Chapter 02:Static Equilibrium

Ex2.1:pg-41

In [2]:
  import math  # Example 2_1


  #To find the tension in the other two Strings
  #As Sigma(Fx)=0
F3=80     #units in Newtons
Fx1=F3*math.sin(37*math.pi/180)    #units in Newtons
Fy1=F3*math.cos(37*math.pi/180)    #units in Newtons
F2=round(Fy1+0)      #units in Newtons
F1=round(Fx1+0)     #units in Newtons
print "Tension in String 1 is F1=",round(F1)," N\n"
print "Tension in String 2 is F2=",round(F2)," N"

Tension in String 1 is F1= 48.0  N

Tension in String 2 is F2= 64.0  N

Ex2.2:pg-41

In [3]:
  import math  # Example 2_2


  #To find the tension in the three cords that hold the object
  #As Sigma(Fx)=0
theta1=37     #units in degrees
theta2=53     #units in degrees
F1_F2=math.cos(theta2*math.pi/180)/math.cos(theta1*math.pi/180)
  #As Sigma(Fy)=0
F3=400    #units in Newtons
F2=round((F3*math.cos(theta1*math.pi/180))/(math.cos(theta1*math.pi/180)**2+math.cos(theta2*math.pi/180)**2))   #units in Newtons
F1=(math.cos(theta2*math.pi/180)/math.cos(theta1*math.pi/180))*F2     #units in Newtons
print "Tension in string 1 is F1=",round(F1)," N\n"
print "Tension in string 2 is F2=",round(F2)," N\n"
  #In textbook the Answer for F2 is printed wrong as 320 N But the correct answer is 319 N

Tension in string 1 is F1= 240.0  N

Tension in string 2 is F2= 319.0  N

Ex2.3:pg-42

In [4]:
  import math  # Example 2_3


  #To find the weight and the Tension in the cords
  #As Sigma(Fx)=0
theta1=53    #units in degrees
theta2=37     #units in degrees
F1=100      #units in Newtons
F=F1/math.cos(theta1*math.pi/180)     #units in Newtons
W=math.cos(theta2*math.pi/180)*F      #units in Newtons
print "The Weight W=",round(W)," N\n"
print "Tension in the chord is F=",round(F)," N"
  #In text book the answers are printed wrong as F=167N and W=133N but the correct answers are W=132N and F=166N

The Weight W= 133.0  N

Tension in the chord is F= 166.0  N

Ex2.5:pg-48

In [5]:
  import math  # Example 2_5


  #To find the Tension T in the Supporting Cable
  #As Sigma(Fx)=0
theta1=30     #units in degrees
theta2=90-theta1    #units in degrees
H_T=math.sin(theta1*math.pi/180)
W=2000     #Units in Newtons
T=W/math.sin(theta2*math.pi/180)     #units in Newtons
H=T*H_T     #units in Newtons
print "Tension in the Supporting Cable T=",round(T)," N"
  #In textbook The answer is printed wrong as T=2310N but the correct answer is T=2309N

Tension in the Supporting Cable T= 2309.0  N

Ex2.6:pg-52

In [6]:
  import math  # Example 2_6


  #To find the forces exerted bythe pedestals on the board
tou=900     #units in Newtons
d1=3    #units in Meters
d2=1.5    #Units in Meters
F1=-(tou*d1)/d2    #Units in Newtons
F2=tou-F1    #units in Newtons
print "The First Force F1=",round(F1)," N\n"
print "The Second Force F2=",round(F2)," N\n"

The First Force F1= -1800.0  N

The Second Force F2= 2700.0  N

Ex2.7:pg-53

In [7]:
  import math  # Example 2_7


  #To find tension in the supporting cable and Components of the force exerted by the hinge
F1=50    #units in Newtons
d1=0.7     #units in meters
F2=100     #units  in Newtons
d2=1.4     #units in meters
d3=1     #units in meters
theta2=53     #units in degrees
T=round(((F1*d1)+(F2*d2))/(d3*math.cos(theta2*math.pi/180)))     #units  in Newtons
theta1=37     #units in degrees
H=math.cos(theta1*math.pi/180)*T     #units  in Newtons

V=F1+F2-(math.cos(theta2*math.pi/180)*T)    #units in Newtons
print "Tension T=",round(T)," N\n"
print "H=",round(H)," N\n"
print "V=",round(V,2)," N"
  #In text book the answer is printed wrong as H=234N but the correct answer is H=232N

Tension T= 291.0  N

H= 232.0  N

V= -25.13  N

Ex2.8:pg-55

In [8]:
  import math  # Example 2_8


  #To find the tension in the Muscle and the Component Forces at elbow
F1=65     #units in Newtons
d1=0.1    #units in Meters
F2=20     #Units in Newtons
d2=0.35     #units in meters
theta1=20     #units in degrees
d3=0.035     #units in Meters
Tm=((F1*d1)+(F2*d2))/(math.cos(theta1*math.pi/180)*d3)     #units in Newtons
V=F1+F2-(Tm*math.cos(theta1*math.pi/180))
H=Tm*math.sin(theta1*math.pi/180)
print "Tension T=",round(Tm)," N\n"
print "H=",round(H)," N\n"
print "V=",round(V)," N"

Tension T= 410.0  N

H= 140.0  N

V= -301.0  N

Ex2.9:pg-55

In [9]:
  import math  # Example 2_9


#To find the forces at the wall and the ground
theta1=53    #units in degrees
d1=3    #units in meters
F1=200    #units in Newtons
d2=4    #units in Meters
F2=400    #units in Newtons
theta2=37    #units in degrees
d3=6     #units in meters
P=((math.cos(theta1*math.pi/180)*d1*F1)+(math.cos(theta1*math.pi/180)*d2*F2))/(math.cos(theta2*math.pi/180)*d3)   #units in Newtons
H=P   #units in Newtons
V=F1+F2     #units in Newtons
print "Force P=",round(P)," N\n"
print "Force V=",round(V)," N\n"
print "Force H=",round(H)," N"
  #In text book the answer is printed wrong as P=H=275N but the correct answer is P=H=276N

Force P= 276.0  N

Force V= 600.0  N

Force H= 276.0  N