Solution to week 1 quiz for PHSX218 Lab

week1.py

import math
import numpy as np

def rule4(Q, A, dA, m, B, dB, n):
    """Computes the error propagation for the form c A^m * B^n"""
    return abs(Q) * math.sqrt((m * (dA / A))**2 + (n * (dB / B))**2)

# Capture measurements
height = 22.65e-3 # meters
radius = 8.60e-3 / 2 # meters
mass = 228.6e-3 # kilograms

# Uncertainty for measurements devices
d_caliper = 0.05e-3 # meters
d_scale = 0.1e-3  # kilograms

# Compute the volume of the cylinder
volume = math.pi * height * (radius)**2 
d_volume = rule4(volume, radius, d_caliper, 2, height, d_caliper, 1)

# Compute the density of the cyclinder
density = mass * volume
d_density = rule4(density, mass, d_scale, 1, volume, d_volume, 1)

# Print the result
print("The density is %2.2E +/- %2.2E kg m^3" % (density, d_density))