initial commit / add all books

19 files changed, 384 insertions, 0 deletions

diff --git a/3204/CH26/EX26.1/Ex26_1.sce b/3204/CH26/EX26.1/Ex26_1.sce
new file mode 100644
index 000000000..19093874f
--- /dev/null
+++ b/3204/CH26/EX26.1/Ex26_1.sce
@@ -0,0 +1,16 @@
+// 1 APPENDIX. Ex no 1. Page no 638

+//Initilization of variables

+P=[-5,2,14] //Point co-ordinates

+//Calculations

+r=sqrt(P(1)^2+P(2)^2+P(3)^2) //Magnitude of the poistion vector

+//Direction cosines

+l=P(1)/r 

+m=P(2)/r

+n=P(3)/r

+//Unit Vector calculations

+r_unit=P/r

+//Results

+clc

+printf("The Position vector is %fi+%fj+%fk \n",P(1),P(2),P(3))

+printf('The value of r is %f*l i + %f*m j + %f*n k \n',r,r,r)

+printf("The unit vector in the direction of r is %fi+%fj+%fk",r_unit(1),r_unit(2),r_unit(3))

diff --git a/3204/CH26/EX26.10/Ex26_10.sce b/3204/CH26/EX26.10/Ex26_10.sce
new file mode 100644
index 000000000..338d36e3b
--- /dev/null
+++ b/3204/CH26/EX26.10/Ex26_10.sce
@@ -0,0 +1,16 @@
+// 1 APPENDIX. Ex no 10. Page no 647

+// Initilization of variables

+// Points as matrices

+O=[-2,3,5]

+P=[1,-2,4]

+Q=[5,2,3]

+F=[4,4,-1] // Force vector

+// Calculations

+// Positon vector ( we will solve only by using r_1 as r_2 also gives the same answer)

+r_1=[P(1)-O(1),P(2)-O(2),P(3)-O(3)]

+// Moment

+// Calculating the cross product

+M=[(r_1(2)*F(3)-r_1(3)*F(2)),(r_1(3)*F(1)-r_1(1)*F(3)),(r_1(1)*F(2)-r_1(2)*F(1))]

+// Results

+clc

+printf('The Moment about point O is %fi %fj+%fk \n',M(1),M(2),M(3))

diff --git a/3204/CH26/EX26.11/Ex26_11.sce b/3204/CH26/EX26.11/Ex26_11.sce
new file mode 100644
index 000000000..662a634a8
--- /dev/null
+++ b/3204/CH26/EX26.11/Ex26_11.sce
@@ -0,0 +1,14 @@
+// 1 APPENDIX. Ex no 11. Page no 647

+// Initilization of variables

+// Points as matrices

+P=[1,-1,2] // Point where force is applied

+O=[2,-1,3] // point where moment is to be found

+F=[3,2,-4] // Force vector

+// Calculations

+// Position vector of point P wrt O

+r=[P(1)-O(1),P(2)-O(2),P(3)-O(3)]

+// Moment

+M=[(r(2)*F(3)-r(3)*F(2)),(r(3)*F(1)-r(1)*F(3)),(r(1)*F(2)-r(2)*F(1))]

+// Resuts

+clc

+printf('The moment of the force is %fi %fj %fk \n',M(1),M(2),M(3))

diff --git a/3204/CH26/EX26.12/Ex26_12.sce b/3204/CH26/EX26.12/Ex26_12.sce
new file mode 100644
index 000000000..5b9ba12d7
--- /dev/null
+++ b/3204/CH26/EX26.12/Ex26_12.sce
@@ -0,0 +1,20 @@
+// 1 APPENDIX. Ex no 12. Page no 648

+// Initilization of variables

+// Different notations have been used at some places

+f=22 // N 

+// Points as matrices

+A=[4,-1,7]

+O=[1,-3,2]

+V=[9,6,-2] // Given vector

+// Calculations

+// Unit vector in the direction of the vector

+v=[V(1),V(2),V(3)]/sqrt(V(1)^2+V(2)^2+V(3)^2)

+// Force

+F=f*[v(1),v(2),v(3)]

