A space station, consisting of a long thin uniform rod of mass 4.6 x 10^6 kg and
ID: 2077564 • Letter: A
Question
A space station, consisting of a long thin uniform rod of mass 4.6 x 10^6 kg and length 677 meters, with two identical uniform hollow spheres, each of mass 2.9 x 10^6 kg and radius 251 meters, attached at the ends of the rod, as shown below. Note that none of the diagrams shown is drawn to scale!
(a) Suppose that the station starts out at rest (not rotating). What we want is to get it spinning about an axis passing through its center of mass, at an angular velocity of 0.11 rad/s, which is just what’s needed to produce 1-g of artificial gravity at the end points. To achieve this, we use rocket motors to apply a constant force F = 3.7 x 10^6 N to each sphere as shown, directed toward the centers of the spheres. How long must the motors fire in order to bring the station from rest up to an angular velocity of 0.11 rad/s? Answer: _________.___ minutes
F aXIS 1-1 FExplanation / Answer
Torque provided T = 2*Fr
=2*(3.7*10^6)*[677/2 + 251]
= 2*(3.7*10^6)*[338.5+251]
= 4362300000 Nm
Moment of inertia I = [ (4.6*10^6)*677^2 / 12 ] + [ 2*{ 2/3*(2.9*10^6)*251^2 + (2.9*10^6)*(338.5+251)^2 ]
= 2.43*10^12 Kgm^2
angular acc. a= T/I = 4362300000 / 2.43*10^12 =1.79*10^-3 rad/s^2
t = w/a = 0.11 / 1.79*10^-3
= 61.38 s
= 1.023 minutes
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.