Answer to Question #108105 in Mechanics | Relativity for A

Question

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?

Answer 1

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