Q078 - Physics For Engineers And Scientists - Solutions

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Amateur Radio and Astronomy website. JO10UX

Question 78 - Review - Chapter 1

Problem:

The nucleus of an iron atom is spherical and his radius is $4.6x10^{-15}m$.

The mass of the nucleus is $9.5x10^{-26} kg$.

Question:

What is the density of the nclear material?

(express your anwer in metric tons per cubic cm)

Solution:

The volume of a sphere is: \begin{equation}Vol = \frac{4}{3}*\pi*r^3\end{equation} The density is: \begin{equation*}\rho = \frac{mass}{volume}\end{equation*}

In [1]:
# Calculations
import numpy as np
radius_Fe = 4.6e-15 # m
mass_Fe = 9.5e-26 # kg
vol_Fe = (4/3) * np.pi * radius_Fe**3
rho_Fe_kg_m3 = mass_Fe / vol_Fe
print(f'The density in kg/m3 is {rho_Fe_kg_m3:0.1e} kg/m3')
The density in kg/m3 is 2.3e+17 kg/m3

1 metric Ton = 1000 kg

In [2]:
rho_Fe_ton_m3 = rho_Fe_kg_m3 / 1000
print(f'The density in Ton/m3 is {rho_Fe_ton_m3:0.1e} Ton/m3')
The density in Ton/m3 is 2.3e+14 Ton/m3

$1 m^3 = 100 * 100 * 100 cm^3 = 10^6 cm^3$

In [3]:
rho_Fe_ton_cm3 = rho_Fe_ton_m3 / 1e6
print(f'The density in Ton/cm3 is {rho_Fe_ton_cm3:0.1e} Ton/cm3')
The density in Ton/cm3 is 2.3e+08 Ton/cm3

Alternative solution:

Alternatively we can use the phyton library Pint to solve the conversion problem, all calculations and conversions are done internally and the values are displayed with the correct units.

In [4]:
# Same using Pint unit conversion lybrary
from pint import UnitRegistry
ureg = UnitRegistry()
_rho_Fe_kg_m3 = rho_Fe_kg_m3 * (ureg.kg / ureg.m**3 )
_rho_Fe_ton_cm3 = _rho_Fe_kg_m3.to(ureg.metric_ton / ureg.cm**3 )
print(f'{_rho_Fe_kg_m3:5.2}')
print(f'{_rho_Fe_ton_cm3:5.2}')
2.3e+17 kilogram / meter ** 3
2.3e+08 metric_ton / centimeter ** 3

سُوۡرَةُ حٰمٓ السجدة / فُصّلَت
ثُمَّ اسْتَوَىٰ إِلَى السَّمَاءِ وَهِيَ دُخَانٌ فَقَالَ لَهَا وَلِلْأَرْضِ ائْتِيَا طَوْعًا أَوْ كَرْهًا قَالَتَا أَتَيْنَا طَائِعِينَ ﴿١١
فَقَضَاهُنَّ سَبْعَ سَمَاوَاتٍ فِي يَوْمَيْنِ وَأَوْحَىٰ فِي كُلِّ سَمَاءٍ أَمْرَهَا ۚ وَزَيَّنَّا السَّمَاءَ الدُّنْيَا بِمَصَابِيحَ وَحِفْظًا ۚ ذَٰلِكَ تَقْدِيرُ الْعَزِيزِ الْعَلِيمِ ﴿١٢


Surah Fussilat: Thereafter turned He to the heaven and it was as smoke, and said Unto it and Unto the earth: come ye twain, willingly or loth. They said: we come willingly. (11) Then He decreed them as seven heavens in two days, and revealed Unto each heaven the command thereof; and We bedecked the nether heaven with lamps and placed therein a guard. That is the ordinance of the Mighty, the Knower. (12)

De hemelen en aarde (waren) een samenhangende massa. Wij hebben ze toen van elkaar gescheiden… Wij hebben de hemel tot een beschermend dak gemaakt … en de dag en de nacht, de zon en de maan geschapen. (Koran 41 11:12)


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