Q063 - Physics For Engineers And Scientists - Solutions

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Question 63 - Problems - Chapter 1

Problem:

The roof of a house has a slope or pitch of 1:1 (that is 45°) The roof has a complex shape, with several gables and dormers (see the fig. below). The aerea of the ground floor is 250 $m^2$

A house with gables and dormers

Question:

What is the area of the roof surface?

Solution:

The slope of the roof at 45 ° is always the lower side divided by the cosine of the corner with the lower side.

The surface will therefore also be larger by a factor $cos(45°) = \frac{\sqrt{2}}{2}$.

$$ {\textrm{Surface}}_{\textrm{roof}} =\frac{{\textrm{Surface}}_{\textrm{ground}} }{\cos \left(45°\right)}\Rightarrow \frac{250\;m^2 }{\frac{\sqrt{2}}{2}}=\frac{2*250\;m^2 }{\sqrt{2}} $$

In [1]:
# Calculations
import numpy as np
Surface_house = 250
Surface_roof = (2 * Surface_house) / np.sqrt(2);
print(f'The surface of the roof is {Surface_roof:.0f} m2')
The surface of the roof is 354 m2

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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