diff options
Diffstat (limited to '3792/CH7')
| -rw-r--r-- | 3792/CH7/EX7.1/Ex7_1.sce | 34 | ||||
| -rw-r--r-- | 3792/CH7/EX7.2/Ex7_2.sce | 32 | ||||
| -rw-r--r-- | 3792/CH7/EX7.3/Ex7_3.sce | 29 | ||||
| -rw-r--r-- | 3792/CH7/EX7.4/Ex7_4.sce | 33 | ||||
| -rw-r--r-- | 3792/CH7/EX7.5/Ex7_5.sce | 51 | ||||
| -rw-r--r-- | 3792/CH7/EX7.6/Ex7_6.sce | 41 | ||||
| -rw-r--r-- | 3792/CH7/EX7.8/Ex7_8.sce | 25 | ||||
| -rw-r--r-- | 3792/CH7/EX7.9/Ex7_9.sce | 20 |
8 files changed, 265 insertions, 0 deletions
diff --git a/3792/CH7/EX7.1/Ex7_1.sce b/3792/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..e4ca762ce --- /dev/null +++ b/3792/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,34 @@ +// SAMPLE PROBLEM 7/1
+clc;funcprot(0);
+// Given data
+L=0.8;// m
+N=60;// rev/min
+betadot=4;// rad/s
+beta=30;// degree
+
+// Solution
+// (a)
+omega_x=betadot;// (i) rad/s
+omega_z=(2*%pi*N/60);// (k) rad/s
+omega=[omega_x,0,omega_z];// (i,j,k) rad/s
+printf("\n(a)The angular velocity of OA,omega=%1.0fi+%1.2fk rad/s",omega(1),omega(3));
+// (b)
+omegadot_z=0;// (k) rad/s
+omegadot_x=omega_z*omega_x;// (i) rad/s
+alpha=omegadot_x+omegadot_z;// (j) rad/s^2
+alpha=[0,alpha,0];// (i,j,k) rad/s^2
+printf("\n(b)The angular acceleration of OA,alpha=%2.1fj rad/s^2",alpha(2));
+// (c)
+r=[0,0.693,0.4];// m
+// v=omega*r;
+v_1=det([omega(2),omega(3);r(2),r(3)]);// m/s
+v_2=-det([omega(1),omega(3);r(1),r(3)]);// m/s
+v_3=det([omega(1),omega(2);r(1),r(2)]);// m/s
+v=[v_1,v_2,v_3];// m/s
+printf("\n(c)The velocity of point A,v=%1.2fi+(%1.2f)j+%1.2fk m/s",v(1),v(2),v(3));
+// (d)
+a_1=det([alpha(2),alpha(3);r(2),r(3)])+det([omega(2),omega(3);v(2),v(3)]);// m/s^2
+a_2=-det([alpha(1),alpha(3);r(1),r(3)])+(-det([omega(1),omega(3);v(1),v(3)]));// m/s^2
+a_3=det([alpha(1),alpha(2);r(1),r(2)])+det([omega(1),omega(2);v(1),v(2)]);// m/s^2
+a=[a_1,a_2,a_3];// m/s^2
+printf("\n(d)The acceleration of point A,v=%2.1fi+(%2.1f)j+(%1.2f)k m/s^2",a(1),a(2),a(3));
diff --git a/3792/CH7/EX7.2/Ex7_2.sce b/3792/CH7/EX7.2/Ex7_2.sce new file mode 100644 index 000000000..f2685b098 --- /dev/null +++ b/3792/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,32 @@ +// SAMPLE PROBLEM 7/2
+clc;funcprot(0);
+// Given data
+N_0=120;// rev/min
+N=60;// rev/min
+gamma=30;// degree
+OCbar=10;// inch
+CAbar=5;// inch
+theta=30;// degree
+
+// Calculation
+// (a)
+omega_0=(2*%pi*N_0)/60;// rad/sec
+omega_1=(2*%pi*N)/60;// rad/sec
+omega=[0,(omega_1*cosd(gamma)),(omega_0+(omega_1*sind(theta)))];// rad/sec
+printf("\n(a)The angular velocity,omega=%1.2fj+%2.2fk rad/s",omega(2),omega(3));
+alpha=[(omega_1*omega_0*cosd(theta)),0,0];// rad/sec^2
+printf("\n(b)The angular acceleration,alpha=%2.1fi rad/s^2",alpha(1));
+r=[0,5,10];// inch
+// (c)
+// v=omega*r;
+v_1=det([omega(2),omega(3);r(2),r(3)]);// in/sec
+v_2=-det([omega(1),omega(3);r(1),r(3)]);// in/sec
