8.10. Review Questions¶
8.10.1. User-defined functions¶
Q07.01 Write a function called ft_to_in() which converts feet to inches. Note the conversion factor is 1 foot = 12 inches. Convert 6 feet into inches using your function.
Q07.02 Write a function called m_to_ft() which converts meters to feet. Note the conversion factor is 1 meter = 3.28084 feet. Convert 5,000 meters into feet using your function.
Q07.03 Use the functions in questions Q07.01 and Q07.02 to convert 2 meters into inches.
Q07.04 Write a function that calculates the area of a circle based on a circle’s radius. The formula for the area of a circle is \(A = \pi r^2\) where \(A\) is area and \(r\) is radius. Use your function to calculate the area of circle with a radius of 5.
Q07.05 Write a function that converts degrees Celsius (\(C\)) to degrees Fahrenheit (\(F\)). The formula to convert between the two temperature scales is \(F = \frac{9}{5} C + 32\). Convert 100 degrees \(C\) to degrees \(F\) using your function.
Q07.06 Write a function that converts Kelvin temperature (\(K\)) to degrees Celsius (\(C\)). The formula to convert between the two temperature scales is \(C = K - 273.15\).
Q07.07 Use the functions in questions Q07.05 and Q07.06 to convert to convert the temperature at Standard Temperature and Pressure (STP) of \(273.15 K\) into degrees \(F\).
Q07.08 Use the functions in questions Q07.05 and Q07.06 to convert to convert the temperature at absolute zero, \(0 K\) into degrees Celsius and degrees Fahrenheit.
Q07.09 Write a function called hp_to_kw() which converts horse power (\(hp\)) into kilowatts (\(kW\)). Note the conversion factor is \(1 hp = 0.7457 kW\). Convert the horsepower of the average horse, \(14.9 hp\), into kilowatts (\(kW\)).
Q07.10 Write a function called fun_logic() that accepts three boolean variables as its input (a, b, and c). The output of fun_logic() will be a single boolean variable that is only True when either a is True, or a, b, and c are all False.
Q07.11 Write a function called pn() that takes in a single number and outputs a string. If the input number is negative, output the string 'negative'. If the input number is positive, output 'positive'. Otherwise, output 'neither'. Test your function with a negative number, a positive number and 0.
8.10.2. Functions with multiple arguments¶
Q07.20 Write a function called cyl_v() that calculates the volume \(V\) of a cylinder based on cylinder height \(h\) and cylinder radius \(r\). The formula for the volume of a cylinder is below:
Use your function cyl_v() to calculate the volume of a cylinder with height = 2.7 and radius = 0.73.
Q07.21 The universal gas law states that the pressure \(P\), and temperature \(T\) of a volume \(V\) of gas with number of particles \(n\) is related by the equation below, where \(R\) is the universal gas constant.
Write a function called gas_v() to calculate the volume \(V\) of a gas based on pressure \(P\), temperature \(T\), number of particles \(n\) and universal gas constant \(R\). Use your function to find the volume of gas with the following parameters:
Q07.22 Most professional bakers weight their ingredients, while many home bakers use measurements like cups and tablespoons to measure out ingredients. Create a function that takes two arguments: ingredient and cups. The function will output the number of grams of the specified ingredient. For example, a skeleton outline of your function might look like:
def bake_conv(ingredient, cups)
<code>
return grams
Your function needs to accept the following ingredients: 'flour' and 'sugar'. The conversion factor for flour is 1 cup flour = 128 grams flour. The conversion factor for sugar is 1 cup sugar = 200 grams sugar. Use your function to convert a recipe that calls for 3 cups of flour and a quarter cup of sugar.
Q07.23 The gravitational force between two celestial bodies (planets, moons, stars etc) is calculated according to:
where \(F_g\) is the gravitational force, \(M\) is the mass of one of the celestial bodies, \(m\) is the mass of the other the celestial body, \(r\) is the distance between the two celestial bodies and \(G\) is the universal gravitational constant. \(G=6.667408 \times 10^{-11} m^3 kg^{-1}s^{-2}\).
(a) Write a function called grav_force() that accepts the mass of two celestial bodies and outputs the gravitational force produced.
Celestial Body |
Mass |
Distance from sun |
|---|---|---|
Sun |
\(1.989\times10^{30} kg\) |
\(0\) |
Earth |
\(5.98\times10^{24} kg\) |
\(149.6 \times 10^9 m\) |
Mars |
\(6.42\times10^{23} kg\) |
\(228 \times 10^9 m\) |
(b) Use your function grav_force() and the table above to calculate the gravitational force between the earth and the sun.
(c) Use your function grav_force() and the table above to calculate the gravitational force between the mars and the sun.
Q07.24 Write a function called add3() that takes in 3 numbers and returns their sum. Only a single output variable (the sum of the three numbers) should be returned.
Test your function by writing code beneath the function definition that calls the function with input you create.
Q07.25 Write a function called asq() that takes in two variables, A and B. Have asq() output 3 values: the sum, the difference and the quotient of A and B as defined below:
sum = A + B
difference = A - B
quotient = A/B
Your function should accept two input arguments and output three values.
