How to Calculate Required Rocket Force for a Spinning Satellite

[caner_cem]

[SOLVED] A Problem About Satellite

Homework Statement

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure.

If the satellite has a mass of 3700 kg, a radius of 5.0 m, and the rockets each add a mass of 250 kg, what is the required steady force of each rocket if the satellite is to reach 33 rpm in 5.5 min, starting from rest?

can anyone help me to solve this problem?

 

[Hootenanny]

Welcome to PF caner cem,

The forum guidelines require you to show some effort or detail your thoughts before we can help you. So, what have you tried thus far?

 

[caner_cem]

sorry, i am in a hurry.

i found the inertia of satellite I =0.5mr^2 and angular accelaration with this w = at = 33 rpm = 33*2*pi/60 = 3.455 rad/s. then calculate the torque
Torque = I*a with this equation after that i divided it 4 to find each rocket torque.
Torque = Frsin(angle between F,r) = Fr i used this equation to find the F but i could not find the right answer i am doing something wrong.

 

[Hootenanny]

How did you calculate the angular acceleration?

What value did you get for the inertia?

Your methodology seems correct, so you must have made an error in the calculation, we can't help you with that unless you show your complete working.

 

[caner_cem]

Inertia=46250 , angular acceleration=0.0105, torque=485.63 and each torque of rocket=121.4 finally F=24.3 but it says it is wrong

i think the problem is accelaration but i do not know another solution.
i used this equation w=a.t, w: angular velocity, a:angular accelaration, t is time

 

[Hootenanny]

Inertia=46250 , angular acceleration=0.0105, torque=485.63 and each torque of rocket=121.4 finally F=24.3 but it says it is wrong

i think the problem is accelaration but i do not know another solution.
i used this equation w=a.t, w: angular velocity, a:angular accelaration, t is time

Your forgetting the moment of inertia of the rockets.

 

[caner_cem]

Your forgetting the moment of inertia of the rockets.

i tried to do adding the inertias of rockets but it did not accept it and i have only one time to write the answer

 

[Hootenanny]

i tried to do adding the inertias of rockets but it did not accept it and i have only one time to write the answer

You need to calculate the inertia of the cylinder and rockets as a single body and use this inertia to calculate the net torque. You can treat the rockets as point masses.

 

[caner_cem]

You need to calculate the inertia of the cylinder and rockets as a single body and use this inertia to calculate the angular acceleration. You can treat the rockets as point masses.

sorry. how can i find the angular accelaration using inertia?

 

[Hootenanny]

sorry. how can i find the angular accelaration using inertia?

Sorry, it was a typo, I meant net torque as opposed to angular acceleration. I have corrected the mistake in my previous post.

 

[caner_cem]

i tried it; when i calculate the inertia with rockets I=58750 and a=0.0105 so net torque=616.875, each rocket needs to provide a torque of 616.875/4=154.22 so F=30.84 but i is wrong:(:(

 

[Hootenanny]

i tried it; when i calculate the inertia with rockets I=58750

You have calculated the moment of inertia incorrectly. What is the moment of inertia for a point particle?

 

[caner_cem]

You have calculated the moment of inertia incorrectly. What is the moment of inertia for a point particle?

then i must use this equation with total mass I =mr^2, is it right?

 

[Hootenanny]

then i must use this equation with total mass I =mr^2, is it right?

That is correct, this will give you the moment of inertia of the rockets. You then need to add this to the moment of inertia of your cylinder to obtain the total moment of inertia.

 

[caner_cem]

That is correct, this will give you the moment of inertia of the rockets. You then need to add this to the moment of inertia of your cylinder to obtain the total moment of inertia.

thank you very much brother. and i am so sorry to take your time.

 

[Hootenanny]

thank you very much brother. and i am so sorry to take your time.

No worries, that's what we're here for! No apology necessary