If wind blows at 39 m/s over a house,

[Carnivroar]

what is the net force on the roof if its area is 320 m^2 and is flat?

I don't even know where to start.

 

[LawrenceC]

What class are you taking?

 

[Carnivroar]

What class are you taking?

physics 1

i think i have to use bernoulli's formula but i don't know how

 

[ehild]

What does Bernouilli's principle state?

ehild

 

[Carnivroar]

what does bernouilli's principle state?

Ehild

1/2ρv₁² + p₁ = 1/2ρv₂² + p₂

 

[ehild]

1/2ρv₁² + p₁ = 1/2ρv₂² + p₂

Correct. If you look at the equation you see that the pressure is smaller when the speed of the air is greater. The speed of air is zero below the roof in the building, v₁=0 and the pressure below the roof is just the usual p₁=1 atm. The wind blows over the roof, its speed is v₂=39 m/s. p₂ =p₁ - 1/2 (rho) v₂².
The pressure means the force exerted to unit surface. The air inside the building exerts F₁=p₁A upward force to the flat roof of area A. The air outside exerts p₂A downward force to the roof. What is the net force then?

ehild

 

[Carnivroar]

This is the answer I'm supposed to get

3.1×10^5

or 310000

Let me try it the way you said

Since V1 = 0 the first term goes away

P1 = 1/2 ρ 39^2 + P2

(1.225 = density of air)

101325 - 1/2 * 1.225 * 1521 = P2

101325 - 931.6125 = 100393.3875

100393.3875 * A = Fnet

100393.3875 * 320 = 32125884

Not right.

What am I doing wrong?

 

[Dick]

This is the answer I'm supposed to get

3.1×10^5

or 310000

Let me try it the way you said

Since V1 = 0 the first term goes away

P1 = 1/2 ρ 39^2 + P2

(1.225 = density of air)

101325 - 1/2 * 1.225 * 1521 = P2

101325 - 931.6125 = 100393.3875

100393.3875 * A = Fnet

100393.3875 * 320 = 32125884

Not right.

What am I doing wrong?

For one thing you should really put units on stuff. For another thing you are only calculating the force on the roof exerted by the air outside the house. There's another force exerted on the roof by the air inside the house that isn't moving. They are in opposite directions.

 

[ehild]

You calculated the force of the blowing air, but you need the net force. Read my previous post.

ehild

 

[Carnivroar]

Oh, okay. Got it now. The problem with this question is that it doesn't give you the value for air density, so even a slight difference in the value you chose will make a difference in the big numbers. With the 1.225 I used above I was getting ~290000 then I used 1.29 and got the ~310000 I needed.

Thanks!

 

[ehild]

You get more accurate result if you express the force symbolically and pug in the data at the end. The net force is
F=PA-P₂A=(P1-P2)A=[P1-(P1-1/2 ρv²)]A=(1/2 ρv²)A
No need to calculate the pressure.
The density of air depends quite much on the temperature and height above sea level.
It should have been given in the problem.

ehild