Added new codeHEADmaster

15 files changed, 289 insertions, 0 deletions

diff --git a/3862/CH5/EX5.1/Ex5_1.sce b/3862/CH5/EX5.1/Ex5_1.sce
new file mode 100644
index 000000000..2bd85cb19
--- /dev/null
+++ b/3862/CH5/EX5.1/Ex5_1.sce
@@ -0,0 +1,33 @@
+clear
+//
+Wa=1000.0 //weight of block a
+Wb=2000.0  //weight of block b
+uab=1.0/4.0   //coefficient of friction between A and B
+ubg=1.0/3.0    //coefficient of friction between g and B
+
+//When P is horizontal
+//considering  equilibrium of block A
+N1=Wa         //Normal Reaction on block A from block B
+F1=uab*N1     //limiting Friction between A and B
+T=F1         //tension
+//considering  equilibrium of block B
+N2=N1+ Wb         //Normal Reaction on block B from G
+
+F2=ubg*N2     //limiting Friction between A and g
+
+P=F1+F2
+printf("\n P= %0.3f  N",P)
+//When P is inclined at angle o
+o=30.0*3.14/180.0
+//considering  equilibrium of block A
+N1=Wa         //Normal Reaction on block A from block B
+F1=uab*N1     //limiting Friction between A and B
+T=F1         //tension
+//considering  equilibrium of block B
+//from
+//N2+Psin30=N1+Wb
+//Pcos30=F1+F2
+//F1=ubg*N2
+N2=(N1+Wb-F1*tan(o))/(1+ubg*tan(o))
+P=(N1+Wb-N2)/sin(o)
+printf("\n P= %0.3f  N",P)
diff --git a/3862/CH5/EX5.11/Ex5_11.sce b/3862/CH5/EX5.11/Ex5_11.sce
new file mode 100644
index 000000000..6261d9690
--- /dev/null
+++ b/3862/CH5/EX5.11/Ex5_11.sce
@@ -0,0 +1,23 @@
+clear
+//
+l=6.0    //length of ladder
+u1=0.4    //coefficient of friction between the wall and the ladder
+w=200.0   //weight of ladder
+u2=0.25    //coefficient of friction between floor and the ladder
+wl=900.0     //weight of load
+ll=5.0      //distance of load
+//force balancing
+//Na Nb   normal reaction at A and B
+//Fa Fb    friction  at A and B
+//Fa=u2*Na              
+//Fb=u1*Nb
+//Na+Fb=w+wl
+//Fa=Nb
+Nb=(wl+w)*u2/(1+u2*u1)
+Na=Nb/u2
+Fa=u2*Na
+Fb=u1*Nb
+//sum of all moments about a is =0
+temp=((w*l*0.5)+(wl*ll)-(Fb*l))/(Nb*l)
+o=atan(temp)*180/3.14
+printf("\n Angle of inclination is  %0.3f  degrees",o)
diff --git a/3862/CH5/EX5.12/Ex5_12.sce b/3862/CH5/EX5.12/Ex5_12.sce
new file mode 100644
index 000000000..259ca17f7
--- /dev/null
+++ b/3862/CH5/EX5.12/Ex5_12.sce
@@ -0,0 +1,14 @@
+clear
+//
+o=45.0*3.14/180.0       //angle of inclination 
+u=0.5                        //coefficient of friction
+r=1.5                    //ratio of mans weight to ladders weight
+o1=45.0*%pi/180.0           //angle of inclination
+//from law of friction
+//Fa = μNa
+//Fb = μNb
+//Fa – Nb = 0 
+//Na + Fb = W + r W
+//ΣMA = 0
+o=(((u*u+u)*(1+r)/((1+u)))-1.0/2.0)/r
+printf("\n length will %0.3f  times",o)
diff --git a/3862/CH5/EX5.13/Ex5_13.sce b/3862/CH5/EX5.13/Ex5_13.sce
new file mode 100644
index 000000000..bee2a03f5
--- /dev/null
+++ b/3862/CH5/EX5.13/Ex5_13.sce
@@ -0,0 +1,15 @@
+clear
+//
+n=1.25                 //number of turns
+o=2*3.14*n              //angle of contact
+u=0.3                 //coefficient of friction
+t=600.0                //force at the other end of the rope
+//if the impending motion of the weight be downward.
