013ee --- /dev/null +++ b/446/CH2/EX2.2/2_2.txt @@ -0,0 +1,2 @@ + Exa-2.2
+The magnitude of velocity Va/g(airplane wrt ground) is 326.535 Km/h at 11.482 degrees north of east.
\ No newline at end of file diff --git a/446/CH2/EX2.3/2_3.sce b/446/CH2/EX2.3/2_3.sce new file mode 100755 index 000000000..c03b6bf65 --- /dev/null +++ b/446/CH2/EX2.3/2_3.sce @@ -0,0 +1,5 @@ +clear
+clc
+disp('Exa-2.3'); // The problem is entirely theoretical hence following the standard procedure we obtain
+printf('The time required for round trip is 2*L/(c*(1-(u/c)^2)). \n');
+printf('The time required to swim across and return is 2*L/(c*sqrt((1-(u/c)^2)))');
\ No newline at end of file diff --git a/446/CH2/EX2.3/2_3.txt b/446/CH2/EX2.3/2_3.txt new file mode 100755 index 000000000..443a866d2 --- /dev/null +++ b/446/CH2/EX2.3/2_3.txt @@ -0,0 +1,3 @@ + Exa-2.3
+The time required for round trip is 2*L/(c*(1-(u/c)^2)).
+The time required to swim across and return is 2*L/(c*sqrt((1-(u/c)^2)))
\ No newline at end of file diff --git a/446/CH2/EX2.4/2_4.sce b/446/CH2/EX2.4/2_4.sce new file mode 100755 index 000000000..f32245412 --- /dev/null +++ b/446/CH2/EX2.4/2_4.sce @@ -0,0 +1,8 @@ +clear
+clc
+disp('Exa-2.3');
+Lo=100*(10^3);c=3*(10^8); //Given values//all the quantities are converted to SI units
+d=2.2*(10^-6); //time between its birth and decay
+t=Lo/c //where Lo is the distance from top of atmosphere to the Earth. c is the velocity of light. t is the time taken
+u=sqrt(1-((d/t)^2)); // using time dilaion fromula for finding u where u is the minimum velocity in terms of c;
+printf('Hence the minimum speed required is %f c.',u);
diff --git a/446/CH2/EX2.4/2_4.txt b/446/CH2/EX2.4/2_4.txt new file mode 100755 index 000000000..a6ae1aa6f --- /dev/null +++ b/446/CH2/EX2.4/2_4.txt @@ -0,0 +1,3 @@ +
+ Exa-2.3
+Hence the minimum speed required is 0.999978 c.
\ No newline at end of file diff --git a/446/CH2/EX2.5/2_5.sce b/446/CH2/EX2.5/2_5.sce new file mode 100755 index 000000000..e34dc1658 --- /dev/null +++ b/446/CH2/EX2.5/2_5.sce @@ -0,0 +1,7 @@ +clear
+clc
+disp('Exa-2.5');
+Lo=100*(10^3); //Lo is converted to Km
+u=0.999978; ////u/c is taken as u since u is represented in terms of c.
+L=Lo*(sqrt(1-u^2)); // from the length contraction formula
+printf('Hence the apparent thickness of the Earth''s surface is %.2f metres.',L);
diff --git a/446/CH2/EX2.5/2_5.txt b/446/CH2/EX2.5/2_5.txt new file mode 100755 index 000000000..9009ff5b6 --- /dev/null +++ b/446/CH2/EX2.5/2_5.txt @@ -0,0 +1,2 @@ + Exa-2.5
+Hence the apparent thickness of the Earth's surface is 663.32 metres
\ No newline at end of file diff --git a/446/CH2/EX2.6/2_6.sce b/446/CH2/EX2.6/2_6.sce new file mode 100755 index 000000000..25dc4d6a5 --- /dev/null +++ b/446/CH2/EX2.6/2_6.sce @@ -0,0 +1,20 @@ +clear
+clc
+disp('Exa-2.6(a)');
+L=65; c=3*10^8;u=0.8*c;
+t=L/u ; //The value of time taken as measured by the observer
+printf('The time for rocket to pass a point as measured by O is %.2e.\n',t); //The value of time taken as measured by the observer
+disp('Exa-2.6(b)');
+Do=65; //given length
+Lo= L/sqrt(1-(u/c)^2); //contracted length of rocket
+printf('Actual length according to O is %.2f.\n',Lo);
+disp('Exa-2.6(c)');
+D=Do*(sqrt(1-(u/c)^2)); //contracted length of platform.
