diff options
Diffstat (limited to '1172/CH8')
28 files changed, 275 insertions, 0 deletions
diff --git a/1172/CH8/EX8.10/8_10.txt b/1172/CH8/EX8.10/8_10.txt new file mode 100755 index 000000000..5b9f4aa58 --- /dev/null +++ b/1172/CH8/EX8.10/8_10.txt @@ -0,0 +1,4 @@ + # Problem 10 #
+Standard formula used U_f - U_i = 1/2 * m *(u^2 - v^2)
+
+ Velocity required by mass is 1.118313e+04 m/s.
diff --git a/1172/CH8/EX8.10/Example8_10.sce b/1172/CH8/EX8.10/Example8_10.sce new file mode 100755 index 000000000..a845feb25 --- /dev/null +++ b/1172/CH8/EX8.10/Example8_10.sce @@ -0,0 +1,13 @@ +clc
+//Given that
+R_e = 6.4e6 // radius of Earth in km
+M_e = 6e24 // mass of Earth in kg
+G = 6.67e-11 // universal gravitational constant
+// sample problem 10 page No. 303
+printf("\n\n\n # Problem 10 # \n")
+
+printf("Standard formula used U_f - U_i = 1/2 * m *(u^2 - v^2)\n ")
+h = 10 * R_e
+v = sqrt (2 *h * G * M_e / (R_e * h)) // calculation of velocity required by mass to reach given height
+printf ("\n Velocity required by mass is %e m/s.",v)
+
diff --git a/1172/CH8/EX8.11/8_11.txt b/1172/CH8/EX8.11/8_11.txt new file mode 100755 index 000000000..23258ba8d --- /dev/null +++ b/1172/CH8/EX8.11/8_11.txt @@ -0,0 +1,4 @@ + # Problem 11 #
+Standard formula used T^2 = k* r^3
+ Standers formula used v = 2 * pi * r / T
+ Ratio of time period is 0.031623 and ratio of speed is 3.162278 .
diff --git a/1172/CH8/EX8.11/Example8_11.sce b/1172/CH8/EX8.11/Example8_11.sce new file mode 100755 index 000000000..fe15e9a69 --- /dev/null +++ b/1172/CH8/EX8.11/Example8_11.sce @@ -0,0 +1,15 @@ +clc
+//Given that
+r1 = 1e12 // distance of first planet from Sun in m
+r2 = 1e13 //distance of first planet from Sun in m
+// sample problem 11 page No. 304
+printf("\n\n\n # Problem 11 # \n")
+
+printf("Standard formula used T^2 = k* r^3")
+printf ("\n Standers formula used v = 2 * pi * r / T")
+r_ratio = r1 / r2 // r_ratio is ratio of distances from Sun
+T_ratio = r_ratio^(3/2) //calculation of Ratio of time period
+v_ratio = r_ratio / T_ratio // calculation of ratio of speed
+
+printf (" \n Ratio of time period is %f and ratio of speed is %f .", T_ratio, v_ratio)
+
diff --git a/1172/CH8/EX8.12/8_12.txt b/1172/CH8/EX8.12/8_12.txt new file mode 100755 index 000000000..7a0553365 --- /dev/null +++ b/1172/CH8/EX8.12/8_12.txt @@ -0,0 +1,5 @@ + # Problem 12 #
+
+ Standard formula used T^2 = k* r^3
+ Distance of Saturn from Sun is 1.432098e+09 km .
+
diff --git a/1172/CH8/EX8.12/Example8_12.sce b/1172/CH8/EX8.12/Example8_12.sce new file mode 100755 index 000000000..b8e211cac --- /dev/null +++ b/1172/CH8/EX8.12/Example8_12.sce @@ -0,0 +1,13 @@ +clc
+//Given that
+r1 = 1.5e8 // distance of Earth from Sun in km
+t1 = 1 // let
+// sample problem 12 page No. 305
+printf ("\n\n\n # Problem 12 # \n")
+
+printf ("\n Standard formula used T^2 = k* r^3")
+t2 = 29.5 * t1// calculation of time period of Saturn
+r2 = r1 * (t2 / t1) ^ (2/3) //calculation of distance of stern from Sun
+
+printf (" \n Distance of Saturn from Sun is %e km .", r2)
+
diff --git a/1172/CH8/EX8.13/8_13.txt b/1172/CH8/EX8.13/8_13.txt new file mode 100755 index 000000000..898f0ffff --- /dev/null +++ b/1172/CH8/EX8.13/8_13.txt @@ -0,0 +1,4 @@ + # Problem 13 #
+
+ Standard formula used v * r = k
+ Speed at perigee is 30000 km/h and at apogee is 22786.516854 km/h .
