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if the satellite has a mass of 3500 kg , a radius of 4.4 m , and the rockets each add a mass of 220 kg , what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min , starting from rest?



Answer :

rafikiedu08

0.145 Newton is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min , starting from rest

mass of satellite ( M ) = 3500 kg

radius of satellite ( r )  = 4.4 m

mass added by each rocket ( m ) = 220 kg

Angular speed of satellite = 32 rpm

Time = 5 mins  

moment of inertia

[tex]I=1/2Mr^2+4mr^2[/tex]

M = 3500 kg  m = 220 kg,  r =4.4 m

I=33880+17036

Insert values into equation ( 1 )

I =20416 kg-m^2

angular acceleration

∝ = ω / t

= ( 2π×32 ) /  3600×5

= 0.0112 rad/s²

steady force required by each rocket

Τ = I × ∝     ( 1 )

T = 4rF

Equation ( 1 ) becomes

4rF = I × ∝

Force = I×∝ / 4r

= ( 228×0.0112 ) / 4×4.4

=2.56/17.6

= 0.145 N .

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