+v_3=det([omega(1),omega(2);r(1),r(2)]);// in/sec
+v=[v_1,v_2,v_3];// in/sec
+printf("\n(c)The velocity of point A,v=%2.1fi+(%1.0f)j+%1.fk in/sec",v(1),v(2),v(3));
+// a=(alpha*r)+(omega*v)
+a_1=det([alpha(2),alpha(3);r(2),r(3)])+det([omega(2),omega(3);v(2),v(3)]);// in/sec^2
+a_2=-det([alpha(1),alpha(3);r(1),r(3)])+(-det([omega(1),omega(3);v(1),v(3)]));// in/sec^2
+a_3=det([alpha(1),alpha(2);r(1),r(2)])+det([omega(1),omega(2);v(1),v(2)]);// in/sec^2
+a=[a_1,a_2,a_3];// in/sec^2
+printf("\n The acceleration of point A,a=%1.0fi+(%1.0f)j+%3.0fk in/sec^2",a(1),a(2),a(3));
diff --git a/3792/CH7/EX7.3/Ex7_3.sce b/3792/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..d05d17cb4 --- /dev/null +++ b/3792/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,29 @@ +// SAMPLE PROBLEM 7/3
+clc;funcprot(0);
+// Given data
+omega_1=6;// rad/s
+r_x=50;// mm
+r_y=100;// mm
+r_z=100;// mm
+
+
+// Calculation
+// v_A=r_x*omega_2;
+v_B=r_y*omega_1;// (i) mm/s
+// v_A=v_B+(omega_n*r_A/B);
+// Expanding the determinant and equating the coefficients of the i, j, k terms give
+function[X]=velocity(y)
+ X(1)=-6-(y(2)-y(3));
+ X(2)=y(4)-((-2*y(1))+y(3));
+ X(3)=0-((2*y(1))-y(2));
+ X(4)=((r_x*y(1))+(r_y*y(2))+(r_z*y(3)));
+endfunction
+y=[1 1 1 1];
+z=fsolve(y,velocity);
+omega_nx=z(1);// rad/s
+omega_ny=z(2);// rad/s
+omega_nz=z(3);// rad/s
+omega_2=z(4);// rad/s
+omega_n=[omega_nx,omega_ny,omega_nz];// rad/s
+omega_n=norm(omega_n);// rad/s
+printf("\nThe angular velocity of crank DA,omega_2=%1.0f rad/s \nThe angular velocity of link AB,omega_n=%1.3f rad/s",omega_2,omega_n);
diff --git a/3792/CH7/EX7.4/Ex7_4.sce b/3792/CH7/EX7.4/Ex7_4.sce new file mode 100644 index 000000000..73ad45fd9 --- /dev/null +++ b/3792/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,33 @@ +// SAMPLE PROBLEM 7/4
+clc;funcprot(0);
+// Given data
+// From sample problem 7/3
+omega_1=6;// rad/s
+omega_2=6;// rad/s
+r_x=50;// mm
+r_y=100;// mm
+r_z=100;// mm
+omega_n=2*sqrt(5);// rad/s
+
+// Calculation
+r_AB=[r_x,r_y,r_z];// mm
+// a_A=[r_x*omega_2^2]i+[r_x*omegadot]j;
+// a_B=[r_y*omega_1^2]k+[0]i;
+omegadot=(omega_n)^2*(r_AB);// rad/s^2
+// omegadot*r_A/B=(100*omegadot_ny-100*omegadot_nz)i+(50*omegadot_nz-100*omegadot_nx)j+(100*omegadot_nx-50omegadot_ny)k
+function[X]=velocity(y)
+ X(1)=28-(y(2)-y(3));
+ X(2)=(y(4)+40)-((-2*y(1))+y(3));
+ X(3)=-32-((2*y(1))-y(2));
+ X(4)=((2*y(1))+(4*y(2))+(4*y(3)));
+endfunction
+y=[1 10 10 10];
+z=fsolve(y,velocity);
+omegadot_nx=z(1);// rad/s^2
+omegadot_ny=z(2);// rad/s^2
+omegadot_nz=z(3);// rad/s^2
+omegadot_2=z(4);// rad/s^2
+omegadot_n=[omegadot_nx,omegadot_ny,omegadot_nz];// rad/s^2
+omegadot_n=norm(omegadot_n);// rad/s^2
+printf("\nThe angular acceleration of crank AD,omegadot_2=%2.0f rad/s \nThe angular acceleration of link AB,omegadot_n=%2.2f rad/s",omegadot_2,omegadot_n);
+
