Question #108105

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets. Suppose that the satellite has a mass of 4000 kg and a radius of 5.0 m , and that the rockets each add a mass of 250 kg.

What is the steady force required of each rocket if the satellite is to reach 43 rpm in 6.5 min , starting from rest?

What is the steady force required of each rocket if the satellite is to reach 43 rpm in 6.5 min , starting from rest?

Expert's answer

Given data,

Angular velocity =43rpm

Time = 6.5min=390second

Mass of the satellite M=4000kg

Mass of the rocket m = 250kg

Radius of the satellite R =5m

Angular velocity "\\omega=43\\times\\frac{2\\pi}{60}=4.50\\ rad s^{-1}"

Angular acceleration "\\alpha",

"\\omega=\\omega_0+\\alpha\\times t"

"\\alpha=\\frac{4.5}{390}=0.0115rads^{-2}"

Inertia is given by

"I=0.5MR^2+4mR^2"

And the net torque,

"\\tau_{net}=I\\times\\alpha=4F\\times R"

"F=\\frac{I\\times\\alpha}{4R}"

"F=\\frac{R(0.5M+4m)\\times\\alpha}{4}"

F=43.125N

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