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"source": [
"# Chapter 02:Static Equilibrium"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.1:pg-41"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tension in String 1 is F1= 48.0 N\n",
"\n",
"Tension in String 2 is F2= 64.0 N\n"
]
}
],
"source": [
" #Example 2_1\n",
"\n",
"\n",
" #To find the tension in the other two Strings\n",
" #As Sigma(Fx)=0\n",
"F3=80 #units in Newtons\n",
"Fx1=F3*math.sin(37*math.pi/180) #units in Newtons\n",
"Fy1=F3*math.cos(37*math.pi/180) #units in Newtons\n",
"F2=round(Fy1+0) #units in Newtons\n",
"F1=round(Fx1+0) #units in Newtons\n",
"print \"Tension in String 1 is F1=\",round(F1),\" N\\n\"\n",
"print \"Tension in String 2 is F2=\",round(F2),\" N\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.2:pg-41"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tension in string 1 is F1= 240.0 N\n",
"\n",
"Tension in string 2 is F2= 319.0 N\n",
"\n"
]
}
],
"source": [
" #Example 2_2\n",
"\n",
"\n",
" #To find the tension in the three cords that hold the object\n",
" #As Sigma(Fx)=0\n",
"theta1=37 #units in degrees\n",
"theta2=53 #units in degrees\n",
"F1_F2=math.cos(theta2*math.pi/180)/math.cos(theta1*math.pi/180)\n",
" #As Sigma(Fy)=0\n",
"F3=400 #units in Newtons\n",
"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\n",
"F1=(math.cos(theta2*math.pi/180)/math.cos(theta1*math.pi/180))*F2 #units in Newtons\n",
"print \"Tension in string 1 is F1=\",round(F1),\" N\\n\"\n",
"print \"Tension in string 2 is F2=\",round(F2),\" N\\n\"\n",
" #In textbook the Answer for F2 is printed wrong as 320 N But the correct answer is 319 N\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.3:pg-42"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The Weight W= 133.0 N\n",
"\n",
"Tension in the chord is F= 166.0 N\n"
]
}
],
"source": [
" #Example 2_3\n",
"\n",
"\n",
" #To find the weight and the Tension in the cords\n",
" #As Sigma(Fx)=0\n",
"theta1=53 #units in degrees\n",
"theta2=37 #units in degrees\n",
"F1=100 #units in Newtons\n",
"F=F1/math.cos(theta1*math.pi/180) #units in Newtons\n",
"W=math.cos(theta2*math.pi/180)*F #units in Newtons\n",
"print \"The Weight W=\",round(W),\" N\\n\"\n",
"print \"Tension in the chord is F=\",round(F),\" N\"\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\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.5:pg-48"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tension in the Supporting Cable T= 2309.0 N\n"
]
}
],
"source": [
" #Example 2_5\n",
"\n",
"\n",
" #To find the Tension T in the Supporting Cable\n",
" #As Sigma(Fx)=0\n",
"theta1=30 #units in degrees\n",
"theta2=90-theta1 #units in degrees\n",
"H_T=math.sin(theta1*math.pi/180)\n",
"W=2000 #Units in Newtons\n",
"T=W/math.sin(theta2*math.pi/180) #units in Newtons\n",
"H=T*H_T #units in Newtons\n",
"print \"Tension in the Supporting Cable T=\",round(T),\" N\"\n",
" #In textbook The answer is printed wrong as T=2310N but the correct answer is T=2309N\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.6:pg-52"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The First Force F1= -1800.0 N\n",
"\n",
"The Second Force F2= 2700.0 N\n",
"\n"
]
}
],
"source": [
" #Example 2_6\n",
"\n",
"\n",
" #To find the forces exerted bythe pedestals on the board\n",
"tou=900 #units in Newtons\n",
"d1=3 #units in Meters\n",
"d2=1.5 #Units in Meters\n",
"F1=-(tou*d1)/d2 #Units in Newtons\n",
"F2=tou-F1 #units in Newtons\n",
"print \"The First Force F1=\",round(F1),\" N\\n\"\n",
"print \"The Second Force F2=\",round(F2),\" N\\n\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.7:pg-53"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tension T= 291.0 N\n",
"\n",
"H= 232.0 N\n",
"\n",
"V= -25.13 N\n"
]
}
],
"source": [
" #Example 2_7\n",
"\n",
"\n",
" #To find tension in the supporting cable and Components of the force exerted by the hinge\n",
"F1=50 #units in Newtons\n",
"d1=0.7 #units in meters\n",
"F2=100 #units in Newtons\n",
"d2=1.4 #units in meters\n",
"d3=1 #units in meters\n",
"theta2=53 #units in degrees\n",
"T=round(((F1*d1)+(F2*d2))/(d3*math.cos(theta2*math.pi/180))) #units in Newtons\n",
"theta1=37 #units in degrees\n",
"H=math.cos(theta1*math.pi/180)*T #units in Newtons\n",
"\n",
"V=F1+F2-(math.cos(theta2*math.pi/180)*T) #units in Newtons\n",
"print \"Tension T=\",round(T),\" N\\n\"\n",
"print \"H=\",round(H),\" N\\n\"\n",
"print \"V=\",round(V,2),\" N\"\n",
" #In text book the answer is printed wrong as H=234N but the correct answer is H=232N\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.8:pg-55"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tension T= 410.0 N\n",
"\n",
"H= 140.0 N\n",
"\n",
"V= -301.0 N\n"
]
}
],
"source": [
" #Example 2_8\n",
"\n",
"\n",
" #To find the tension in the Muscle and the Component Forces at elbow\n",
"F1=65 #units in Newtons\n",
"d1=0.1 #units in Meters\n",
"F2=20 #Units in Newtons\n",
"d2=0.35 #units in meters\n",
"theta1=20 #units in degrees\n",
"d3=0.035 #units in Meters\n",
"Tm=((F1*d1)+(F2*d2))/(math.cos(theta1*math.pi/180)*d3) #units in Newtons\n",
"V=F1+F2-(Tm*math.cos(theta1*math.pi/180))\n",
"H=Tm*math.sin(theta1*math.pi/180)\n",
"print \"Tension T=\",round(Tm),\" N\\n\"\n",
"print \"H=\",round(H),\" N\\n\"\n",
"print \"V=\",round(V),\" N\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex2.9:pg-55"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Force P= 276.0 N\n",
"\n",
"Force V= 600.0 N\n",
"\n",
"Force H= 276.0 N\n"
]
}
],
"source": [
" #Example 2_9\n",
"\n",
"\n",
"#To find the forces at the wall and the ground\n",
"theta1=53 #units in degrees\n",
"d1=3 #units in meters\n",
"F1=200 #units in Newtons\n",
"d2=4 #units in Meters\n",
"F2=400 #units in Newtons\n",
"theta2=37 #units in degrees\n",
"d3=6 #units in meters\n",
"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\n",
"H=P #units in Newtons\n",
"V=F1+F2 #units in Newtons\n",
"print \"Force P=\",round(P),\" N\\n\"\n",
"print \"Force V=\",round(V),\" N\\n\"\n",
"print \"Force H=\",round(H),\" N\"\n",
" #In text book the answer is printed wrong as P=H=275N but the correct answer is P=H=276N\n"
]
}
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