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Consult Multiple-Concept Example 14 for background pertinent to this problem. In designing rotating space stations to provide for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the negative effects of motion sickness begin to appear when the rotational motion is faster than two revolutions per minute. On the other hand, the magnitude of the centripetal acceleration at the astronauts’ feet should equal the magnitude of the acceleration due to gravity on earth. Thus, to eliminate the difficulties with motion sickness, designers must choose the distance between the astronauts’ feet and the axis about which the space station rotates to be greater than a certain minimum value. What is this minimum value?

223$m$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

Hope College

University of Sheffield

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

02:20

In designing rotating spac…

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02:07

Rotating Space Stations. O…

01:24

01:47

BIO Weightlessness and art…

01:01

The National Aeronautics a…

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03:38

Artificial gravity in spac…

03:57

One problem for humans li…

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One problem for humans liv…

04:59

and this problem. We're told to design a space station that is rotating with a certain frequency, as well as one that is able to create the same acceleration of gravity that the astronauts on it would be experiencing on Earth. So even though the question Texas pretty long but it is really asking, is how do we relate velocity and radius that we can achieve a given acceleration? Luckily, we know an equation that relates, Exactly. There's three variables we know that V squared over R is equal to angular acceleration and Eric and in our case, angular acceleration is equal to G, since that's what we want to achieve. Now we want to sell for our but in this case, we don't know V so we have too many unknowns. Luckily, we can rewrite the in terms of quantities that we know we're giving our frequency, which is two rotations per minute. That means that we complete one full rotation every 30 seconds, right? And so that means that that is the value of our period 30 seconds. Now we know equation that relates to a period and velocity. That's the fact that T is equal to two pi r over the and that could easily be written to simply be V equals two pi r over tea. And those are all quantities that we either No, I want to find. So let's plug that into our equation. We do that. We find that four pi squared r squared was t squared. Time are, and that's equal to Elsa. And so now we want to solve for are so let's rearrange to do just that and we get that our is equal to G t squared all over four Pi squared and look at that now It's all in terms of quantities that we know gee is 9.8 meters per second squared t is 30 seconds like we figured out earlier, and four pi squared is just constant. We plug all that in, we find that our radius, in order to achieve Oliver constraints, is 223 meters, and that is gonna be the answer to this

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