Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Multiple-Concept Example 14 deals with the issues on which this problem focuses. To create artificial gravity, thespace station shown in the drawing is rotating at a rate of 1.00 rpm. The radii of the cylindrically shaped chambers have the ratio $r_{A} / r_{B}=4.00 .$ Each chamber $A$ simulates an acceleration due to gravity of 10.0 $\mathrm{m} / \mathrm{s}^{2} .$ Find values for $\quad(\mathrm{a}) r_{\mathrm{A}}, \quad(\mathbf{b}) r_{\mathrm{B}}$ and $(\mathbf{c})$ the acceleration due to gravitythat is simulated in chamber $\mathrm{B}$ .

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

912$m$228$m$2.50$m / s^{2}$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Michigan - Ann Arbor

University of Washington

University of Winnipeg

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.

02:57

Multiple-Concept Example 1…

02:41

To create artificial gravi…

00:32

A cylindrical space statio…

05:13

Artificial gravity. One wa…

02:07

Rotating Space Stations. O…

01:16

A rotating space station i…

03:38

Artificial gravity in spac…

01:13

01:11

The formula$$N=\frac{1…

01:47

To find the rotational rat…

02:32

the first thing that we have to do in this problem is find the radius of the first part of our space station. Given that we know the angular acceleration that is desired at that point, you know how to approach this. Let's first make sure that all are givens are in terms of quantities that we can use. And the only thing that we have to really do for that is realized that our frequency of one rotations per minute means that our period must be 60 seconds, since period is the amount of time that it takes to complete one full rotation and 60 seconds is a force equal to a minute. All right, so we can eat. We're gonna use period now to solve the rest of this problem. We know that T is equal to two pi r over V, which means that we can rearrange your soul for velocity, a quantity that were not given in this problem. We also know the angular acceleration is equal to V squared over Gore. That means that we can plug in the quantity that we just solved for, nor dissolved for an angular acceleration. So we get Elsa is equal to four pi squared r a over t squared Now we know Elsa A We have a desired quantity that we want to get we want to solve for are so we rearrange the other are equal to Alfa t squared over four pi squared and in order sulphur are always to do now is plug in Alfa is 10 meters per second squared He is 60 seconds as we just found and four pi squared is a constant So a final results for r A is going to be equal to after we round 928 Oh, sorry. My bet Non 38 900 and 12 Muse Great. So now that's my final answer for A and something for B is gonna be really straightforward were given the ratio between the two radio I at the beginning of the problem. So this means that r A is equal to four b and since we know are A it's 912 we know that r B must be equal to 228 meters There we go that serious Ruby All right. Final part of the problem were us to solve for the angular acceleration at point B. And this is gonna be pretty quick, too. Earlier when we were working a part A. We found on an equation for the angular acceleration. It's four pi squared R B over t B squared. The only thing that's changed is is that in fact, they were using the radius a bee. And I just made a mistake because the important thing for solving this is realizing that tea is constant everywhere for object, right? No matter, the object is always gonna take the same amount of time to rotate no matter where you are. So when we plug into this equation for pi squared times R B, which we found movie I've just found is equal 2 228 all over four seconds squared, which is 60 seconds we get that are angular acceleration a point B is 2.50 meters per second squared, which is our answer for part

View More Answers From This Book

Find Another Textbook