Question 1: Programming practice 20 marks (5 marks per question) We will start with some questions that get you to write some very simple python code. Remember, you must include both the code and the answer to the question in your answer sheet. Don’t use a calculator, always use python! Here is an example question: “Write a python program to calculate the number of seconds in a year (exclude leap years).” Your solution should look like this:

60s in a minute, 60 minutes in an hour, 24 hours in a day, 365 days in a year.

print(1365246060) Result: 31536000

Notice how I included a comment to explain what I’m doing. You will get marks for commenting your code, try to add a comment for every line of code to show you know what it does. Also notice how I include the output of my code to show it gets the right answer. You’ll lose marks without the output but you’ll get no marks at all without the code!

Questions: Computational Physics 322

1. a) Write some python code that converts 80km/h into m/s. b) Include the answer in your report.
2. a) Write some python code to calculate the resistance of a resistor with a potential difference of 1.5V across it and a 0.1mA current running through it (hint: remember Ohm’s law?). b) Include the answer in your report.
3. a) You find a rectangular object made of an unknown material. Its base is square, with a side measuring 3cm, and it has a length of 10cm and a weight of 200g. Use python to calculate the density of this object. b) Include the answer in your report.
4. a) Write some python code to calculate the kinetic energy (in Joules) of a 10 tonne truck travelling at 60km/h. b) Include the answer in your report.

Solutoin: ########################################

Q1.1

#This code convert 80 km/h to meters per second and print the result print(80/3.6) #result:22.22

Q1.2

#This code calculate the resistor of the current using potential differece and current. print(1.5/1e-3) #result:15000

Q1.3

#This code calculate the density in kg per cubic meter. print((200/1000)/(((3e-2)**2)*(10e-2))) #result:2222.222222222222

Q1.4

#this code calculate the kinetic energy of the truck in joules. print(0.5*(100010)(60/3.6)**2) #result:1388888.8888888892

########################################

Question 2: Functions 15 marks (5 marks per question) Let’s practice writing simple python functions. Functions are critical to writing good programs for two reasons: they allow you to rerun code again and again without having to rewrite it and it allows you to abstract complicated code, which becomes very important for bigger programs. Here is an example question, similar to the previous but where I ask for a function: “Write a function that takes as an input argument a number of years and calculates the number of seconds in those years (exclude leap years).” Your solution should look like this: def convert_to_seconds(num_of_years):

60s in a minute, 60 minutes in an hour, 24 hours in a day, 365 days in a year.

return num_of_years365246060 This time, I can call my function as many times as I want for different inputs. For each question, I will ask you to test your function with a few inputs. Remember to comment your code and include the output for the test inputs I give you. Questions:

1. a) Write a function that takes two input arguments, m and n, and returns m + n. b) Test your code for m = 7 and n = 26 and include the answers in your report.
2. a) Write a function that takes a string as an input argument and returns the second letter of the string. b) Test your code for “computational” and “awesome” and include the answers in your report.
3. a) Write a function that takes time, t, as an input argument and returns the velocity of a freefalling body t seconds after it has been released. Assume no air resistence and zero initial velocity. b) Test your code for 3s and 39s and include the answers in your report.

Solution: ########################################

Q2.1

This code calculate the sum with.

Define the function to add two numbers

def addition(m, n): return m + n

Define the numbers

m = 7 n = 26

Call the function and print the result

result = addition(m, n) print(result)

Q2.2

This code returns the second letter of the input string

def second_letter(input_string):

#check the length of the string
if len(input_string) < 2:
    return "Error: The input string is too short to have a second letter."
return input_string[1]

Example usage

result = second_letter("computational") print(result) result = second_letter("awesome") print(result)

Q2.3

This function calculates the velocity of a free-falling body t seconds after it has been released.

def free_fall_velocity(t):

# Acceleration due to gravity in m/s^2
g = 9.81  
# Equation of motion.
velocity = g * t
return velocity

Example usage

time_seconds = 3 result = free_fall_velocity(time_seconds) print(f"The velocity of the body after {time_seconds} seconds is {result:.2f} m/s") time_seconds = 39 result = free_fall_velocity(time_seconds) print(f"The velocity of the body after {time_seconds} seconds is {result:.2f} m/s")

Question 3: Conditional statemets 15 marks (5 marks per question) These questions focus on the concept of if statements. If statements are critical in any program as they allow a computer to make a decision based on some input. Here is a good tutorial on if statements: https: Computational Physics 322 //realpython.com/python-conditional-statements/ Remember for each question, you must include both the well-commented code and the answer to the question in your answer sheet. Questions:

1. a) Write a python program that checks a variable, x: it should print “positive” if x is greater than zero, “negative” if less than zero and “zero” if it is exactly equal to zero. b) Test your code for 7, -3 and 0 and include the answers in your report.
2. a) Write a python program that checks the length of a string, stored in a variable called s. If the string is longer than 5 characters, print “too long”. Otherwise, print “ok”. b) Test your code for the strings “cosmological” and “ohm” and include the answers in your report.
3. a) Write a python program to check if a variable, x, is divisible by 2, 3 or 5. If it is divisible by more than one of these numbers, print all the numbers out of 2, 3 and 5 that it is divisible by. If it is not divisible by any of them, print “not divisible by 2, 3 or 5”. Assume x is an integer. b) Test your code for 12, 7 and 60 and include the answers in your report.

Solution:

########################################

Q3.1

Put your code here

Define the variable x

x = int(input("Enter a number: ")) # Taking input from the user

Check the value of x and print the corresponding message

if x > 0: #the value is positive. print("positive") elif x < 0: #the value is negative. print("negative") else: #the value is zero. print("zero")

Q3.2

Put your code here

Define the string variable s

s = input("Enter a string: ") # Taking input from the user

Check the length of the string and print the corresponding message

if len(s) > 5: print("too long") else: print("ok")

Q3.3

Put your code here

Define the variable x

x = int(input("Enter an integer: ")) # Taking input from the user

Initialize an empty list to store the divisors

divisors = []

Check divisibility and append to the list if divisible

if x % 2 == 0: divisors.append(2) if x % 3 == 0: divisors.append(3) if x % 5 == 0: divisors.append(5)

Print the results

if divisors: print("The number is divisible by:", ', '.join(map(str, divisors))) else: print("not divisible by 2, 3 or 5")

########################################

Question 4: Root finding 5 marks Use python to find the roots (https://www.britannica.com/science/root-mathematics) of the following equation: f(x) = 10 − xln(x) = 0 You may solve this problem any way you choose. I recommend starting with the built-in scipy solver called “fsolve”. You’ll get some marks if you can use it successfully. You’ll get more marks if you can write your own root-solver from scratch. Even if this seems daunting, give it a try! The simplest approach involves looping1 over a range of possible values until you find one close to zero...

Solution:

########################################

Put your code here

import numpy as np from scipy.optimize import fsolve

Define the function whose root we want to find

def func(x): return 10 - x * np.log(x)

Initial guess for the root

initial_guess = 1.0

Use fsolve to find the root

root = fsolve(func, initial_guess)

Print the result

print(f"The root of the equation is approximately: {root[0]}")

########################################