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 middot 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 = 150 squareroot t 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 = 0.18 s

Explanation / Answer

m = 130 Kg

I = 50 Kg.m^2

F = 150 sqrt(t)

x = 0.60 m

NOw, for the final angular speed = 0.4 rad/s

change in moemntum = impulse torque acting

50 * (0.40) = integration(150 * sqrt(t).0.60 dt) from 0 to t s

solving for t

50 * 0.40 = 150 * 0.60 * t^(3/2)/(3/2)

solving for t

t = 0.48 s
the time taken is a) 0.48 s

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