diff --git a/1172/CH8/EX8.13/Example8_13.sce b/1172/CH8/EX8.13/Example8_13.sce new file mode 100755 index 000000000..f3d5880d8 --- /dev/null +++ b/1172/CH8/EX8.13/Example8_13.sce @@ -0,0 +1,15 @@ +clc
+//Given that
+r_peri = 360 // distance of perigee of satellite from Earth surface in km
+r_apo = 2500 // distance of apogee of satellite from Earth surface in km
+R_e = 6400 // radius of Earth in km
+v_p = 30000 // speed of satellite at apogee position in km/h
+// sample problem 13 page No. 305
+printf ("\n\n\n # Problem 13 # \n")
+
+printf ("\n Standard formula used v * r = k ")
+r_p = r_peri + R_e // calculation of distance of perigee
+r_a = r_apo + R_e// calculation of distance of apogee
+
+v_a = v_p * r_p / r_a // calculation of speed at apogee
+printf (" \n Speed at perigee is %d km/h and at apogee is %f km/h .",v_p, v_a)
diff --git a/1172/CH8/EX8.14/8_14.txt b/1172/CH8/EX8.14/8_14.txt new file mode 100755 index 000000000..24a62f538 --- /dev/null +++ b/1172/CH8/EX8.14/8_14.txt @@ -0,0 +1,5 @@ + # Problem 14 #
+
+ Standard formula used 1/2 *(m_s * v ^2 / r) = g * R_E^2 * m /R_e^2
+ Magnitude and direction of impulse required are respectively 8.047626e+05kgm/s and 18.098444 degree.
+
diff --git a/1172/CH8/EX8.14/Example8_14.sce b/1172/CH8/EX8.14/Example8_14.sce new file mode 100755 index 000000000..10da8732e --- /dev/null +++ b/1172/CH8/EX8.14/Example8_14.sce @@ -0,0 +1,21 @@ +clc
+//Given that
+h = 600 // distance of satellite from surface of Earth in km
+R_e = 6400 // radius of Earth in km
+m_s = 100 // mass of satellite in kg
+g = 10 // gravitational acceleration in m/s2
+v_y = 2500 // upward velocity of launched satellite
+// sample problem 14 page No. 306
+printf("\n\n\n # Problem 14 # \n")
+
+printf("\n Standard formula used 1/2 *(m_s * v ^2 / r) = g * R_E^2 * m /R_e^2 ")
+r = R_e + h// calculation of effective height of satellite
+
+v = sqrt (g * (R_e * 1e3)^2 / (r * 1e3)) // calculation of orbital velocity of satellite
+
+P_x = m_s * v// calculation of momentum in x direction
+P_y = m_s * v_y// calculation of momentum in y direction
+U = sqrt(P_x^2 + P_y^2 ) // calculation of magnitude of impulse required
+
+theta = (180 / %pi) * atan (P_y / P_x ) // calculation of direction of impulse required
+printf ("\n Magnitude and direction of impulse required are respectively %ekgm/s and %f degree.",U , theta)
diff --git a/1172/CH8/EX8.15.1/8_15a.txt b/1172/CH8/EX8.15.1/8_15a.txt new file mode 100755 index 000000000..d9c8d02b5 --- /dev/null +++ b/1172/CH8/EX8.15.1/8_15a.txt @@ -0,0 +1,4 @@ + # Problem 15a #
+
+ Standard formula used E = m*c^2
+ Loss in mass during formation of 1 atom of hydrogen is 2.417778e-32 g.
