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Vladimir79 [104]
3 years ago
13

The construction of a flat rectangular roof (6.17 m × 5.92 m) allows it to withstand a maximum net outward force of 2.00 × 104 N

. The density of the air is 1.29 kg/m3. At what wind speed will this roof blow outward?
Physics
1 answer:
Blababa [14]3 years ago
5 0

Answer:

v_2=29.13\ m/s

Explanation:

It is given that,

Dimension of the rectangular roof, (6.17 m × 5.92 m)

The maximum net outward force, F=2\times 10^4\ N

The density of air, \rho=1.29\ kg/m^3

The Bernoulli equation is used to find wind speed of this roof blow outward. It is given by :

P_1+\dfrac{1}{2}\rho v_1^2=P_2+\dfrac{1}{2}\rho v_2^2

Here, v_1=0 (since air inside the roof is not moving)

v_2=\sqrt{\dfrac{2(P_1-P_2)}{\rho}}

Since, F=(P_1-P_2)A

v_2=\sqrt{\dfrac{2F}{\rho A}}

v_2=\sqrt{\dfrac{2\times 2\times 10^4}{1.29\times 6.17\times 5.92 }}

v_2=29.13\ m/s

So, the wind speed of  this roof blow outward is 29.13 m/s. Hence, this is the required solution.

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Answer:

a) Δf = 0.7 n , e)   f = (15.1 ± 0.7) 10³ Hz

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        f = n / 2π L² √( E /ρ)

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       f = n / 2π (0.2335)² √ (210 10⁹/7800)

       f = n /0.34257 √ (26.923 10⁶)

       f = n /0.34257    5.1887 10³

       f = 15.1464 10³ n

a) We are asked for the uncertainty of the frequency (Df)

       Δf = | df / dL | ΔL + df /dE ΔE + df /dρ Δρ

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       ΔE = Δρ = 0

       Δf = df /dL  ΔL

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        Δf = 0.7 n

b, c) The uncertainty with the width and thickness of the canteliver is associated with the density

 

In your expression there is no specific dependency so the uncertainty should be zero

The exact equation for the natural nodes is

          f = n / 2π L² √ (E e /ρA)

where A is the area of ​​the cantilever and its thickness,

In this case, they must perform the derivatives, calculate and approximate a significant figure

        Δf = | df / dL | ΔL + df /de  Δe + df /dA  ΔA

        Δf = 0.7 n + n 2π L² √(E/ρ A) | ½  1/√e | Δe

               + n / 2π L² √(Ee /ρ) | 3/2 1√A23  |

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        A = b h

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        A = 82.17 10⁻⁶ m²

        DA = dA /db ΔB + dA /dh Δh

        dA = h Δb + b Δh

        dA = 3.3 10⁻³ 0.005 10⁻³ + 24.9 10⁻³ 0.005 10⁻³

        dA = (3.3 + 24.9) 0.005 10⁻⁶

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let's calculate each term

         A ’= n / 2π L² √a (E/ρ A) | ½ 1 /√ e | Δe

         A ’= n/ 2π L² √ (E /ρ)      | ½ 1 / (√e/√ A) |Δe

        A ’= 15.1464 10³ n ½ 1 / [√ (24.9 10⁻³)/ √ (81.17 10⁻⁶)] 0.005 10⁻³

        A '= 0.0266  n

        A ’= 2.66 10⁻² n

       A ’’ = n / 2π L² √ (E e /ρ) | 3/2  1 /√A³ |

       A ’’ = n / 2π L² √(E /ρ) √ e | 3/2  1 /√ A³ | ΔA

       A ’’ = n 15.1464 10³ 3/2 √ (24.9 10⁻³) /√ (82.17 10⁻⁶) 3 1.4 10⁻⁷

       A ’’ = n 15.1464 1.5 1.5779 / 744.85 1.4 10⁴

       A ’’ = 6,738 10²

we write the equation of uncertainty

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 d)    Δf = 7 10² n

e) the natural frequency n = 1

       f = (15.1 ± 0.7) 10³ Hz

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