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-Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose a dancer (or skater) is spinning at a very fast 2.6 revolutions per second about a vertical axis through the center of his head. Although the distance varies from person to person, the inner ear is approximately 7.0 cm from the axis of spin. part A What is the radial acceleration (in m/s^2 ) of the endolymph fluid? part B What is the radial acceleration (in g's) of the endolymph fluid? 2-A model of a helicopter rotor has four blades, each of length 4.00m from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 540rev/min . A-What is the linear speed of the blade tip? B-What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravity, g?

Respuesta :

1)

Answer:

[tex]a = 18.68 m/s^2[/tex]

Part b)

[tex]a = 1.9 g[/tex]

Explanation:

Rate of the spinning of the dancer is given as

[tex]f = 2.6 rev/s[/tex]

angular speed is given as

[tex]\omega = 2\pi f[/tex]

[tex]\omega = 2\pi(2.6) = 16.33 rad/s[/tex]

distance of the ear is given as

[tex]r = 7 cm = 0.07 m[/tex]

Part a)

Radial acceleration is given as

[tex]a = \omega^2 r[/tex]

[tex]a = (16.33)^2(0.07)[/tex]

[tex]a = 18.68 m/s^2[/tex]

Part b)

also we know that

[tex]g = 9.81 m/s[/tex]

so now we have

[tex]\frac{a}{g} = \frac{18.68}{9.81}[/tex]

[tex]a = 1.9 g[/tex]

2)

Answer:

Part a)

[tex]v = 226.2 m/s[/tex]

Part b)

[tex]a = 1.304 \times 10^3 g[/tex]

Explanation:

Length of the blades = 4.00 m

frequency of the blades = 540 rev/min

[tex]f = 540 \times \frac{1}{60} = 9 rev/s[/tex]

so angular speed is given as

[tex]\omega = 2\pi f[/tex]

[tex]\omega = 2\pi(9) = 56.5 rad/s[/tex]

Part a)

Linear speed of the tip of the blade is given as

[tex]v = r\omega[/tex]

[tex]v = (4.00)(56.5)[/tex]

[tex]v = 226.2 m/s[/tex]

Part b)

Radial acceleration of the tip of the blade

[tex]a = \frac{v^2}{r}[/tex]

[tex]a = \frac{226.2^2}{4}[/tex]

[tex]a = 1.28 \times 10^4 m/s^2[/tex]

also we know

[tex]\frac{a}{g} = \frac{1.28 \times 10^4}{9.81}[/tex]

[tex]a = 1.304 \times 10^3 g[/tex]

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