+printf('Contracted length according to O'' is %.2e.\n',D);
+disp('Exa-2.6(d)');
+t1=Lo/u; //time needed to pass according to O'.
+printf('Time taken according to O is %.2e.\n',t1);
+disp('Exa-2.6(e)');
+t2=(Lo-D)/u; //time intervals between the two instancs
+printf('Time taken according to O'' is %.2e.\n',t2);
+disp('The value of t1 and t2 did not match');
diff --git a/446/CH2/EX2.6/2_6.txt b/446/CH2/EX2.6/2_6.txt new file mode 100755 index 000000000..e19d8d747 --- /dev/null +++ b/446/CH2/EX2.6/2_6.txt @@ -0,0 +1,17 @@ +
+ Exa-2.6(a)
+The time for rocket to pass a point as measured by O is 2.71e-007.
+
+ Exa-2.6(b)
+Actual length according to O is 108.33.
+
+ Exa-2.6(c)
+Contracted length according to O' is 3.90e+001.
+
+ Exa-2.6(d)
+Time taken according to O is 4.51e-007.
+
+ Exa-2.6(e)
+Time taken according to O' is 2.89e-007.
+
+ The value of t1 and t2 did not match.
\ No newline at end of file diff --git a/446/CH2/EX2.7/2_7.sce b/446/CH2/EX2.7/2_7.sce new file mode 100755 index 000000000..b197d1362 --- /dev/null +++ b/446/CH2/EX2.7/2_7.sce @@ -0,0 +1,6 @@ +clear
+clc
+disp('Exa-2.7');
+v1=0.6; u=0.8; c=1; // all the values are measured in terms of c hence c=1
+v= (v1+u)/(1+(v1*u/c^2));
+printf('The speed of missile as measured by an observer on earth is %.2f c.',v);
\ No newline at end of file diff --git a/446/CH2/EX2.7/2_7.txt b/446/CH2/EX2.7/2_7.txt new file mode 100755 index 000000000..870bf1ef2 --- /dev/null +++ b/446/CH2/EX2.7/2_7.txt @@ -0,0 +1,3 @@ +
+ Exa-2.7
+The speed of missile as measured by an observer on earth is 0.95 c.
\ No newline at end of file diff --git a/446/CH2/EX2.8/2_8.sce b/446/CH2/EX2.8/2_8.sce new file mode 100755 index 000000000..33e3a67b3 --- /dev/null +++ b/446/CH2/EX2.8/2_8.sce @@ -0,0 +1,8 @@ +clear
+clc
+disp('Exa-2.8');
+w1=600;w2=434; // w1=recorded wavelength;w2=actual wavelength
+ // c/w1 = c/w2 *(sqrt(1-u/c)/(1+u/c))
+k=w2/w1;
+x=(1-k^2)/(1+k^2); //solving for u/c
+printf('The speed of galaxy wrt earth is %.2f c',x);
diff --git a/446/CH2/EX2.8/2_8.txt b/446/CH2/EX2.8/2_8.txt new file mode 100755 index 000000000..546a642f1 --- /dev/null +++ b/446/CH2/EX2.8/2_8.txt @@ -0,0 +1,2 @@ + Exa-2.8
+The speed of galaxy wrt earth is 0.31 c
\ No newline at end of file diff --git a/446/CH2/EX2.9/2_9.sce b/446/CH2/EX2.9/2_9.sce new file mode 100755 index 000000000..aed1e3955 --- /dev/null +++ b/446/CH2/EX2.9/2_9.sce @@ -0,0 +1,7 @@ +clear
+clc
+disp('Exa-2.9');
+v1x=0.6;v1y=0;v2x=0;v2y=.8;c=1; // all the velocities are taken wrt c
+v21x=(v2x-v1x)/(1-(v1x*v2x/c^2)); //using lorentz velocity transformation
+v21y=(v2y*(sqrt(1-(v1x*c)^2)/c^2))/(1-v1y*v2y/c^2)
+printf('The velocity of rocket 2 wrt rocket 1 along x and y directions is %.2f c & %.2f c respectively',v21x,v21y);
\ No newline at end of file diff --git a/446/CH2/EX2.9/2_9.txt b/446/CH2/EX2.9/2_9.txt new file mode 100755 index 000000000..31c36c656 --- /dev/null +++ b/446/CH2/EX2.9/2_9.txt @@ -0,0 +1,2 @@ + Exa-2.9
+The velocity of rocket 2 wrt rocket 1 along x and y directions is -0.60 c & 0.64 c respectively
\ No newline at end of file |