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A 80kg astronaut is training in human centrifuge to prepare for a launch. The astronaut uses the centrifuge to practice having a

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The answers on the model of the human centrifuge ready for the launch to each question of the statement are listed below:

a) A force of 2479.210 newtons is acting on the astronaut's back.

b) A <em>net centripetal</em> force of 2479.210 newtons is acting on the astronaut.

c) The <em>centripetal</em> acceleration of the astronaut is 30.990 meters per square second.

d) The astronaut has a <em>linear</em> speed of approximately 19.284 meters per second.

e) The <em>angular</em> speed of the astronaut is 1.607 radians per second (15.346 revolutions per minute).

<h3>How to apply Newton's laws to analyze a process in a human centrifuge training</h3>

The human centrifuge experiments a <em>centripetal</em> acceleration when it reaches a <em>peak</em> angular speed. In this question we must apply Newton's laws of motion and concepts of <em>centripete</em> and <em>centrifugal</em> forces to answer the questions. Now we proceed to answer the questions:

<h3>How much force is acting on the astronaut's back?</h3>

By the third Newton's law the astronaut experiments a <em>rection</em> force (<em>F</em>), in newtons, which has the same magnitude to <em>centrifugal</em> force but opposed to that force. The magnitude of the force acting on the back of the astronaut is equal to:

$F = 3.16\cdot (80\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)$

$F = 2479.210\,N$

A force of 2479.210 newtons is acting on the astronaut's back. $\blacksquare$

<h3>What is the net centripetal force on the astronaut?</h3>

By the second and third Newton's laws we know that the <em>net centripetal</em> force on the astronaut is equal to the magnitude of the force found in the previous question. Thus, a <em>net centripetal</em> force of 2479.210 newtons is acting on the astronaut. $\blacksquare$

<h3>What is the astronaut's centripetal acceleration?</h3>

The centripetal acceleration of the astronaut (<em>a</em>), in meters per square second, is found by dividing the result of the previous question by the mass of the astronaut (<em>m</em>), in kilograms:

$a = \frac{F}{m}$ (1)

If we know that F = 2479.210 newtons and m = 80 kilograms, then the centripetal acceleration of the astronaut is:

$a = \frac{2479.210\,N}{80\,kg}$

$a = 30.990\,\frac{m}{s^{2}}$

The <em>centripetal</em> acceleration of the astronaut is 30.990 meters per square second. $\blacksquare$

<h3>What is the astronaut's linear speed?</h3>

By definition of <em>uniform circular</em> motion, we have the following formula for the <em>linear</em> velocity of the astronaut (<em>v</em>):

$v = \sqrt{a\cdot r}$ (1)