HW Rotation #1 Begin Date: 3/21/2018 12:00:00 AM-Due Date: 4/1/2018 11:59:00 PM

Question

HW Rotation #1 Begin Date: 3/21/2018 12:00:00 AM-Due Date: 4/1/2018 11:59:00 PM End Date: 5/30/2018 i 1:59:00 PM (6%) Problem 7: NASA scientists suggest using rotating cylindrical shuttle to replicate gravity while in a weightless environment. Consider such a shuttle that has a diameter of d 71 m. Otheexpertta 50% Part (a) what is the speed v in meters per second, the shuttle must rotate at its outer edge to replicate the force of gravity on e Grade Summa Deductions Potential Submissions Attempts rema (3% per attem detailed view tan) coso cotan asinacos) 1 2 3 0 atan acotansinh coshO anh cotanh0 Degrees Radians Hint I give up Submit Feedback: 0% deduction per feedback. Hines: 2% deduction per hint Hints remaining: 2 50% Part (b) At what rate, in revolutions per minute, is the station rotating?

Explanation / Answer

According to the given problem,

Diameter = 71 m. So radius (r) = 71/2 = 35.5 m

We require that centripetal acceleration at outer edge = g = 9.81 m/s²

Centripetal acceleration = v²/r = 9.81
(a)
v² = 35.5 * 9.81 = 348.255
v = 18.66 m/s

(b)
time = distance / speed

The distance moved by a fixed point on the edge when it completes one revolution = 2?r = 223.05 m

1 revolution therefore takes 223.05 / 18.66 = 11.95 s

Each minute it will complete (60 / 15.98) = 5.02 rpm.

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