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Flauer [41]
3 years ago
6

Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 miles per hour) when the jet stream

descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of 225 m2? Typical air density in Boulder is 1.14 kg/m3, and the corresponding atmospheric pressure is 8.89 ✕ 104 N/m2. (Bernoulli's principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)
Physics
1 answer:
siniylev [52]3 years ago
5 0

Answer:

F = 260 kN

Explanation:

given,                                

speed = 45 m/s            

Area = 225 m²                    

air density = 1.14 Kg/m³                

Atmospheric pressure =  8.89 ✕ 10⁴ N/m²

Using  Bernoulli equation          

assuming the level is same        

P_1 - P_2 = \dfrac{1}{2}\rho V^2

\Delta P= \dfrac{1}{2}\rho V^2          

\Delta P= \dfrac{1}{2}\times 1.14 \times 45^2

\Delta P=1154.25\ Pa

Force = Pressure x area              

Force =1154.25 x 225        

F = 259706.25 N                              

F = 260 kN                      

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Answer;

Average speed  = 47.5 km/hr

Explanation and solution;

Average Speed = Total distance /Total time

Total distance;

-In the first two hours travelling at 40km/hr, total distance traveled is 80km.

(40 × 2) = 80 km

-In next two hours distance covered is 110 km. (55 ×2)

Total distance = 110 + 80 = 190 km

Total time = 2 + 2 = 4 hours

Average Speed = Total distance /Total time

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                         = 47.5 km/hr

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mixas84 [53]

Answer:

The radius of its orbit is R \approx 1.899\times 10^{9}\,m.

Explanation:

Let suppose that Callisto rotates around Jupiter in a circular path and at constant speed, then we understand that net acceleration of this satellite is equal to the centripetal acceleration due to gravity of Jupiter. That is:

\omega^{2}\cdot R = a_{net} (1)

Where:

\omega - Angular speed, measured in radians per second.

R - Radius of the orbit, measured in meters.

a_{net} - Net acceleration, measured in meters per square second.

In addition, angular speed can be described in terms of period (T), measured in seconds:

\omega = \frac{2\pi}{T} (2)

And the net acceleration by the Newton's Law of Gravitation:

a_{net} = \frac{G\cdot m}{R^{2}} (3)

Where:

G - Gravitation constant, measured in cubic meters per kilogram-square second.

m - Mass of Jupiter, measured in kilograms.

Now we apply (2) and (3) in (1) to derive an expression for the radius of the orbit:

\frac{4\pi^{2}\cdot R}{T^{2}} = \frac{G\cdot m}{R^{2}}

R^{3} = \frac{G\cdot m \cdot T^{2}}{4\pi^{2}}

R = \sqrt[3]{\frac{G\cdot m\cdot T}{4\pi^{2}} } (4)

If we know that G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}, m = 1.90\times 10^{27}\,kg and T = 1460160\,s, then the radius of the orbit of Callisto is:

R = \sqrt[3]{\frac{(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} )\cdot (1.90\times 10^{27}\,kg)\cdot (1460160\,s)^{2}}{4\pi^{2}} }

R \approx 1.899\times 10^{9}\,m

8 0
3 years ago
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