+T2=t*%e**(u*o)
+W=T2
+printf("Maximum weight is %f",W)
+printf("\n answer in textbook is wrong") 
+//if the impending motion of weight be upwards
+T1=t*%e**(-1*u*o)
+W=T1
+printf("\n  Minimum weight is %f",W)
diff --git a/3862/CH5/EX5.14/Ex5_14.sce b/3862/CH5/EX5.14/Ex5_14.sce
new file mode 100644
index 000000000..882e71c85
--- /dev/null
+++ b/3862/CH5/EX5.14/Ex5_14.sce
@@ -0,0 +1,23 @@
+clear
+//
+ur=0.20       //The coefficient of friction  between the rope and the fixed drum
+uo=0.30        //The coefficient of friction  between other surfaces
+cosa=4.0/5.0 //cos of angle of inclination
+sina=3.0/5.0 //sin of angle of inclination
+Ww=1000.0  //weight
+o=3.14   //angle of contact of rope with pulley
+//for unknown weight
+//force balance perpendicular to the plane
+//N1 = W cos α
+//fr=uoN1
+//force balance along the plane
+//T1 = F1 + W sin α
+//for 1000 N body
+//force balance perpendicular to the plane
+//N2=N1+Wwcosa
+//fr2=uoN2
+//force balance along the plane
+//T2= Wwsina -F1 -F2
+//T2=T1*e^(ur*o)
+W=(Ww*sina-uo*Ww*cosa)/(((uo*cosa+sina)*(2.71**(uo*o)))+(uo*cosa+uo*cosa))
+printf("\n Weight is  %0.3f  N",W)
diff --git a/3862/CH5/EX5.15/Ex5_15.sce b/3862/CH5/EX5.15/Ex5_15.sce
new file mode 100644
index 000000000..4eae92a1f
--- /dev/null
+++ b/3862/CH5/EX5.15/Ex5_15.sce
@@ -0,0 +1,16 @@
+clear
+//
+u=0.3           //coefficient of friction
+r=250           //radius of brake drum
+l=300            //length of lever arm
+M=300000.0      //torque
+o=r*3.14/180.0
+l2=50.0
+//using
+//T2 = T1e^(μθ)         T1 and T2 are tension
+//(T2-T1)r=M
+T1=M/(r*(2.71**(u*o)-1))
+T2=(2.71**(u*o))*T1
+//Consider the lever arm. Taking moment about the hinge
+p=T2*l2/l                     //force P applied at the end of the brake lever
+printf("force P applied at the end of the brake lever %0.3f N",p)
diff --git a/3862/CH5/EX5.16/Ex5_16.sce b/3862/CH5/EX5.16/Ex5_16.sce
new file mode 100644
index 000000000..f7a55c7a0
--- /dev/null
+++ b/3862/CH5/EX5.16/Ex5_16.sce
@@ -0,0 +1,16 @@
+clear
+//
+d1=500.0         //diameter of a shaft
+d2=100.0        //diameter of a shaft
+D=3000.0                   //distance between shafts in mm
+T=1000.0              //Maximum permissible tension in the belt
+U=0.25           //coefficient of friction between the belt and the pulley
+R=220.0              //revlution per minute of larger shaft
+//Length of belt = Arc length DC + Arc length FE + 2BG
+O1=3.14+2*asin((d1+d2)/(2*D))
+L=(d1/2+d2/2)*O1+2*D*cos(asin((d1+d2)/(2*D)))
+printf("\n Length of belt is  %0.3f  mm",L)
+T1=T/(2.71**(U*O1))
+Velocity_of_the_belt =d1/2*(R*2*3.14/60.0)
+Power_transmitted=(T-T1)*Velocity_of_the_belt
+printf("\n Power Transmitted %0.3f  Watt",Power_transmitted)
diff --git a/3862/CH5/EX5.17/Ex5_17.sce b/3862/CH5/EX5.17/Ex5_17.sce
new file mode 100644
index 000000000..381270730
--- /dev/null
+++ b/3862/CH5/EX5.17/Ex5_17.sce
@@ -0,0 +1,17 @@
+clear
+//
+d1=500.0         //diameter of a shaft
+d2=100.0        //diameter of a shaft
+D=3000.0                   //distance between shafts in mm
+T=1000.0              //Maximum permissible tension in the belt
