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A device for acclimating military pilots to the high accelerations they must experience consists of a horizontal beam that rotates horizontally about one end while the pilot is seated at the other end. In order to achieve a radial acceleration of 29.9 m/s2 with a beam of length 5.33 m , what rotation frequency is required

User Tompa
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1 Answer

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Answer:

Rotation frequency is 0.377 hertz.

Step-by-step explanation:

After a careful reading of statement, we need to apply the concept of radial acceleration due to uniform circular motion, whose formula is:


a_(r) = \omega^(2)\cdot L (Eq. 1)

Where:


a_(r) - Radial acceleration, measured in meters per square second.


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


L - Length of the beam, measured in meters.

Now we clear the angular velocity within:


\omega = \sqrt{(a_(r))/(L) }

If
a_(r) = 29.9\,(m)/(s^(2)) and
L = 5.33\,m, the angular velocity is:


\omega = \sqrt{(29.9\,(m)/(s^(2)) )/(5.33\,m) }


\omega \approx 2.368\,(rad)/(s)

The frequency is the number of revolutions done by device per second and can be found by using this expression:


f = (\omega)/(2\pi) (Eq. 2)

Where
f is the frequency, measured in hertz.

If we know that
\omega \approx 2.368\,(rad)/(s), then rotation frequency is:


f = (2.368\,(rad)/(s) )/(2\pi)


f = 0.377\,hz

Rotation frequency is 0.377 hertz.

User Muffel
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