+// Position vector of point A wrt O

+r=[A(1)-O(1),A(2)-O(2),A(3)-O(3)]

+// Moment

+M=[(r(2)*F(3)-r(3)*F(2)),(r(3)*F(1)-r(1)*F(3)),(r(1)*F(2)-r(2)*F(1))]

+// Results

+clc

+printf('The moment is %fi + %fj + %f k \n',M(1),M(2),M(3))

diff --git a/3204/CH26/EX26.13/Ex26_13.sce b/3204/CH26/EX26.13/Ex26_13.sce
new file mode 100644
index 000000000..5a20f1d56
--- /dev/null
+++ b/3204/CH26/EX26.13/Ex26_13.sce
@@ -0,0 +1,26 @@
+// 1 APPENDIX. Ex no 13. Page no 648

+// Initilization of vriables

+// Notations have been changed

+// Force Vector

+F=[50,-80,30]

+// from fig.13

+theta1=30 // angles by which the axis is rotated ( all in degrees)

+theta2=60

+theta3=90

+theta4=120

+theta5=0

+// Calculations

+// Unit vector in u-direction

+u_unit=[1*cosd(theta1),1*cosd(theta2),1*cosd(theta3)]

+// Unit vector in v-direction

+v_unit=[1*cosd(theta4),1*cosd(theta1),1*cosd(theta3)]

+// Unit vector in w-direction

+w_unit=[1*cosd(theta3),1*cosd(theta3),1*cosd(theta5)]

+// Components of force

+// finding the dot product as

+u=F(1)*u_unit(1)+F(2)*u_unit(2)+F(3)*u_unit(3) // N

+v=F(1)*v_unit(1)+F(2)*v_unit(2)+F(3)*v_unit(3) // N

+w=F(1)*w_unit(1)+F(2)*w_unit(2)+F(3)*w_unit(3) // N

+// Results

+clc

+printf('The components of the force is,along u=%f N,along v=%f N,along w=%f N \n',u,v,w)

diff --git a/3204/CH26/EX26.14/Ex26_14.sce b/3204/CH26/EX26.14/Ex26_14.sce
new file mode 100644
index 000000000..444dae94c
--- /dev/null
+++ b/3204/CH26/EX26.14/Ex26_14.sce
@@ -0,0 +1,32 @@
+// 1 APPENDIX. Ex no 14. Page no 649

+// Initilization of variables

+// Some notations have been assumed

+f=100 // N // magnitude of force

+// Co-ordinates of corners of the box as matrices

+A=[0,0,0]

+B=[0.5,0,0]

+C=[0.5,0,1]

+D=[0,0,1]

+E=[0,0.5,0]

+F=[0.5,0.5,0]

+G=[0.5,0.5,1]

+H=[0,0.5,1]

+// Calculations

+// Force vector

+Fmag=f/sqrt((F(1)-C(1))^2+(F(2)-C(2))^2+(F(3)-C(3))^2)

+F=Fmag*[F(1)-C(1),F(2)-C(2),F(3)-C(3)]

+// Position vector

+r_EC=[C(1)-E(1),C(2)-E(2),C(3)-E(3)]

+// Moment about point E

+// Calculating the cross product

+M_E=[(r_EC(2)*F(3)-r_EC(3)*F(2)),(r_EC(3)*F(1)-r_EC(1)*F(3)),(r_EC(1)*F(2)-r_EC(2)*F(1))] // N.m // The value taken for F is incorrect in textbook.

+// Unit vector

+n_AE=[E(1)-A(1),E(2)-A(2),E(3)-A(3)]/sqrt((E(1)-A(1))^2+(E(2)-A(2))^2+(E(3)-A(3))^2)

+// Moment of force about axis AE

+// finding the dot product

+M_AE=M_E(1)*n_AE(1)+M_E(2)*n_AE(2)+M_E(3)*n_AE(3) // N.m

+// Results

+clc

+printf('The moment of the force about point E is %fi - %fj + %fk N.m \n',M_E)

+printf('The moment of force about axis AE is -%f N.m \n',M_AE)

