aramutselv

2022-01-03

(II) A 180km/h wind blowing over the flat roof of a house causes the roof to lift off the house. If the house is $6.2\text{}m\times 12.4\text{}m$ in size, estimate the weight of the roof. Assume the roof is not nailed down

kalfswors0m

Beginner2022-01-04Added 24 answers

Given:

The speed of the wind,$v=180\text{}k\frac{m}{h}$

$=(180\times \frac{1000}{3600})\frac{m}{s}$

$=50\text{}\frac{m}{s}$

The area of the house,$A=(6.2\times 12.4)$

$=76.88\text{}{m}^{2}$

Find the weight of roof.

Here,

Density of air$=(0.00129\times {10}^{3}\text{}k\frac{g}{{m}^{3}})=1.29\text{}k\frac{g}{{m}^{3}}$

Now,

The pressure of the wind,$P=\frac{1}{2}\rho {v}^{2}$

$P=\frac{1}{2}\left(1.29\right)\left({50}^{2}\right)=1612.5\text{}\frac{N}{{m}^{2}}$

We know that,

Pressure,$P=\frac{F}{A}$

Here,

F = the force on the roof

A = the area of the roof.

So,

$F=P\times A=(1612.5\times 76.88)=123969\text{}N$

Therefore,

The weight of the roof,$w=123969\text{}N$

The speed of the wind,

The area of the house,

Find the weight of roof.

Here,

Density of air

Now,

The pressure of the wind,

We know that,

Pressure,

Here,

F = the force on the roof

A = the area of the roof.

So,

Therefore,

The weight of the roof,

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