Force Required by Rockets and Angular Acceleration

In summary, to get a flat, uniform cylindrical satellite spinning at the correct rate, engineers must fire four tangential rockets with a required steady force of 14 N each. This can be calculated using the torque equation and the moment of inertia for a cylinder.
  • #1
PeachBanana
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Homework Statement


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

If the satellite has a mass of 4800 kg and a radius of 2.7m , what is the required steady force of each rocket if the satellite is to reach 29 rpm in 6.0 min?

Homework Equations



F = ma
ω final - ω initial / t = α
F/4 = force required by each rocket

The Attempt at a Solution



I converted everything to radians, seconds, etc.

I assumed the initial angular velocity was 0 rad./s.
3.0368 rad./s / 360 s. = 0.00843 rad./s^2

The rockets are being fired tangentially so I then found tangential acceleration.
(2.7 m)(0.00843 rad./s^2) = 0.022761 m/s^2

Then I used F = ma

F = (4800 kg)(0.022761 m/s^2)
F = 109.2528 N

F/4 = 27 N
 

Attachments

  • TheFourRockets.jpg
    TheFourRockets.jpg
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  • #2
You are mixing translational and rotational equations here. You must stick to rotation. Instead of F = ma, you must use the rotational analog.
 
  • #3
I think I'm a tad bit closer now.

torque = moment of inertia*angular acceleration

torque = (4800 kg)*(2.7m)^2*(0.00843 rad./s^2)

torque = 294.98256 N * m

Since I want my units to contain only Newtons, shouldn't I divide by the radius?

294.98256 N * m / 2.7 m = 109.2528 N

109.2528 N / 4 = 27 N per rocket

which can't be correct because it's the same as I did before.
 
  • #4
You're using the wrong moment of inertia; the spacecraft is a cylinder, not a cylindrical shell.
 
  • #5
tms - Thank you. I obtained the correct answer of about 14 N per rocket.
 

Related to Force Required by Rockets and Angular Acceleration

1. What is the force required for a rocket to launch?

The force required for a rocket to launch depends on several factors, such as the mass of the rocket, the acceleration required, and the distance it needs to travel. To calculate the force, you can use the formula F=ma, where F is the force, m is the mass, and a is the acceleration.

2. How does the force required by rockets change with angular acceleration?

The force required by rockets changes with angular acceleration due to the conservation of angular momentum. As the angular acceleration increases, the torque on the rocket also increases, requiring more force to maintain its angular velocity.

3. What is the relationship between force required by rockets and rocket fuel?

The force required by rockets is directly related to the amount of rocket fuel used. The more fuel a rocket has, the more force it can produce, leading to a higher acceleration. However, using more fuel also means a heavier rocket, which can impact the overall performance.

4. How do different rocket designs affect the force required and angular acceleration?

Different rocket designs can have a significant impact on the force required and angular acceleration. For example, a longer rocket with a smaller diameter will require more force to launch due to its increased mass. On the other hand, a shorter and wider rocket may require less force for the same angular acceleration.

5. How do external factors, such as air resistance, affect the force required and angular acceleration of a rocket?

External factors, such as air resistance, can have a significant impact on the force required and angular acceleration of a rocket. Air resistance can create drag on the rocket, requiring more force to maintain its velocity. This can also affect the angular acceleration, as the rocket may need to adjust its trajectory to overcome the drag.

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