+// The value of M_AE & M_E is incorrect in the textbook.Incorrect value of force vector is taken in calculation of M_E

diff --git a/3204/CH26/EX26.15/Ex26_15.sce b/3204/CH26/EX26.15/Ex26_15.sce
new file mode 100644
index 000000000..4a3910c4f
--- /dev/null
+++ b/3204/CH26/EX26.15/Ex26_15.sce
@@ -0,0 +1,35 @@
+// 1 APPENDIX. Ex no 15. Page no 652

+// Initilization of variables

+// Consider fig. 16. The co-ordinates of various points are

+// Co-ordinates as matrices

+// Some of the notations have been changed

+f1=5 // kN

+f2=7.5 // kN

+f3=10 // kN

+A=[0,0,0]

+E=[0,1,0]

+D=[0,0,2]

+F=[3,1,0]

+G=[3,1,2]

+H=[0,1,2] // co-ordinates of H not given in book. ref fig.16 for the same

+// Calculations

+// Force vectors

+F1=(f1/sqrt((F(1)-E(1))^2+(F(2)-E(2))^2+(F(3)-E(3))^2))*[F(1)-E(1),F(2)-E(2),F(3)-E(3)]

+F2=(f2/sqrt((D(1)-H(1))^2+(D(2)-H(2))^2+(D(3)-H(3))^2))*[D(1)-H(1),D(2)-H(2),D(3)-H(3)]

+F3=(f3/sqrt((G(1)-E(1))^2+(G(2)-E(2))^2+(G(3)-E(3))^2))*[G(1)-E(1),G(2)-E(2),G(3)-E(3)]

+// Resultant force

+R=F1+F2+F3 // kN

+// Position vectors

+r_AE=[E(1)-A(1),E(2)-A(2),E(3)-A(3)]

+r_AD=[D(1)-A(1),D(2)-A(2),D(3)-A(3)]

+// Moment of forces about A

+// Calculating the cross product

+M1=[(r_AE(2)*F1(3)-r_AE(3)*F1(2)),(r_AE(3)*F1(1)-r_AE(1)*F1(3)),(r_AE(1)*F1(2)-r_AE(2)*F1(1))]

+M2=[(r_AD(2)*F2(3)-r_AD(3)*F2(2)),(r_AD(3)*F2(1)-r_AD(1)*F2(3)),(r_AD(1)*F2(2)-r_AD(2)*F2(1))]

+M3=[(r_AE(2)*F3(3)-r_AE(3)*F3(2)),(r_AE(3)*F3(1)-r_AE(1)*F3(3)),(r_AE(1)*F3(2)-r_AE(2)*F3(1))]

+// Rseultant moment

+M_R=M1+M2+M3 // KN.m

+// Results

+clc

+printf('The resultant force is %fi %fj + %fk kN \n',R)

+printf('The resultant moment of all the forces about point A is %fi + %fj %fk kN.m \n',M_R)

diff --git a/3204/CH26/EX26.16/Ex26_16.sce b/3204/CH26/EX26.16/Ex26_16.sce
new file mode 100644
index 000000000..78074d267
--- /dev/null
+++ b/3204/CH26/EX26.16/Ex26_16.sce
@@ -0,0 +1,11 @@
+// 1 APPENDIX. Ex no 16. Page no 654

+// Initiization of variables

+F=20 // kN // Force acting at O

+M_x=76 // kNm

+M_y=82 // kNm

+// Calculations

+x=M_x/F // m

+z=M_y/F // m

+// Results

+clc

+printf('The point of application should be shifted to: x=%f m and z=%f m \n',x,z)

diff --git a/3204/CH26/EX26.17/Ex26_17.sce b/3204/CH26/EX26.17/Ex26_17.sce
new file mode 100644
index 000000000..fe9be14b0
--- /dev/null
+++ b/3204/CH26/EX26.17/Ex26_17.sce
@@ -0,0 +1,20 @@
+// 1 APPENDIX. Ex no 17. Page no 655

+// Initilization of variables

+W=5000 // N

+// Co-ordinates of various points

+A=[0,4.5,0]

+B=[2.8,0,0]

+C=[0,0,-2.4]

+D=[-2.6,0,1.8]

+// Calculations

+// Ref textbook for the values of tenion in the cable AB, AC & AD. The values consist of variables which cannot be defined here

