How fast must the astronaut's head be moving

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SUMMARY

The discussion centers on calculating the speed of an astronaut's head in a rotating arm device, specifically designed to simulate high acceleration environments. The arm length is 8.84g, and the maximum sustained acceleration is 12.5g. To determine the head's speed, users must apply the formula for centripetal acceleration, which relates velocity, radius, and acceleration. Additionally, the difference in acceleration between the astronaut's head and feet is calculated based on a height of 2.00m.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula: a = v^2/r
  • Basic knowledge of rotational motion and angular velocity
  • Familiarity with units of measurement, specifically meters per second (m/s) and revolutions per minute (rpm)
  • Ability to perform algebraic manipulations and solve equations
NEXT STEPS
  • Research the physics of centripetal acceleration and its applications in rotational systems
  • Learn how to convert linear velocity to angular velocity (rpm) in rotating systems
  • Explore the effects of different gravitational forces on human physiology in simulated environments
  • Investigate the design and function of centrifuge devices used in astronaut training
USEFUL FOR

Aerospace engineers, physics students, and professionals involved in astronaut training or human factors in high-acceleration environments will benefit from this discussion.

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Homework Statement


In this device, an arm 8.84g 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 12.5g

- How fast must the astronaut's head be moving to experience this maximum acceleration? m/s

- What is the difference between the acceleration of his head and feet if the astronaut is 2.00m tall? m/s^2

- How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration? 1/T= __rpm


Homework Equations


v^2/r ? something similar maybe


The Attempt at a Solution


i have probably attempted every set-up besdies the one that works. I have used the numbers in every different way to try and figure this out. I have tried 22 different ways and can not figure this out for my life
 
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