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"source": [
"# Chapter 1 - Physics and Engineering"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1 - pg 11"
]
},
{
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"execution_count": 2,
"metadata": {
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Percentage Error (percentage) = 4.0\n"
]
}
],
"source": [
"#calculate the percentage error\n",
"#Given:\n",
"l=9.3; # length in cm\n",
"b=8.5;# breadth in cm\n",
"h=5.4;# height in cm\n",
"#calculations\n",
"V= l*b*h; # Volume in cm**3\n",
"delta_l = 0.1; delta_b = 0.1; delta_h = 0.1; # scale has a least count = 0.1 cm\n",
"# absolute error \n",
"delta_V = (b*h*delta_l + l*h*delta_b +l*b*delta_h); # in cm**3\n",
"#relative error \n",
"re = delta_V/V;\n",
"p= re*100; # Evaluating percentage error\n",
"#results\n",
"print \"Percentage Error (percentage) = \",round(p,0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2 - pg 12"
]
},
{
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"execution_count": 3,
"metadata": {
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"outputs": [
{
"name": "stdout",
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"text": [
"Percentage error (percentage) = 2.86\n",
"Result obtained differs from that in textbook, because delta_M walue is taken 0.1 g , instead of 0.2 g as mentioned in the problem statement.\n"
]
}
],
"source": [
"#calculate the percentage error\n",
"#Given :\n",
"M= 10.0; #weight in g\n",
"V= 5.80;#volume in cm**3\n",
"#calculations\n",
"Rho = M/V; # Density in g/cm**3\n",
"delta_M= 0.2 # apparatus has a least count of 0.2 g\n",
"delta_V= 0.05# apparatus has a least count of 0.05 cm**3\n",
"delta_Rho = (delta_M/V) +((M*delta_V)/V**2);# absolute error in g/cm**3\n",
"re = delta_Rho/Rho ; #Evaluating Relative Error\n",
"p = re*100;# Evaluating Percentage Error\n",
"#results\n",
"print \"Percentage error (percentage) = \",round(p,2)\n",
"print'Result obtained differs from that in textbook, because delta_M walue is taken 0.1 g , instead of 0.2 g as mentioned in the problem statement.'\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3 - pg 16"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Actual Value of c/r ranges between 5.9 - 6.6 and Percentage error = 5.3 percentage. \n",
"(b)Actual Value of c/r ranges between 6.281 - 6.288 and Percentage error = 0.06 percentage.\n"
]
}
],
"source": [
"#calculate the Actual val of c/r ranges and percentage error\n",
"#Given:\n",
"#(a) \n",
"import math\n",
"lc = 0.1# least count in cm\n",
"c = 6.9 #Circumference c in cm\n",
"r= 1.1 # radius of circle in cm\n",
"val =2*math.pi;\n",
"# Circumference,c= 2*pi*r or c/r = 2*pi\n",
"# Error in c/r is , delta(c/r)= [(c/r**2)+(1/r)](LC/2) , LC is Least Count .\n",
"E= ((c/r**2)+(1./r))*(lc/2.);#Error in c/r is delta(c/r)\n",
"ob = c/r; # Observed Value\n",
"#Actual Value of c/r ranges between\n",
"ac1 = ob-E;# Evaluating Minimum value for c/r \n",
"ac2 = ob+E;# Evaluating Maximum value for c/r\n",
"p = (E/ob)*100.; #Evaluating percentage error\n",
"#results\n",
"print \"(a)Actual Value of c/r ranges between\",round(ac1,1), \"-\",round(ac2,1),\" and Percentage error =\",round(p,1),\" percentage. \"\n",
"#(b)\n",
"lc1 = 0.001;#Now the least count is 0.001 cm\n",
"c1 = 6.316;#Circumference in cm\n",
"r1=1.005;#Circle radius in cm \n",
"E1 =((c1/r1**2) + (1/r1))*(lc1/2); # Error in c/r is delta(c/r)\n",
"ob1= c1/r1; #Observed Value\n",
"p1=(E1/ob1)*100.;#Evaluating percentage error\n",
"#Actual Value of c/r ranges between\n",
"a1= ob1-E1;#Evaluating Minimum value for c/r\n",
"a2= ob1+E1;#Evaluating Maximum value for c/r\n",
"print \"(b)Actual Value of c/r ranges between\",round(a1,3),\"-\",round(a2,3),\"and Percentage error =\",round(p1,2),\" percentage.\"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4 - pg 17"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a) It is is 15.0 percentage lower than the experimental value.\n",
"(b) It is 0.6 percentage higher than the experimental value.\n"
]
}
],
"source": [
"#calculate the percentage lower or higher than experimental value\n",
"#Given\n",
"import math\n",
"# (a) Newton's Theory\n",
"# v= (P/rho)**2 , P= Pressure , rho = density\n",
"P = 76.; # 76 cm of Hg pressure\n",
"V= 330. ; # velocity of sound in m/s\n",
"rho = 0.001293; # density for dry air at 0 degrees celsius in g/cm**3\n",
"g = 980.;#gravitational acceleration in cm/s**2\n",
"#Density of mercury at room temperature is 13.6 g/cm**3 \n",
"# 1 cm**2 = 1.0*10**-4 m**2\n",
"#calculations\n",
"v = math.sqrt(((P*13.6*g)/rho)*10**-4); # velocity of sound in m/s\n",
"p= ((V-v)/V)*100; # % lower than the experimental value\n",
"#results\n",
"print \"(a) It is is\",round(p,0),\" percentage lower than the experimental value.\"\n",
"\n",
"# (b) Laplace's Theory \n",
"# v= ((gama*P)/rho)**2., gamma = adiabatic index Thus,\n",
"#Given :\n",
"gama = 1.41 # Adiabatic index\n",
"#Density of mercury at room temperature is 13.6 g/cm**3 \n",
"# 1 cm**2 = 1.0*10**-4 m**2\n",
"v1 = math.sqrt(((gama*P*13.6*g)/rho)*10**-4);# velocity of sound in m/s\n",
"p1 = ((V-round(v1))/V)*100;# % higher than the eperimental value\n",
"#results\n",
"print \"(b) It is\",round(abs(p1),1),\"percentage higher than the experimental value.\""
]
}
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