Physics, 16.11.2020 22:50 jessixa897192

2. An 85.5 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 12.0 m) and spun at a constant angular velocity of 18.4 rpm. Answer the following: (a) What is the angular velocity of the centrifuge in ?
(b) What is the linear velocity of the astronaut at the outer edge of the centrifuge?
(c) What is the centripetal acceleration of the astronaut at the end of the centrifuge?
(d) How many g’s does the astronaut experience?
(e) What is the centripetal force experienced by the astronaut?

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Rotational kinematics and Newton's second law allow to find the results for the astronaut's movement in the centrifuge are:

a) The angular velocity is: w = 1.927 rad / s

b) The linear velocity is: v = 23.1 m / s

c) The centripetal acceleration is: a = 6.417 10³ m / s²

d) The centripetal acceleration is: a = 6.548 10² g

e) The centripetal force F = 5.49 10⁵ N

given parameters

The mass of the astronaut m = 85.5 kg Centrifuge radii r = 12.0 m Angular velocity w = 18.4 rpm (2prad / 1rev) (1min / 60s) = 1.927 rad / s

To find

a) angular velocity

b) linear velocity

c) centripetal acceleration

d) acceleration in units of gravity (g)

e) the centripetal force

The angular velocity is defined as the rotated angle in the unit of time.

$w = \frac{\Delta \theta}{t}$

Angular and linear variables are related.

v = w r

Where w is the angular velocity, θ is the angle, t the time, v the lienal velocity and R the radius of the cetnrifuga

Let's answer the questions:

a) The angular velocity of the centrifuge and the astronaut are equal

w = 1.927 rad / s

b) Linear velocity

v = 1.927 12.0

v = 23.1 m / s

c) Centripetal acceleration has the formula:

a = $\frac{v^2}{R}$

a = $\frac{23.1^2}{12.0}$

a = 6.417 10³ m / s²

d) The value of this eceleration as a function of gravity

$\frac{a}{g}$ = 6.417 10³ / 9.8

$\frac{a}{g}$ = 6.548 10²

a = 6.548 10² g

e) The centripetal force

F = ma

F = 85.5 6.417 10³

F = 5.49 10⁵ N

In conclusion, using rotational kinematics and Newton's second law we can find the results for the movement of the astronaut in the centrifuge are:

a) The angular velocity is: w = 1.927 rad / s

b) The linear velocity is: v = 23.1 m / s

c) The centripetal acceleration is: a = 6.417 10³ m / s²

d) The centripetal acceleration is: a = 6.548 10² g

e) The centripetal force F = 5.49 10⁵ N

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2. An 85.5 kg astronaut is training for accelerations that he will experience upon reentry. He is pl...

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