Torque Force of Rockets On A Satellite

[Lancelot59]

Homework Statement

A satellite has a mass of 4000 kg, a radius of 4.9 m. 4 rockets tangentially mounted each add a mass of 220 kg, what is the required steady force of each rocket if the satellite is to reach 31 rpm in 5.1 min, starting from rest?

Homework Equations

[tex]\Sigma[/tex]T=I [tex]\alpha[/tex]

The Attempt at a Solution

Simple enough. I had already solved pretty much the same problem in my textbook.

I got [tex]\alpha[/tex] by taking the RPM as the delta V_tangental and then multiplying it by 2[tex]\Pi[/tex]/60, and then dividing it by 306 seconds.

Then for I I used (1/2)Mr² for the satellite body, and treated the rockets as point particles using mr², and multiplying by 4.


I = (1/2)Mr² + 4(mr²)


I wound up with about 183 Newtons per rocket, which the program says is wrong. This online system has a habit of telling you your stuff is wrong when in fact you're doing everything correctly. It uses some silly method of rounding off each step instead of just the final answer.

Am I doing something wrong?

 

[tiny-tim]

Hi Lancelot59!

(have an alpha: α and an omega: ω and a sigma: ∑ and a pi: π )

A satellite has a mass of 4000 kg, a radius of 4.9 m. 4 rockets tangentially mounted each add a mass of 220 kg, what is the required steady force of each rocket if the satellite is to reach 31 rpm in 5.1 min, starting from rest?
…
I got [tex]\alpha[/tex] by taking the RPM as the delta V_tangental and then multiplying it by 2[tex]\Pi[/tex]/60, and then dividing it by 306 seconds.

erm … why 2π/60 ?

v = rω

 

[Lancelot59]

Well the speed is in rotations per minute. So I changed it into radians per second.

31RPM x (2pi radians/1 rpm) x (1 minute/60 seconds)

I tried using v=r[tex]\omega[/tex] which gave me twice the [tex]\alpha[/tex] but the thing still says it's wrong. I calculated the moment of inertia to be 69148.8.

 

[tiny-tim]

Well the speed is in rotations per minute. So I changed it into radians per second.

31RPM x (2pi radians/1 rpm) x (1 minute/60 seconds)

I tried using v=r[tex]\omega[/tex] which gave me twice the [tex]\alpha[/tex] but the thing still says it's wrong. I calculated the moment of inertia to be 69148.8.

ah, I got confused by your V_tangential (still am, actually)!

Your equations, and moment of inertia, look ok, except I don't understand where you're using v =rω.

I have a feeling that your attempt to introduce V is somehow spoiling he result.

 

[Lancelot59]

Well then how could I find alpha?