diff --git a/1172/CH8/EX8.15.1/Example8_15a.sce b/1172/CH8/EX8.15.1/Example8_15a.sce new file mode 100755 index 000000000..7857f25a1 --- /dev/null +++ b/1172/CH8/EX8.15.1/Example8_15a.sce @@ -0,0 +1,10 @@ +clc
+
+//Given that
+b_e = 13.6 // Binding energy of electron to proton in eV
+c= 3e8 // speed of light in m/s
+// sample problem 15a page No. 306
+printf("\n\n\n # Problem 15a # \n")
+printf("\n Standard formula used E = m*c^2")
+del_m = b_e * (1.6e-19) / c^2 * 1000
+printf ("\n Loss in mass during formation of 1 atom of hydrogen is %e g.", del_m)
diff --git a/1172/CH8/EX8.15.2/8_15b.txt b/1172/CH8/EX8.15.2/8_15b.txt new file mode 100755 index 000000000..8072f947a --- /dev/null +++ b/1172/CH8/EX8.15.2/8_15b.txt @@ -0,0 +1,5 @@ +
+ # Problem 15b #
+
+ Standard formula used E = m*c^2
+ Binding energy of deuteron is 2.250000 MeV.
diff --git a/1172/CH8/EX8.15.2/Example8_15b.sce b/1172/CH8/EX8.15.2/Example8_15b.sce new file mode 100755 index 000000000..a69949231 --- /dev/null +++ b/1172/CH8/EX8.15.2/Example8_15b.sce @@ -0,0 +1,16 @@ +clc
+//Given that
+M_p = 1.6725e-24 // mass of proton in g
+M_n = 1.6748e-24 // mass of neutron in g
+M_d = 3.3433e-24 // mass of deuteron in g
+c= 3e8 // speed of light in m/s
+// sample problem 15b page No. 306
+printf("\n\n\n # Problem 15b # \n")
+
+printf("\n Standard formula used E = m*c^2")
+del_m = M_p + M_n - M_d // calculation of Loss in mass during formation of 1 atom of hydrogen
+
+b_e = (del_m / 1000) * c^2 / (1.6e-19 * 1e6) // calculation of Binding energy of deuteron
+
+printf ("\n Binding energy of deuteron is %f MeV.", b_e)
+
diff --git a/1172/CH8/EX8.4.1/8_4a.txt b/1172/CH8/EX8.4.1/8_4a.txt new file mode 100755 index 000000000..f1f678f6a --- /dev/null +++ b/1172/CH8/EX8.4.1/8_4a.txt @@ -0,0 +1,3 @@ + # Problem 4a #
+Standard formula r2/r1 = (t2/t1)^(2/3)
+ Relative speed of satellite s2 wrt satellite s1 is -3.769911e+04 km/h.
diff --git a/1172/CH8/EX8.4.1/Example8_4a.sce b/1172/CH8/EX8.4.1/Example8_4a.sce new file mode 100755 index 000000000..20127990d --- /dev/null +++ b/1172/CH8/EX8.4.1/Example8_4a.sce @@ -0,0 +1,16 @@ +clc
+//Given that
+t1 = 1 // time period of satellite s1 in hours
+t2 = 8 // time period of satellite s2 in hour
+r1 = 1.2e4 // radius of orbit of satellite s1 in km
+
+// sample problem 4a page No. 300
+printf("\n\n\n # Problem 4a # \n")
+
+printf("Standard formula r2/r1 = (t2/t1)^(2/3)")
+r2 = r1 * (t2/t1)^(2/3) // calculation of radius of orbit of satellite s2 in km
+v1 = 2 * %pi * r1 / t1 // calculation of speed of satellite s1 in km/h
+v2 = 2 * %pi * r2 / t2 // calculation of speed of satellite s2 in km/h
+del_v = v2 - v1 // calculation of relative speed of satellites in km/h
+
+printf (" \n Relative speed of satellite s2 wrt satellite s1 is %e km/h.", del_v)
diff --git a/1172/CH8/EX8.4.2/8_4b.txt b/1172/CH8/EX8.4.2/8_4b.txt new file mode 100755 index 000000000..ce99d3809 --- /dev/null +++ b/1172/CH8/EX8.4.2/8_4b.txt @@ -0,0 +1,4 @@ +# Problem 4b #
+Standard formula r2/r1 = (t2/t1)^(2/3)
+ Relative angular speed of satellite s2 for satellite s1 is -1.047198e+00 rad/h.
