(2007?Shanghai Simulation) On February 28 this year, the passenger train from Urumqi to Aksu encountered dusty weather. Due to the instantaneous strong wind, the 9th to 19th carriages were damaged.

(1) The output electric power is: P=f?v?η=αρ0Av2?v?η=αρ0Av3η, the coefficient α=0.5 in the formula?

So?P=0.5 ×1.25×4×27.93×0.2?W=1.1×104?W?

(2) The mass of suspended particles in the air with V air = 1m3 is m = ρ concentrated V air = 5.8 × 10- 8×1kg=5.8×10-8?kg

The total volume of suspended particles V=mρ′=5.8×10?82×103kg=2.9×10-11?m3

The volume of a single suspended particle

V0=43πr3=43×3.14×(?5×10?82?)3?m3=6.5×10-23?m3?

1m3 The number of inhalable particles?n=η′VV0=+f(150×2.9×10?11, 6.5×10?23)=8.9×1011?pieces?

(3) When the wind force f? and sand particles Only when the gravity satisfies the relationship: f≥mg? can blowing sand weather be formed, that is,

αρ0Av2=αρ0πr2v2≥ρs×43π?r3×g?

We get?v≥4ρsrg3αρ0 ≈4.07?m/s?

(4) Suppose the side length of the cube is L and the gravity is G. When the wind moment M wind is equal to the cube weight moment MG, the cube will overturn, so

f×L2=G×L2

In the formula, f=αρ0Av2=αρ0L2v2; G=mg=ρVg=ρL3g

Obtain?αρ0L2v2=ρL3g?

That is, L=αρ0v2ρg

Because?G=ρL3g=ρ×(?αρ0v2ρg)3×g=α3ρ30ρ2g2v6, it can be seen that?G∝v6

So when the wind speed increases, The wind force f will increase sharply, causing the train to overturn and cause a derailment accident. ?

Answer: (1) The electrical power output by this generator is 1.1×104 W when the wind speed is 27.9m/s;

(2) 1.0m3 air contains about 8.9 ×1011 inhalable particles;

(3) The wind speed causing sand blowing weather near the ground is at least 4.07 m/s;

(4) The gravity and wind speed of the object Proportional to the sixth power, when the wind speed increases, the wind force f will increase sharply, causing the train to overturn and cause a derailment accident.