diff --git a/3792/CH7/EX7.5/Ex7_5.sce b/3792/CH7/EX7.5/Ex7_5.sce new file mode 100644 index 000000000..a098ea34c --- /dev/null +++ b/3792/CH7/EX7.5/Ex7_5.sce @@ -0,0 +1,51 @@ +// SAMPLE Pr_BOBLEM 7/5
+clc;funcprot(0);
+// Given data
+omega=3;// rad/s
+p=8;// rad/s
+gamma=30;// degree
+y=0.300;// m
+z=0.120;// m
+
+// Calculation
+// Velocity
+omega=[0,0,3];// rad/s
+r_B=[0,0.350,0];// m
+v_B1=det([omega(2),omega(3);r_B(2),r_B(3)]);// m/s
+v_B2=-det([omega(1),omega(3);r_B(1),r_B(3)]);// m/s
+v_B3=det([omega(1),omega(2);r_B(1),r_B(2)]);// m/s
+v_B=[v_B1,v_B2,v_B3];// m/s
+// Note that k*i=J=jcos(gamma)-ksin(gamma),K*j=-i*cos(gamma) and K*k=i*sin(gamma)
+r_AB=[0,y,z];// m
+// omega*r_AB=3K*(yj+zk);
+omegaintor_AB=(-(omega(3)*(y*cosd(gamma))))+(omega(3)*(z*sind(gamma)));// m/s
+p=[0,8,0];// rad/s
+v_rel1=det([p(2),p(3);r_AB(2),r_AB(3)]);// m/s
+v_rel2=-det([p(1),p(3);r_AB(1),r_AB(3)]);// m/s
+v_rel3=det([p(1),p(2);r_AB(1),r_AB(2)]);// m/s
+v_rel=[v_rel1,v_rel2,v_rel3];// m/s
+v_A=v_B(1)+omegaintor_AB+v_rel(1);// m/s
+printf("\nThe velocity of point A,v_A=%0.4fi m/s",v_A);
+// Acceleration
+a_B1=det([omega(2),omega(3);v_B(2),v_B(3)]);// m/s^2
+a_B2=-det([omega(1),omega(3);v_B(1),v_B(3)]);// m/s^2
+a_B3=det([omega(1),omega(2);v_B(1),v_B(2)]);// m/s^2
+a_B=[a_B1,a_B2,a_B3];// m/s^2
+a_B=[0,((a_B(2)*(cosd(gamma)))),-(a_B(2)*(sind(gamma)))];// m/s^2
+omegadot=0;// m/s^2
+// Assume O=omega*(omega*r_A/B)
+O=[0,((omega(3)*omegaintor_AB*(cosd(gamma)))),-omega(3)*(omegaintor_AB*(sind(gamma)))];// m/s^2
+// Assume O_1=2*omega*v_rel
+O_1=[0,((2*omega(3)*v_rel(1)*(cosd(gamma)))),-2*omega(3)*(v_rel(1)*(sind(gamma)))];// m/s^2
+a_rel1=det([p(2),p(3);v_rel(2),v_rel(3)]);// m/s^2
+a_rel2=-det([p(1),p(3);v_rel(1),v_rel(3)]);// m/s^2
+a_rel3=det([p(1),p(2);v_rel(1),v_rel(2)]);// m/s^2
+a_rel=[a_rel1,a_rel2,a_rel3];// m/s^2
+a_A=[(a_B(1)+(omegadot*r_AB(1))+O(1)+O_1(1)+a_rel1),(a_B(2)+(omegadot*r_AB(2))+O(2)+O_1(2)+a_rel2),(a_B(3)+(omegadot*r_AB(3))+O(3)+O_1(3)+a_rel3)];// m/s^2
+a_A=norm(a_A);// m/s^2
+printf("\nThe acceleration of point A,a_A=%1.2f m/s",a_A);
+// Angular Acceleration
+// Note that k*i=J=jcos(gamma)-ksin(gamma),K*j=-i*cos(gamma) and K*k=i*sin(gamma)
+omega=[3,8];// rad/s (K,j)(k*j=-i*cos(gamma))
+alpha=[0+(-omega(1)*omega(2)*cosd(gamma))];// (i) rad/s^2
+printf("\nThe angular acceleration of the disk,alpha=%2.1fi rad/s^2",alpha);
diff --git a/3792/CH7/EX7.6/Ex7_6.sce b/3792/CH7/EX7.6/Ex7_6.sce new file mode 100644 index 000000000..5a6ce6d19 --- /dev/null +++ b/3792/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,41 @@ +// SAMPLE PROBLEM 7/6
+clc;funcprot(0);
+// Given data
+m=70;// The mass of bent plate in kg
+omega=30;// rad/s
+x_A=0.125;// m
+y_A=0.100;// m
+x_B=0.075;// m
+y_B=.150;// m
+d_x=0.0375;// m
+d_y=0.125;// m
+d_z=0.075;// m
+
+// Calculation
+// Part A
+m_A=x_A*y_A*m;// kg
+m_B=x_B*y_B*m;// kg
+I_xxA=((m_A/12)*(y_A^2+x_A^2))+(m_A*((x_A/2)^2+(y_A/2)^2));// kg.m^2
