Spacecraft could create a type of artificial gravity by spinning fast enough to create a radial acceleration equal to 9.8 m/s2. If a giant space station with a mass of 2.8 x 1017 kg and a radius of 5.05 x 106 m wanted to create that type of artificial gravity, what angular velocity would be required? O 1.39 x 103 rad/s 7030 rad/s 4.95 x 107 rad/s O 1.94 x 10-6 rad/s
Spacecraft could create a type of artificial gravity by spinning fast enough to create a radial acceleration equal to 9.8 m/s2. If a giant space station with a mass of 2.8 x 1017 kg and a radius of 5.05 x 106 m wanted to create that type of artificial gravity, what angular velocity would be required? O 1.39 x 103 rad/s 7030 rad/s 4.95 x 107 rad/s O 1.94 x 10-6 rad/s
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Artificial Gravity in Spacecraft
Spacecraft could create a type of artificial gravity by spinning fast enough to create a radial acceleration equal to 9.8 m/s².
#### Problem Statement:
If a giant space station with a mass of \(2.8 \times 10^{17}\) kg and a radius of \(5.05 \times 10^6\) m wanted to create that type of artificial gravity, what angular velocity would be required?
#### Answer Choices:
- \(1.39 \times 10^{-3} \text{ rad/s}\)
- \(7030 \text{ rad/s}\)
- \(4.95 \times 10^7 \text{ rad/s}\)
- \(1.94 \times 10^{-6} \text{ rad/s}\)
To solve this, we can use the formula for radial (centripetal) acceleration \(a_r = \omega^2 r\), where \(\omega\) is the angular velocity and \(r\) is the radius.
Given:
- Radial acceleration, \(a_r = 9.8 \text{ m/s}^2\)
- Radius, \(r = 5.05 \times 10^6 \text{ m}\)
Rearranging the formula to solve for \(\omega\):
\[ \omega = \sqrt{\frac{a_r}{r}} \]
Substituting the given values:
\[ \omega = \sqrt{\frac{9.8}{5.05 \times 10^6}} \]
Performing the calculation:
\[ \omega \approx 1.39 \times 10^{-3} \text{ rad/s} \]
Thus, the correct answer is:
- \(1.39 \times 10^{-3} \text{ rad/s}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24666b77-75da-49bd-bf84-8c4674dedd2c%2F0e3adaf2-1e29-4e73-b427-2343e432bcd6%2Fjvhdjbg.png&w=3840&q=75)
Transcribed Image Text:### Artificial Gravity in Spacecraft
Spacecraft could create a type of artificial gravity by spinning fast enough to create a radial acceleration equal to 9.8 m/s².
#### Problem Statement:
If a giant space station with a mass of \(2.8 \times 10^{17}\) kg and a radius of \(5.05 \times 10^6\) m wanted to create that type of artificial gravity, what angular velocity would be required?
#### Answer Choices:
- \(1.39 \times 10^{-3} \text{ rad/s}\)
- \(7030 \text{ rad/s}\)
- \(4.95 \times 10^7 \text{ rad/s}\)
- \(1.94 \times 10^{-6} \text{ rad/s}\)
To solve this, we can use the formula for radial (centripetal) acceleration \(a_r = \omega^2 r\), where \(\omega\) is the angular velocity and \(r\) is the radius.
Given:
- Radial acceleration, \(a_r = 9.8 \text{ m/s}^2\)
- Radius, \(r = 5.05 \times 10^6 \text{ m}\)
Rearranging the formula to solve for \(\omega\):
\[ \omega = \sqrt{\frac{a_r}{r}} \]
Substituting the given values:
\[ \omega = \sqrt{\frac{9.8}{5.05 \times 10^6}} \]
Performing the calculation:
\[ \omega \approx 1.39 \times 10^{-3} \text{ rad/s} \]
Thus, the correct answer is:
- \(1.39 \times 10^{-3} \text{ rad/s}\)
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