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The National Aeronautics and Space Administration (NASA) studies the physiological effects of large accelerations on astronauts. Some of these studies use a machine known as a centrifuge. This machine consists of a long arm, to one end of which is attached a chamber in which the astronaut sits. The other end of the arm is connected to an axis about which the arm and chamber can be rotated. The astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 15 m from the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 7.5 times the acceleration due to gravity?

33$m / s$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Rutgers, The State University of New Jersey

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.

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in this problem, we have to find the speed at which a rotating Trebor must be moving in order for anyone inside it to feel an acceleration of 7.5 times the acceleration of gravity G. And were also given the radius of that chamber 15 years. All right, so in this problem, we know that we have a centripetal force and B squared over R. Since we're moving in a circular motion and that is gonna be the net force in our problem, so it is gonna set it equal to M A. We don't really care about any forces pointing upward or downward on the person in the chamber. We can cancel out our EMS to get that V. We get rid of this squared square root instead. V is equal to the square root of alpha. Times are all right. Well, we know what we want, Elsa. To be 7.5 times the gravitational acceleration on earth and that's gonna multiplied by our radius. 15 muse. Okay, so we've played in 9.8 meters per second. Squared four are gravitational acceleration, and we get that V is equal to 33.2 meters per second, which we're gonna round to the nearest hole number. So that V equals 33 meters per second, which is the answer to this problem.

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