+// We re-arrange and define the equations of equilibrium as matrices and solve them as,

+P=[0.528,0.0,-0.472;0.0,0.47,-0.327;0.85,0.88,0.818]

+Q=[0;0;5000]

+X=inv(P)*Q

+// Results

+clc

+printf('Tension in cable AD is %f N \n',X(3))

+printf('Tension in cable AB is %f N \n',X(1))

+printf('Tension in cable AC is %f N \n',X(2))

+// The answer may vary slightly due to decimal point error. Ans for T_AB is incorrect in textbook.

diff --git a/3204/CH26/EX26.18/Ex26_18.sce b/3204/CH26/EX26.18/Ex26_18.sce
new file mode 100644
index 000000000..cc441356c
--- /dev/null
+++ b/3204/CH26/EX26.18/Ex26_18.sce
@@ -0,0 +1,21 @@
+// 1 APPENDIX. Ex no 18. Page no 656

+// Initilization of variables

+P=5 // kN

+Q=3 // kN

+C=5 // kNm // couple

+//  ref fig.20 // Notations have been assumed

+z1=1.5 // m

+z2=0.625 // m

+z3=0.5 // m

+x1=3.5 // m

+x2=0.625 // m

+// Calculations

+// sum M_x=0

+R_A=((P*z2)+(Q*z3)+C)/z1 // kN

+// M_z=0

+R_C=((Q*x1)+(P*x2))/x1 // kN

+// sum F_y=0

+R_B=P+Q-R_A-R_C // kN

+// Results

+clc

+printf('The reactions are: R_A=%f kN ,R_C=%f kN and R_B=%f kN \n',R_A,R_C,R_B)

diff --git a/3204/CH26/EX26.19/Ex26_19.sce b/3204/CH26/EX26.19/Ex26_19.sce
new file mode 100644
index 000000000..cceb47fc2
--- /dev/null
+++ b/3204/CH26/EX26.19/Ex26_19.sce
@@ -0,0 +1,29 @@
+// 1 APPENDIX. Ex no 19. Page no 657
+// Initilization of variables
+F=2 // kN
+W=1 // kN
+// Co-ordinates as matrices
+A=[0,0,0]
+C=[0,0,1.2]
+B=[0,0,2.5]
+D=[-1,1,0]
+E=[1,1,0]
+F=[0,0,1]
+G=[0,0,2]
+// Force vector
+f=[0,-2,0]
+// Weight vector
+w=[0,-1,0]
+// Calculations
+// we have 5 unknowns: A_x,A_y,A_z,T_FE & T_GD
+// we define and solve eqn's 1,2,3,4&5 using matrix as,
+P=[1,0,0,0.58,-0.41;0,1,0,0.58,0.41;0,0,1,-0.58,-0.82;0,0,0,0.58,0.82;0,0,0,0.58,-0.82]
+Q=[0;3;0;6.25;0]
+
+X=inv(P)*Q
+
+// Results
+clc
+printf('The components of reaction at A are: A_x=%f kN , A_y=%f kN and A_z=%f kN \n',X(1),X(2),X(3))
+printf('The tensions in the cable are: T_FE=%f kN and T_GD=%f kN \n',X(4),X(5))
+// The solution in the textbook is incorrect and yeilds singularity in matrix calculation.
diff --git a/3204/CH26/EX26.2/Ex26_2.sce b/3204/CH26/EX26.2/Ex26_2.sce
new file mode 100644
index 000000000..733735b94
--- /dev/null
+++ b/3204/CH26/EX26.2/Ex26_2.sce
@@ -0,0 +1,27 @@
+// 1 APPENDIX. Ex no 2. Page no 639

+//Initilizatin of variable

+F=10 //N

+P_1=[2,4,3] 

+P_2=[1,-5,2]

+

+//Calculations

+d_x=P_2(1)-P_1(1) 

+d_y=P_2(2)-P_1(2)

+d_z=P_2(3)-P_1(3)

+d=sqrt(d_x^2+d_y^2+d_z^2)

