An astronaut with thruster pack has a combined mass of 130 kg and a mass moment
ID: 1509718 • Letter: A
Question
An astronaut with thruster pack has a combined mass of 130 kg and a mass moment of inertia about the combined mass center of 50 kg-m^2. The astronaut is initially not rotating when the thruster pack is fired. If the thruster initially generates a force according to the equation F = 150squareroott N, where t is in seconds, determine the duration of time the thruster needs to fire to provide the astronaut with a counterclockwise angular velocity of 0.4 rad/s. a) t = 0.48 s b) t = 0.38 s c) t= 0.28 s d) t = 0.18sExplanation / Answer
a) 0.48 s
given
I = 50 kg.m^2
wi = 0
wf = 0.4 rad/s
Torque, T = r*F
= 0.6*150*sqrt(t)
= 90*sqrt(t)
we know, T = dL/dt (here L is angular momentum)
dL = T*dt
intgerla dL = integral T*dt
(Lf - Li) = integral 90*sqrt(t)*dt
Lf - 0 = 90*t^(3/2)/(3/2)
I*wf = 60*t^(3/2)
50*0.4 = 60*t^(3/2)
1 = 3*t^(3/2)
t = (1/3)^(2/3)
= 0.48 s