+I_yyA=(m_A/3)*(y_A)^2;// kg.m^2
+I_zzA=(m_A/3)*(x_A)^2;// kg.m^2
+I_xyA=0;// kg.m^2
+I_xzA=0;// kg.m^2
+I_yzA=0+(m_A*(x_A/2)*(y_A/2));// kg.m^2
+// Part B
+I_xxB=((m_B/12)*(y_B^2))+((m_B)*(d_y^2+d_z^2));// kg.m^2
+I_yyB=((m_B/12)*(x_B^2+y_B^2))+(m_B*(d_x^2+d_z^2));// kg.m^2
+I_zzB=((m_B/12)*(x_B^2))+(m_B*((x_A)^2+(d_x^2)));// kg.m^2
+I_xyB=0+(m_B*d_x*d_y);// kg.m^2
+I_xzB=0+(m_B*d_x*d_z);// kg.m^2
+I_yzB=0+(m_B*d_y*d_z);// kg.m^2
+I_xx=I_xxA+I_xxB;// kg.m^2
+I_yy=I_yyA+I_yyB;// kg.m^2
+I_zz=I_zzA+I_zzB;// kg.m^2
+I_xy=I_xyA+I_xyB;// kg.m^2
+I_xz=I_xzA+I_xzB;// kg.m^2
+I_yz=I_yzA+I_yzB;// kg.m^2
+// (a)
+H_o=[-(omega*I_xz),-(omega*I_yz),(omega*I_zz)];// The angular momentum of the body in N.m.s
+// (b)
+T=(1/2)*(omega)*[H_o(3)];//(k.i=0,k.j=0,k.k=1) The kinetic energy in J
+printf("\n(a)The angular momentum H of the plate about point O,H_O=%0.4fi+(%0.4f)j+%0.4fk \n(b)The kinetic energy of the plate,T=%1.2f J",H_o(1),H_o(2),H_o(3),T);
diff --git a/3792/CH7/EX7.8/Ex7_8.sce b/3792/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..230175198 --- /dev/null +++ b/3792/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,25 @@ +// SAMPLE PROBLEM 7/8
+clc;funcprot(0);
+// Given data
+m=1000;// The mass of turbine rotor in kg
+k=0.200;// m
+N=500;// rev/min
+rho=400;// The radius of gyration in m
+v=25*0.514;// m/s
+d_AG=0.6;// m
+d_GB=0.9;// m
+d_AB=d_AG+d_GB;// m
+g=9.81;// The acceleration due to gravity in m/s^2
+
+// Calculation
+// The moment principle from statics easily gives
+W=m*g;// N
+R_1=(m*g)*d_AG;// N
+R_2=W-R_1;// N
+omega=(v/rho);// rad/s
+I=m*k^2;// kg-m^2
+deltaR=(I*omega*((2*%pi*N)/60))/d_AB;
+R_A=R_1-deltaR;// N
+R_B=R_2+deltaR;// N
+printf("\nThe vertical components of the bearing reactions at A and B,R_A=%4.0f N and R_B=%4.0f N",R_A,R_B);
+// The answer provided in the textbook is wrong
diff --git a/3792/CH7/EX7.9/Ex7_9.sce b/3792/CH7/EX7.9/Ex7_9.sce new file mode 100644 index 000000000..fae018e14 --- /dev/null +++ b/3792/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,20 @@ +// SAMPLE PROBLEM 7/9
+clc;funcprot(0);
+// Given data
+t=4;// s
+theta=20;// degree
+p=(2*%pi)/4;// rad/s
+
+// Calculation
+// (a)
+// I_zz=(56/3)*mr^2;
+// I_xx=(32/3)*mr^2;
+// By using coefficient of I_xx and I_zz
+I=56/3;// The moment of inertia
+I_0=32/3;// The moment of inertia
+costheta=1;// radian
+n=I/((I_0-I)*costheta);// The ratio of angular rates
+// (b)
+tau=((2*%pi)/p)*abs(((I_0-I)/I)*cosd(theta));// s
+beta=atand((I/I_0)*tand(theta));// degree
+printf("\n(a)The number of complete cycles,n=%1.2f \n The minus sign indicates retrograde precession where, in the present case,and p are essentially of opposite sense. Thus, the station will make seven wobbles for every three revolutions. \n(b)The period of precession,tau=%1.3f s",n,tau);
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