+Fx=(F/d)*d_x //N

+Fy=(F/d)*d_y //N

+Fz=(F/d)*d_z //N

+//Direction cosines

+l=Fx/F

+m=Fy/F

+n=Fz/F

+//Angles

+theta_x=acosd(l) //degrees

+theta_y=acosd(m) //degrees

+theta_z=acosd(n) //degrees

+

+//Result

+clc

+printf("The force in vector notation is %fi%fj%fk\n",Fx,Fy,Fz)

+printf("Thetax=%f degrees,Thetay=%f degrees,Thetaz=%f degrees",theta_x,theta_y,theta_z)  

diff --git a/3204/CH26/EX26.3/Ex26_3.sce b/3204/CH26/EX26.3/Ex26_3.sce
new file mode 100644
index 000000000..95418aa40
--- /dev/null
+++ b/3204/CH26/EX26.3/Ex26_3.sce
@@ -0,0 +1,20 @@
+// 1 APPENDIX. Ex no 3. Page no 640
+//initiliation of variables
+T=2500 //N
+//Co-ordinates
+Q=[40,0,-30]
+P=[0,80,0]
+
+//Calculations
+mag_QP=sqrt((P(1)-Q(1))^2+(P(2)-Q(2))^2+(P(3)-Q(3))^2) //Magnitude
+QP=[(P(1)-Q(1)),(P(2)-Q(2)),(P(3)-Q(3))] 
+F=(T/mag_QP)*QP //N
+thetax=acosd(F(1)/T) //degrees
+thetay=acosd(F(2)/T) //degrees
+thetaz=acosd(F(3)/T) //degrees
+
+//Result
+clc
+printf("The force vector is %fi+%fj+%fk N\n",F(1),F(2),F(3))
+//Answer in the textbook is printed as 1600 which is incorrect
+printf("The angles are thetax=%f,thetay=%f and thetaz=%f degrees",thetax,thetay,thetaz)
diff --git a/3204/CH26/EX26.4/Ex26_4.sce b/3204/CH26/EX26.4/Ex26_4.sce
new file mode 100644
index 000000000..c746c284e
--- /dev/null
+++ b/3204/CH26/EX26.4/Ex26_4.sce
@@ -0,0 +1,14 @@
+// 1 APPENDIX. Ex no 4. Page no 642
+//initilization of variables
+A=[2,-1,1]
+B=[1,1,2]
+C=[3,-2,4]
+//Calculations
+R=[A(1)+B(1)+C(1),A(2)+B(2)+C(2),A(3)+B(3)+C(3)] //Resultant
+mag=sqrt(R(1)^2+R(2)^2+R(3)^2)
+//Unit vector
+U=R/mag 
+//Result
+clc
+printf("The unit vector is %fi%fj+%fk",U(1),U(2),U(3))
+//Answer for k part is incorrect in the textbook
diff --git a/3204/CH26/EX26.5/Ex26_5.sce b/3204/CH26/EX26.5/Ex26_5.sce
new file mode 100644
index 000000000..41c627ca2
--- /dev/null
+++ b/3204/CH26/EX26.5/Ex26_5.sce
@@ -0,0 +1,14 @@
+// 1 APPENDIX. Ex no 5. Page no 642
+//initilization of variables
+A=[2,-6,-3]
+B=[4,3,-1] 
+//Calculations
+AdotB=A(1)*B(1)+A(2)*B(2)+A(3)*B(3) 
+magA=sqrt(A(1)^2+A(2)^2+A(3)^2) 
+magB=sqrt(B(1)^2+B(2)^2+B(3)^2)
+theta=acosd(AdotB/(magA*magB)) //degrees
+
+//Result
+clc
+printf("The product of both the vectors is %f\n",AdotB)
+printf("The angle between them is %f degrees",theta)
diff --git a/3204/CH26/EX26.6/Ex26_6.sce b/3204/CH26/EX26.6/Ex26_6.sce
new file mode 100644
index 000000000..c2b1e718e
--- /dev/null
+++ b/3204/CH26/EX26.6/Ex26_6.sce
@@ -0,0 +1,13 @@
+// 1 APPENDIX. Ex no 6. Page no 643
+//initilization of variables
+A=[4,-3,1]
+P=[2,3,-1]
+Q=[-2,-4,3]
+//Calculations
+B=[Q(1)-P(1),Q(2)-P(2),Q(3)-P(3)]
+AdotB=A(1)*B(1)+A(2)*B(2)+A(3)*B(3)
+magB=sqrt(B(1)^2+B(2)^2+B(3)^2)
+Acostheta=AdotB/magB
+//Result
+clc
+printf("The value of A.costheta is %f",Acostheta)
diff --git a/3204/CH26/EX26.7/Ex26_7.sce b/3204/CH26/EX26.7/Ex26_7.sce
new file mode 100644
index 000000000..82d92ed38
--- /dev/null
+++ b/3204/CH26/EX26.7/Ex26_7.sce
@@ -0,0 +1,12 @@
+// 1 APPENDIX. Ex no 7. Page no 643
+//Initilization of variables
+F=[5,10,-15]
+a=[1,0,3]
+b=[3,-1,-6]
+//Calculations
+d=b-a
+work=F.*d
+Work=work(1)+work(2)+work(3)
+//Result
+clc
+printf("The work done is %f units",Work)
diff --git a/3204/CH26/EX26.8/Ex26_8.sce b/3204/CH26/EX26.8/Ex26_8.sce
new file mode 100644
index 000000000..948f16730
--- /dev/null
+++ b/3204/CH26/EX26.8/Ex26_8.sce
@@ -0,0 +1,16 @@
+// 1 APPENDIX. Ex no 8. Page no 644
+//initilization of variables
+A=[2,-6,-3]
+B=[4,3,-1]
+//Calculations
+AcrossB=[(A(2)*B(3)-B(2)*A(3)),A(3)*B(1)-A(1)*B(3),A(1)*B(2)-A(2)*B(1)]
+mag=sqrt(AcrossB(1)^2+AcrossB(2)^2+AcrossB(3)^2)
+n=AcrossB/mag
+magA=sqrt(A(1)^2+A(2)^2+A(3)^2)
+magB=sqrt(B(1)^2+B(2)^2+B(3)^2)
+theta=asind(mag/(magA*magB))
+//Result
+clc
+printf("The cross prcoduct of the two vectors is %fi %fj+%fk\n",AcrossB(1),AcrossB(2),AcrossB(3)) // the answer for j part is wrong in textbook
+printf("The angle between the two is %f degrees",theta)
+// Only 1 value for theta has been solved. Ref textbook for the other value
diff --git a/3204/CH26/EX26.9/Ex26_9.sce b/3204/CH26/EX26.9/Ex26_9.sce
new file mode 100644
index 000000000..5d26dd827
--- /dev/null
+++ b/3204/CH26/EX26.9/Ex26_9.sce
@@ -0,0 +1,28 @@
+// 1 APPENDIX. Ex no 9. Page no 645

