Concept explainers
(a)
Period of rotation needed to provide an artificial gravity of
(a)
Answer to Problem 69P
Period of rotation needed to provide an artificial gravity of
Explanation of Solution
The edge of the station is moving in a circle. A centripetal acceleration is needed for this motion.
Write the expression for centripetal acceleration.
Here,
Equate equation (I) to
Write the expression for period.
Conclusion:
Substitute,
Substitute,
Therefore, the period of rotation needed to provide an artificial gravity of
(b)
The speed needed to move the rim.
(b)
Answer to Problem 69P
The speed needed to move the rim is
Explanation of Solution
From the part (a), it is clear that the speed needed to move the rim is
Conclusion:
Therefore, the speed needed to move the rim is
(c)
Apparent weight of the person if he run along the rim at
(c)
Answer to Problem 69P
Apparent weight of the person if he run along the rim at
Explanation of Solution
The overall velocity along the arc of the circle if the velocity in the opposite sense of that the rim’s rotation can be expressed as,
Here,
Conclusion:
Substitute,
The apparent weight of the person decreases proportional to the reduced centripetal acceleration due to the lower velocity of the person.
Substitute,
It can be express in terms of
Therefore, apparent weight of the person if he run along the rim at
(d)
The apparent weight of person if he run instead in the direction of rotation.
(d)
Answer to Problem 69P
The apparent weight of person if he run instead in the direction of rotation is
Explanation of Solution
The overall velocity along the arc of the circle if the velocity aligned with that the rim’s rotation can be expressed as,
Conclusion:
Substitute,
The apparent weight of the person increase proportional to the reduced centripetal acceleration due to the larger velocity of the person.
Substitute,
It can be express in terms of
Therefore, the apparent weight of person if he run instead in the direction of rotation is
(e)
The direction in which the person run to get the best workout.
(e)
Answer to Problem 69P
The direction in which the person run to get the best workout is
Explanation of Solution
If the person run in the direction of rotation, then the rotation speed can increase effectively. The centripetal acceleration can increase by increasing rotation speed. Thereby effective weight weighing more while working out will definitely make the workout more difficult.
Conclusion:
Therefore, the direction in which the person run to get the best workout is
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Chapter 5 Solutions
College Physics, Volume 1
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