How Is Average Force Calculated When Air Hits a Building?

[Morass]

Homework Statement

Air in a 110km/hr wind strikes head-on the face of a building 45m wide by 60m high and is brought to rest. If air has a mass of 1.3kg/m^3 calculate the average force exerted on the building.

Homework Equations

p = mv
delta P = Fav * t
dp/dt = F

The Attempt at a Solution

I know that the total impulse can be calculated by finding the total mass multiplied by the velocity. The mass is density multiplied by volume. But I'm unsure what the "volume" is in this case. Also, I am not sure how to relate the impulse to the average force as there is no time interval given. Should I be using differentials to represent very small amounts, namely dv and dt, to approach this problem?

 

[anathema]

Thank you for posting this interesting problem. Your approach using the equations for impulse and average force is a good start. In order to solve this problem, you will need to consider the volume of air that is hitting the building. In this case, the volume can be calculated by multiplying the height and width of the building (45m x 60m = 2700m^2).

Next, you will need to calculate the mass of the air that is hitting the building. As you correctly stated, mass is equal to density multiplied by volume. In this case, the density of air is given as 1.3kg/m^3 and the volume is 2700m^2. Therefore, the mass of the air is 3510kg.

Now, using the equation for impulse (p = mv), we can calculate the total impulse exerted on the building. The velocity of the air is given as 110km/hr, which is equivalent to 30.55m/s. Therefore, the total impulse is equal to 107,260.5 kg*m/s.

Finally, to calculate the average force exerted on the building, we can use the equation F = dp/dt. Since we do not have a specific time interval, we can use a very small time interval (dt) to approximate the average force. This can be represented by using differentials as you suggested. Therefore, the average force can be calculated as F = (dp/dt) = (107,260.5 kg*m/s)/(dt).

I hope this helps guide you in solving the problem. If you have any further questions or need clarification, please do not hesitate to ask. Keep up the good work in your studies!