+// Initilization of Variable 

+// NOTE:Some Notation has been change to avoid conflict

+// Points As martices

+A=[0,1,2]

+B=[1,3,-2]

+P=[3,6,4]

+a_s=2 // Angular speed in rad/s

+

+// Calculations

+C=[B(1)-A(1),B(2)-A(2),B(3)-A(3)]

+magC=(C(1)^2+C(2)^2+C(3)^2)^0.5 // Magnitude of the Vector C 

+// Unit vector

+C_unit=[C(1)/magC,C(2)/magC,C(3)/magC] // Unit vector

+// Position Vector

+r=[P(1)-A(1),P(2)-A(2),P(3)-A(3)]

+// Velocity Vector

+// Calculating the cross product as,

+V=[(C(2)*r(3)-C(3)*r(2)),(C(3)*r(1)-C(1)*r(3)),(C(1)*r(2)-C(2)*r(1))]

+// Vector notation

+V_n=(a_s/magC)*[V(1),V(2),V(3)]

+// Velocity Magnitude

+magV=sqrt(V(1)^2+V(2)^2+V(3)^2)

+v=(a_s/magC)*magV

+// Result

+clc

+printf("The vector notation of velocity is %fi %fj %fk \n",V_n(1),V_n(2),V_n(3))

+printf("The magnitude of the Velocity Vector is %f \n",v)