8.10.3. Functions with default arguments¶
Q07.30 (a) Rewrite the function in problem Q07.20 called gas_v() with the default values \(n = 6.02 \times 10^{23}\), \(R = 8.314\) and \(P = 101,325\).
(a) Use your modified function gas_v() to calculate the volume of a gas at \(T = 500 K\) using the default arguments.
(b) Use your modified function gas_v() to calculate the volume of a gas at \(T = 500K\), under half the pressure \(p = 101,325/2\).
Q07.31 In engineering mechanics, the tensile stress \(\sigma\) applied to a solid cylinder is equal to the tensile force on the cylinder \(F\) divided by the cylinder’s cross sectional area \(A\) according to the formula below:
The standard diameter \(d\) of a cylinder pulled in tension in a tensile test using the ASTM D8 standard is \(d=0.506\) inches.
Use the formula for stress \(\sigma\) and area \(A\) above to write a function called stress() that calculates stress \(\sigma\) based on force \(F\) and diameter \(d\). Use \(d=0.506\) as the default diameter, but allow the user to specify a different diameter if they want.
Use your stress() function to calculate the tensile stress \(\sigma\) in a cylinder with the default diameter and a tensile force \(F = 12,000\).
Q07.32 One way to calculate how much an investment will be worth is to use the Future Value formula:
Where \(FV\) is the future value, \(I_0\) is the initial investment, \(r\) is the yearly rate of return, and \(n\) is the number of years you plan to invest.
(a) Write a function called future_value() which accepts an initial investment \(I_0\) and a number of years \(n\) and calculates the future value \(FV\). Include \(r=0.05\) as the default yearly rate of return.
(b) Use your future_value() function to calculate the future value of an initial investment of 2000 dollars over 30 years with the default yearly rate of return
(c) Use your future_value() function to calculate the future value of the same initial investment of 2000 dollars over 30 years, but a rate of return of 8% (0.08).
(d) Use your future_value() function to determine when 2000 dollars is invested over 30 years, how much more do you make if the rate of return is 10% (0.10) instead of 5% (0.05).
Q07.33 Write a function called s() that takes in 3 variables, a, b, and c. Have your function s() output the sum of a, b and c. If no value is passed in for c, set c to the default value of 100.
8.10.4. Nested Functions¶
Q07.36 In mechanical engineering, there are a couple different units of stress. Units of stress include: Pascals (\(Pa\)), Mega Pascals (\(MPa\)), pounds per square inch (psi) and kilopounds per square inch (\(ksi\)).
(a) Write a function called pa_to_mpa to convert between Pascals (\(Pa\)) and Mega Pascals (\(MPa\)). The conversion factor is \(1 MPa = 10^6 Pa\)
(b) Write a function called mpa_to_ksi to convert between Mega Pascals (\(MPa\)) and kilopounds per square inch (\(ksi\)). The conversion factor is \(1 ksi = 6.89476 MPa\)
(c) Write a function called ksi_to_psi to convert between kilopounds per square inch (\(ksi\)) and pounds per square inch (\(psi\)). The conversion factor is \(1000 psi = 1 ksi\)
(d) Combine the three functions pa_to_mpa, mpa_to_ksi, ksi_to_psi into a single function pa_to_psi. Do this by calling the other functions as part of the pa_to_psi function, not by rewriting the same code you wrote in parts (a), (b), and (c).
(e) Convert 2,500 \(Pa\) into \(psi\) using your pa_to_psi function.
8.10.5. Functions in other files¶
Q07.40 Create a separate .py file called greetings.py. Inside of greetings.py include the code:
def hi():
print("Hi!")
Import your newly created greatings.py file and run the function hi().
Q07.41 Create a separate .py file called greetings.py. Inside of greetings.py include the code:
def hello(name):
print("Hello " + name)
Import your newly created greatings.py file and run the function hello() with your name as an input argument.
Q07.42 Create a separate file .py file called areas.py. Inside of areas.py include the code:
def triangle(base,height):
area = 0.5*base*height
print("Triangle Area: ", area)
def rectangle(length, width):
area = length* width
print("Rectangle Area: ", area)
Import your newly created areas.py file and run the functions triangle() and rectangle() with the same two input arguments: 2 and 3.
8.10.6. Errors, Explanations, and Solutions¶
For the sections of code below, run the lines of code. Then explain the error in your own words. Below your error explanation, rewrite and run an improved section of code that fixes the error.
Q07.80 Run the code below and explain the error. Rewrite the code and run it error free.
def add_me(num)
return num + 2
add_me(1)
Q07.81 Run the code below and explain the error. Rewrite the code and run it error free.
def add_you[num]:
return num + 2
add_you(2)
Q07.82 Run the code below and explain the error. Rewrite the code and run it error free.
def my_func():
print('yup')
my_func('yup')
Q07.83 Run the code below and explain the error. Rewrite the code and run it error free.
def nope():
print('nope')
nope()
Q07.84 Run the code below and explain the error. Rewrite the code and run it error free.
def plus(2+2):
return 4
nothing()
Q07.85 Run the code below and explain the error. Rewrite the code and run it error free.
def first_a(a):
return a[0]
first_a(1)