An astronaut with thruster pack has a combined mass of 130 kg and a mass moment

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 = 0.18s

Explanation / 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

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