Concept explainers
At what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.70 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 9, Fig 5-33 )
The time required for one revolution of the cylindrical spaceship.
Answer to Problem 54P
Solution:
9.59 s
Explanation of Solution
Given:
Diameter of the cylindrical spaceship,
Radius of the cylindrical spaceship,
Simulated gravity,
Formula Used:
According to the Newton’s second law of motion,
The centripetal acceleration is given by
Where, m is the mass, v is the velocity, a is the acceleration and r is the radius.
Calculation:
From the above, we can write
The velocity of the spaceshipcan be obtained by
Therefore, the accelerationof the spaceship is
Equating the above acceleration to the given simulated gravity,
Conclusion:
Therefore, the time required for one revolution of the cylindrical spaceship is 9.59 seconds.
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