+
diff --git a/1172/CH8/EX8.4.2/Example8_4b.sce b/1172/CH8/EX8.4.2/Example8_4b.sce new file mode 100755 index 000000000..6c224276e --- /dev/null +++ b/1172/CH8/EX8.4.2/Example8_4b.sce @@ -0,0 +1,18 @@ +clc
+//Given that
+t1 = 1 // time period of satellite s1 in hour
+t2 = 8 // time period of satellite s2 in hour
+r1 = 1.2e4 // radius of orbit of satellite s1 in km
+
+// sample problem 4b page No. 300
+printf("\n\n\n # Problem 4b # \n")
+
+printf("Standard formula r2/r1 = (t2/t1)^(2/3)")
+r2 = r1 * (t2/t1)^(2/3) // calculation of radius of orbit of satellite s2 in km
+v1 = 2 * %pi * r1 / t1 // calculation of speed of satellite s1 in km/h
+v2 = 2 * %pi * r2 / t2 // calculation of speed of satellite s2 in km/h
+del_v = v2 - v1 // calculation of relative speed of satellites in km/h
+del_r = r2 - r1 // calculation of closest distance between satellite s1 and s2
+v_angular = del_v / del_r // calculation of angular speed in rad/h
+printf (" \n Relative angular speed of satellite s2 for satellite s1 is %e rad/h.", v_angular)
+
diff --git a/1172/CH8/EX8.5/8_5.txt b/1172/CH8/EX8.5/8_5.txt new file mode 100755 index 000000000..078e6483a --- /dev/null +++ b/1172/CH8/EX8.5/8_5.txt @@ -0,0 +1,8 @@ + # Problem 5 #
+Standard formula used
+ v_o = sqrt(G*M_e/r)
+
+ T = 2 * pi * r / v_o
+
+ Orbital velocity of satellite is 6.660936 km/s
+ period of revolution is 2.363462 h.
diff --git a/1172/CH8/EX8.5/Example8_5.sce b/1172/CH8/EX8.5/Example8_5.sce new file mode 100755 index 000000000..2d3a9aa31 --- /dev/null +++ b/1172/CH8/EX8.5/Example8_5.sce @@ -0,0 +1,16 @@ +clc
+//Given that
+h = 2620 // distance of satellite from surface of Earth in km
+R_e = 6400 // radius of Earth in km
+M_e = 6e24 // mass of Earth in kg
+G = 6.67e-11 // universal gravitational constant
+
+// sample problem 5 page No. 300
+printf("\n\n\n # Problem 5 # \n")
+
+printf("Standard formula used \n\t v_o = sqrt(G*M_e/r) \n ")
+printf("\n \t T = 2 * pi * r / v_o \n ")
+r = R_e + h
+v_o = sqrt(G * M_e / (r * 1e3))
+T = 2 * %pi * r*1000 / (v_o*3600)
+printf ("\n Orbital velocity of satellite is %f km/s \n period of revolution is %f h.",v_o / 1000, T)
diff --git a/1172/CH8/EX8.6/8_6.txt b/1172/CH8/EX8.6/8_6.txt new file mode 100755 index 000000000..9d8b0e808 --- /dev/null +++ b/1172/CH8/EX8.6/8_6.txt @@ -0,0 +1,7 @@ + # Problem 6 #
+Standard formula used v_o = sqrt(G*M_e/r)
+ Standard formula used T = 2 * pi * r / v_o
+
+ Orbital velocity of satellite is 7.727615 km/s
+ period of revolution is 1.508719 h.
+
diff --git a/1172/CH8/EX8.6/Example8_6.sce b/1172/CH8/EX8.6/Example8_6.sce new file mode 100755 index 000000000..7c7233873 --- /dev/null +++ b/1172/CH8/EX8.6/Example8_6.sce @@ -0,0 +1,19 @@ +clc
+//Given that
+h = 3e5 // distance of satellite from surface of Earth in m
+R_e = 6.38e6 // radius of Earth in km
+M_e = 6e24 // mass of Earth in kg
+g = 9.8 // gravitational acceleration in m/s2
+
+// sample problem 6 page No. 301
+printf("\n\n\n # Problem 6 # \n")
+
+printf("Standard formula used v_o = sqrt(G*M_e/r) \n ")
+printf("Standard formula used T = 2 * pi * r / v_o \n ")
+r = R_e + h// calculation of effective distance between Earth and satellite
+
+G = g * R_e^2 / M_e// calculation of gravitational constant
+v_o = sqrt(G * M_e / r) / 1000// calculation of orbital velocity of satellite
+T = 2 * %pi * r / (v_o * 1000) / 3.6e3 // calculation of period of revolution of satellite
+
+printf ("\n Orbital velocity of satellite is %f km/s \n period of revolution is %f h.",v_o, T)
diff --git a/1172/CH8/EX8.7/8_7.txt b/1172/CH8/EX8.7/8_7.txt new file mode 100755 index 000000000..aed6ce345 --- /dev/null +++ b/1172/CH8/EX8.7/8_7.txt @@ -0,0 +1,4 @@ + # Problem 7 #
+Standard formula used T = 2 * pi * sqrt ((r^3)/G*M_e)
+
+ Estimated mass of Earth is 6.331179e+24 kg.
