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At its Ames Research Center, NASA uses its large 20-G centrifuge to test the effects of very large accelerations (hypergravity) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and the astronaut is strapped in at the other end. Suppose that he is aligned along the arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this machine is typically 12.5 g .Part AHow fast must the astronaut's head be moving to experience this maximum acceleration?Part BWhat is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?Part CHow fast in rpm (revolutions per minute) is the arm turning to produce the maximum sustained acceleration?

Respuesta :

Answer:

Explanation:

  • applying the concept of centripetal acceleration;
  • ac = v^2/r
  • where r = radius of circular orbit = 8.84m
  • v = square root (ac x r)
  • given ac = maximum sustained acceleration = 12.5g, g = 9.81m/s^2
  • from v = square root( ac x r)

v = square root ( 12.5 x 9.81 x 8.84)

v = 32.92m/s =astronauts speed

b) astronaut acceleration ;

from ac = w^2 r

w = square root ( ac/r)

w = square root(12.5g/8.84)

= square root( 12.5 x 9.81 /8.84)

= 3.72rad/s

c) What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall ; new r' = 8.84 - 2.00 , r' = 6.84m

  • from ac = w^2r
  • = 3.72^2 x 6.84 = 94.88m/s^2
  • therefore difference = 12.5g - 94.88
  • 12.5 x 9.81 - 94.88 = 27.745m/s^2

d) How fast in rpm (revolutions per minute) is the arm turning to produce the maximum sustained acceleration ; i.e convert w in rads/s to rvpm

= 3.72 x 60 / 2 x 3.142

= 35.52rvpm = the angular speed

where rvpm = revolutions per minute

snehashish65

(A) The maximum speed of the astronaut's head is 32.92 m/s.

(B)  The required difference between the acceleration of his head and feet is  [tex]27.745\;\rm m/s^{2}[/tex].

(C)  The required angular speed of arms is 35.52 rotations per minute.

Given data:

The length of arm is, r = 8.84 m.

The maximum value of sustained acceleration is, a = 12.5g.

(A)

The center seeking acceleration of a body is known as centripetal acceleration. The expression is given as,

[tex]a = \dfrac{v^{2}}{r}\\\\v=\sqrt{a \times r}\\\\v=\sqrt{12.5g \times 8.84}\\\\v=\sqrt{12.5 \times 9.8 \times 8.84}\\\\v=32.92 \;\rm m/s[/tex]

Thus, the maximum speed of the astronaut's head is 32.92 m/s.

(B)

With difference in length between the head and feet, the new length is,

r' = 8.84 - 2.00 = 6.84 m

Then the difference in acceleration is,

a' = a - a''

a'' is the acceleration of astronaut. And its value is,

[tex]a'' = \omega^{2} \times r'\\\\a'' = \dfrac{a}{r} \times r'\\\\a'' = \dfrac{12.5g}{8.84} \times 6.84\\\\a''=\dfrac{12.5 \times 9.8}{8.84} \times 6.84 = 94.88 \;\rm m/s^{2}[/tex]

Then, the difference in acceleration is,

[tex]a' = 12.5g - 94.88\\\\a' = 12.5(9.8) - 94.88 = 27.745\;\rm m/s^{2}[/tex]

Thus, the required difference between the acceleration of his head and feet is  [tex]27.745\;\rm m/s^{2}[/tex].

(C)

The angular speed of arm in rotations per minute is,

[tex]\omega = 2 \pi n/60 \\\\\\\sqrt{\dfrac{a}{r}}= \dfrac{2 \pi \times n}{60}\\\\\\\sqrt{\dfrac{12.5 \times 9.8}{8.84}}= \dfrac{2 \pi \times n}{60}\\\\\\n = 35.52 \;\rm rpm[/tex]

Thus, the required angular speed of arms is 35.52 rotations per minute.

Learn more about the rotational motion here:

https://brainly.com/question/1388042

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