How Do You Calculate Rocket Propulsion and Acceleration?

[redred7]

Homework Statement

A small 120kg rocket is fired vertically, propelled by an engine with a thrust of 6500N. The engine ejects gas at a rate of 4.5kg/s.
a) Calculate the change in velocity of the gases relative to the engine
b) after 20 s what will be the rockets accleration.

Homework Equations

F * delta T = m * delta V

The Attempt at a Solution

(6500-1176)(1) = (120-4.5)delta V
5324= 115.5V
V= 46 m/s


I am not sure if I hav the correct force (because I am not sure if I should subtract Ff), correct mass (because I believe that mass is contant in this formula as there isn't delta M)

 

[alphysicist]

Hi redred7,

Homework Statement

A small 120kg rocket is fired vertically, propelled by an engine with a thrust of 6500N. The engine ejects gas at a rate of 4.5kg/s.
a) Calculate the change in velocity of the gases relative to the engine
b) after 20 s what will be the rockets accleration.

Homework Equations

F * delta T = m * delta V

The Attempt at a Solution

(6500-1176)(1) = (120-4.5)delta V
5324= 115.5V
V= 46 m/s


I am not sure if I hav the correct force (because I am not sure if I should subtract Ff), correct mass (because I believe that mass is contant in this formula as there isn't delta M)

Yes, the mass is changing. The problem states that every second the mass changes by 4.5kg. So in your equation keep the term that has the change in mass.

 

[thomate1]

and correct time.

I would like to point out that the given information is not sufficient to accurately solve for the change in velocity of the gases relative to the engine. We need to know the initial velocity of the gases and the duration of the engine burn in order to use the impulse-momentum equation. Additionally, we need to consider the effects of air resistance and the mass of the rocket itself, which will affect the acceleration.

However, assuming that the initial velocity of the gases is 0 m/s and the engine burns for 20 seconds, we can use the given equation and solve for the change in velocity of the gases relative to the engine as follows:

F * delta T = m * delta V
(6500 N - 1176 N) * (20 s) = (120 kg - 4.5 kg) * (delta V)
106,480 Ns = 115.5 kg * delta V
delta V = 923.5 m/s

This means that the velocity of the gases relative to the engine will increase by 923.5 m/s after 20 seconds.

For part b, we can use the momentum equation to calculate the acceleration of the rocket as follows:

P = m * v
(120 kg) * (923.5 m/s) = (120 kg) * (a)
a = 923.5 m/s^2

Therefore, the rocket will have an acceleration of 923.5 m/s^2 after 20 seconds. However, as mentioned earlier, this is a simplified calculation and does not take into account other factors such as air resistance and the mass of the rocket. We would need more information to accurately solve for the acceleration of the rocket.