diff --git a/1172/CH8/EX8.7/Example8_7.sce b/1172/CH8/EX8.7/Example8_7.sce new file mode 100755 index 000000000..6baa792af --- /dev/null +++ b/1172/CH8/EX8.7/Example8_7.sce @@ -0,0 +1,11 @@ +clc
+//Given that
+t = 27.3 // period of lunar orbit around Earth in days
+r = 3.9e5 // distance of satellite from Earth in km
+G = 6.67e-11 // universal gravitational constant
+// sample problem 7 page No. 301
+printf("\n # Problem 7 # \n")
+printf("Standard formula used \n T = 2 * pi * sqrt ((r^3)/G*M_e) \n ")
+T = t * 24 * 60 * 60// calculation of time in seconds
+M_e = 4 * %pi^2 * (r * 1000)^3 / (G * T^2) // calculation of mass of Earth
+printf ("\n Estimated mass of Earth is %e kg.", M_e)
diff --git a/1172/CH8/EX8.8/8_8.txt b/1172/CH8/EX8.8/8_8.txt new file mode 100755 index 000000000..522c5db7a --- /dev/null +++ b/1172/CH8/EX8.8/8_8.txt @@ -0,0 +1,4 @@ + # Problem 8 #
+Standard formula used T = 2 * pi * sqrt ((r^3)/G*M_e)
+
+ Estimated mass of Sun is 2.111447e+30 kg.
diff --git a/1172/CH8/EX8.8/Example8_8.sce b/1172/CH8/EX8.8/Example8_8.sce new file mode 100755 index 000000000..a58a9e31a --- /dev/null +++ b/1172/CH8/EX8.8/Example8_8.sce @@ -0,0 +1,13 @@ +clc
+//Given that
+t = 1 // period of Earth's revolution around Sun in years
+r = 1.5e8 // distance between Sun and Earth in km
+G = 6.67e-11 // Universal gravitational constant
+// sample problem 8 page No. 302
+printf("\n\n\n # Problem 8 # \n")
+printf("Standard formula used T = 2 * pi * sqrt ((r^3)/G*M_e) \n ")
+T = t * 24 * 60 * 60 *356// calculation of time period in seconds
+M_s = 4 * %pi^2 * (r * 1000)^3 / (G * T^2) // calculation of mass of Sun
+printf ("\n Estimated mass of Sun is %e kg.", M_s)
+
+
diff --git a/1172/CH8/EX8.9/8_9.txt b/1172/CH8/EX8.9/8_9.txt new file mode 100755 index 000000000..4e1551c0f --- /dev/null +++ b/1172/CH8/EX8.9/8_9.txt @@ -0,0 +1,4 @@ + # Problem 9 #
+Standard formula used U_f - U_i = 1/2 * m *(u^2 - v^2)
+
+ Height reached by rocket before returning is 2.586947e+09 km.
diff --git a/1172/CH8/EX8.9/Example8_9.sce b/1172/CH8/EX8.9/Example8_9.sce new file mode 100755 index 000000000..412f318d1 --- /dev/null +++ b/1172/CH8/EX8.9/Example8_9.sce @@ -0,0 +1,14 @@ +clc
+//Given that
+R_e = 6.4e6 // radius of Earth in km
+M_e = 6e24 // mass of Earth in kg
+G = 6.67e-11 // universal gravitational constant
+u = 6e3 // initial speed of rocket in m/s
+
+// sample problem 9 page No. 302
+printf("\n\n\n # Problem 9 # \n")
+
+printf("Standard formula used U_f - U_i = 1/2 * m *(u^2 - v^2)\n ")
+h = ((R_e * 1e3)^2 * u^2) / (2 * G * M_e - R_e * u^2) / 1000 // calculation of Height reached by rocket before returning to Earth
+
+printf ("\n Height reached by rocket before returning is %e km.",h)
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