+U=0.25           //coefficient of friction between the belt and the pulley
+R=220.0              //revlution per minute of larger shaft
+O1=3.14+2*asin((d1-d2)/(2*D))
+O2=3.14-2*asin((d1-d2)/(2*D))
+//Length of belt = Arc length DC + Arc length FE + 2BG
+L=(d1/2*O1+d2/2*O2)+2*D*cos(asin((d1-d2)/(2*D)))
+printf("\n Length of belt is  %0.3f  mm",L)
+T1=T/(2.71**(U*O2))
+Velocity_of_the_belt =d1/2*(R*2*3.14/60.0)
+Power_transmitted=(T-T1)*Velocity_of_the_belt
+printf("\n Power Transmitted %0.3f  Watt",Power_transmitted)
diff --git a/3862/CH5/EX5.2/Ex5_2.sce b/3862/CH5/EX5.2/Ex5_2.sce
new file mode 100644
index 000000000..a2aedc35b
--- /dev/null
+++ b/3862/CH5/EX5.2/Ex5_2.sce
@@ -0,0 +1,14 @@
+clear
+//
+Wa=300.0 //weight of upper block 
+Wb=900.0  //weight of lower block 
+u1=1.0/3.0   //coefficient of friction between upper block and lower block
+u2=1.0/3.0    //coefficient of friction between g and  lower block
+
+//using 
+//N1=Wacoso          Normal Reaction
+//F1=u1*N1           Friction
+//N2=Wbcoso+N1
+//F2=u2*N2
+o=atan((u1*Wa+u2*Wb+u2*Wa)/Wb)*180/3.14
+printf("\n %0.3f °",o)
diff --git a/3862/CH5/EX5.3/Ex5_3.sce b/3862/CH5/EX5.3/Ex5_3.sce
new file mode 100644
index 000000000..284963ee9
--- /dev/null
+++ b/3862/CH5/EX5.3/Ex5_3.sce
@@ -0,0 +1,22 @@
+clear
+//
+W=500.0    //weight of block
+F1=200.0     //force up the inclined plane when block is moving down
+F2=300.0     //force up the inclined plane when block is at rest
+//When block starts moving down the plane
+//sum of all forces perpendicular to the plane = 0
+//N =Wcoso
+//sum of all forces parallel to the plane = 0
+//Fr+F1=Wsino
+//sino-ucoso=F1/w    1
+//When block starts moving up the plane
+//sum of all forces perpendicular to the plane = 0
+//N =Wcoso
+//sum of all forces parallel to the plane = 0
+//Wsino+Wucoso=F2
+//using these equations
+o=asin((F1*0.5/W)+(F2*0.5/W))   //angle of inclination
+printf("\n Angle of inclination is  %0.3f  ",o*180/3.14)
+//using 1
+u=sin(o)-F1/W
+printf("\n coefficient of friction is %0.3f  ",u)
diff --git a/3862/CH5/EX5.4/Ex5_4.sce b/3862/CH5/EX5.4/Ex5_4.sce
new file mode 100644
index 000000000..98f73d9b8
--- /dev/null
+++ b/3862/CH5/EX5.4/Ex5_4.sce
@@ -0,0 +1,17 @@
+clear
+//
+uag=0.5   //coefficient of friction between block A and the plane
+ubg=0.2   //coefficient of friction between block B and the plane
+Wb=500.0  //weight of block B
+Wa=1000.0  //weight of block A
+//Considering equilibrium of block A,
+//sum of all forces along the plane is 0
+//N1=Wacoso ,Fr=uagN1
+//sum of all forces perpendicaular to  the plane is 0
+//T=uagWacoso-Wasino
+//Considering equilibrium of block A,
+//sum of all forces along the plane is 0
+//N2=Wbcoso ,Fr=uagN2
+//sum of all forces perpendicaular to  the plane is 0
+//T=Wbsino-ubgwbsino
+o=atan((uag*Wa+ubg*Wb)/(Wa+Wb))*180.0/3.14
diff --git a/3862/CH5/EX5.5/Ex5_5.sce b/3862/CH5/EX5.5/Ex5_5.sce
new file mode 100644
index 000000000..cff5d1ab8
--- /dev/null
+++ b/3862/CH5/EX5.5/Ex5_5.sce
@@ -0,0 +1,16 @@
+clear
+//
+Wl=750.0  //weight of lower block
+Wu=500.0  //weight of upper block
