Math Problem Statement

A large, doughnut-shaped section of a spacecraft is being designed for long-term space flight. The outer wall of the rotating section will become the floor for the astronauts, and the centripetal acceleration produced by the floor will simulate gravity. If this section of the spacecraft has a radius of 400.0 m, what speed will produce an acceleration of 9.81 m/s 2 ?

Solution

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Math Problem Analysis

Mathematical Concepts

Centripetal Acceleration
Circular Motion
Kinematics

Formulas

Centripetal acceleration formula: a_c = v² / r
Formula for velocity: v = √(a_c * r)

Theorems

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Suitable Grade Level

Grades 10-12