How to Calculate Required Rocket Force for a Spinning Satellite

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In summary, the conversation is about solving a problem involving a satellite with a mass of 3700 kg and a radius of 5.0 m, which needs to reach 33 rpm in 5.5 min by firing four tangential rockets. The student initially had difficulty with the calculation of the required force of each rocket, but after receiving guidance, they were able to correctly calculate the moment of inertia and the net torque, leading to the correct solution.
  • #1
caner_cem
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[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?
 

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  • #2
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?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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
 
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  • #6
caner_cem said:
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.
 
  • #7
Hootenanny said:
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
 
  • #8
caner_cem said:
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.
 
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  • #9
Hootenanny said:
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?
 
  • #10
caner_cem said:
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.
 
  • #11
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:(:(
 
  • #12
caner_cem said:
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?
 
  • #13
Hootenanny said:
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?
 
  • #14
caner_cem said:
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.
 
  • #15
Hootenanny said:
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.
 
  • #16
caner_cem said:
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 :smile:
 

1. What is a satellite?

A satellite is an object that orbits around a larger object, such as a planet. In the context of space science, a satellite typically refers to an artificial object that is launched into orbit around the Earth for various purposes, such as communication, navigation, and scientific research.

2. What is the problem with satellites?

One of the main problems with satellites is the issue of space debris. When a satellite reaches the end of its life or becomes non-operational, it can create debris that can collide with other objects in space, potentially causing damage and endangering other satellites. This problem is becoming increasingly serious as more satellites are launched into orbit.

3. How do satellites stay in orbit?

Satellites stay in orbit due to the balance between the force of gravity and their own velocity. The gravitational pull of the Earth keeps the satellite in orbit, while its velocity keeps it from falling to the ground. In addition, satellites may also use thrusters or solar sails to adjust their orbit if necessary.

4. What are the benefits of satellites?

Satellites have a wide range of benefits, including communication, navigation, weather forecasting, and scientific research. They allow us to communicate with people all over the world, accurately navigate our way to different locations, predict and track weather patterns, and gather valuable data about our planet and the universe.

5. How are satellites launched into orbit?

Satellites are launched into orbit using rockets, which provide the necessary thrust to overcome the Earth's gravitational pull and enter into orbit. Some satellites are launched directly into their desired orbit, while others are first placed into a low-Earth orbit and then use their own propulsion systems to reach their final orbit.

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