+o1=60.0*3.14/180.0   //angle of inclined plane
+o2=30.0 *3.14/180.0 // anlge at which pull is applied
+u=0.2     //coefficient of friction
+//for 750 N block
+//Σ Forces normal to the plane = 0 
+N1=Wl*cos(o1)
+F1=u*N1
+//Σ Forces parallel to the plane = 0
+T=F1+Wl*sin(o1)
+//Σ Forces horizontal to the plane = 0
+P=(T+u*Wu)/(cos(o2)+u*sin(o2))
+printf("\n %0.3f N",P)
diff --git a/3862/CH5/EX5.6/Ex5_6.sce b/3862/CH5/EX5.6/Ex5_6.sce
new file mode 100644
index 000000000..56751a264
--- /dev/null
+++ b/3862/CH5/EX5.6/Ex5_6.sce
@@ -0,0 +1,27 @@
+clear
+//
+o1=60.0*3.14/180.0    //angle of inclination of plane AC
+o2=30.0*3.14/180.0    //angle of inclination of plane BC
+Wbc=1000.0  //weight of block on plane BC
+ubc=0.28    //coefficient of friction between the load and the plane BC 
+uac=0.20   //coefficient of friction between the load and the plane AC
+//for least weight 
+N1=Wbc*cos(o2)                            //Normal Reaction
+F1=ubc*N1                                       //frictional Force
+T=Wbc*sin(o2)-F1                          //Tension
+//for block on plane AC
+//N2=Wcoso1
+//F2=uac*N2
+//T=F2+W sino2
+W=T/(uac*cos(o1)+sin(o1))
+printf("\n Least Weight is %0.3f  N",W)
+//for greatest weight 
+N1=Wbc*cos(o2)                            //Normal Reaction
+F1=ubc*N1                                       //frictional Force
+T=Wbc*sin(o2)+F1                          //Tension
+//for block on plane AC
+//N2=Wcoso1
+//F2=uac*N2
+//T=F2+W sino2
+W=T/(-1*uac*cos(o1)+sin(o1))
+printf("\n Greatest Weight is %0.3f  N",W)
diff --git a/3862/CH5/EX5.7/Ex5_7.sce b/3862/CH5/EX5.7/Ex5_7.sce
new file mode 100644
index 000000000..9781c9674
--- /dev/null
+++ b/3862/CH5/EX5.7/Ex5_7.sce
@@ -0,0 +1,22 @@
+clear
+//
+u=0.4     //The coefficient of friction on the horizontal plane
+oi=30     //angle of inclined plane
+o=20.0  //The limiting angle of  friction for block B on the inclined plane
+wb=5000.0   //weight of block b
+ub=tan(o*3.14/180.0)            //coefficcient of friction on plane
+//for block B
+//N1 N2 N3 are normal reaction
+//F1 F2  are frictional forces
+//F1=ub*N1   
+//N1 sinoi + F1 cos oi=wb
+N1=wb/(sin(oi*3.14/180.0)+ub*cos(oi*3.14/180.0))
+F1=ub*N1
+C=N1*cos(oi*3.14/180.0)-F1*sin(oi*3.14/180.0)
+
+//force balance on A in horizontal balance
+F2=C
+N2=F2/u
+//force balance on A in vertical balance
+W=N2
+printf("\n Weight  %0.3f  N",W)
diff --git a/3862/CH5/EX5.8/Ex5_8.sce b/3862/CH5/EX5.8/Ex5_8.sce
new file mode 100644
index 000000000..a20ff3285
--- /dev/null
+++ b/3862/CH5/EX5.8/Ex5_8.sce
@@ -0,0 +1,14 @@
+clear
+//
+w=20000.0    //weight of upper block
+o=15.0      //The angle of friction for all surfaces of contact
+u=tan(o)  //coefficient of friction
+//R1 R2 are forces
+Or1=15.0     //angle force R1 makes with x axis
+Or2=35.0       //angle force R2 makes with Y axis
+R2=w*sin((90-Or1)*3.14/180.0)/sin((90+Or1+Or2)*3.14/180.0)
+//applyig lamis theorem on block B
+Or1=15.0     //angle force R3 makes with Y axis
+Or2=35.0       //angle force R2 makes with Y axis
+P=R2*sin((180-Or1-Or2)*3.14/180.0)/sin((90+Or1)*3.14/180.0)
+printf("\n Force = %0.3f  N",P)