# Finding Reactive Force and Fuel Burn Rate of a Rocket Lift-Off

• Simka
I using the correct formula to find mu?Yes, you are using the correct formula to find mu, but you need to also consider the force of gravity in your calculations. In summary, to find the engine's reactive force and fuel burn rate, you need to use Newton's third law, which takes into account the force of gravity. This will give you a more accurate answer for mu.
Simka
A rocket, mass m=4000kg, lifts off the ground vertically with acceleration of a=0.2g. The velocity of gass emmiting from it is u=1200m/s (with respect to the rocket). Find engine's reactive force and then fuel burn rate (mu).

This is what i managed to do:
rocket's speed at any moment t (with respect to the ground) is a*t
gass's speed at any moment t (with respect to the ground) is u-a*t

Mass of rocket at any time t is m-mu*t
Mass of fuel that is burned is mu*t
rocket's mass multiplied by it's speed and gass's mass multiplied by its speed are equal, so

(m-mu*t)*a*t=mu*t*(u-a*t)

and i get that m*a*t=mu*t*u

mu=(m*a)/u=6.53 kg/s

but... I was given 4 answers (5.9kg/s 9.8kg/s 39.2kg/s 19.8kg/s) and mine is wrong...

Any ideas anyone?

Simka said:
A rocket, mass m=4000kg, lifts off the ground vertically with acceleration of a=0.2g. The velocity of gass emmiting from it is u=1200m/s (with respect to the rocket). Find engine's reactive force and then fuel burn rate (mu).

This is what i managed to do:
rocket's speed at any moment t (with respect to the ground) is a*t
gass's speed at any moment t (with respect to the ground) is u-a*tMass of rocket at any time t is m-mu*t
Mass of fuel that is burned is mu*t
rocket's mass multiplied by it's speed and gass's mass multiplied by its speed are equal...
You are forgetting about gravity. Use Newton's third law: The rate of change of momentum of the rocket + force of gravity = rate of change of momentum of the gas being expelled:

$$F_{rocket} = mg + ma = - F_{gas} = - vdm/dt$$

AM

Last edited:

## What is reactive force and how does it affect a rocket lift-off?

Reactive force is the force that propels a rocket upwards during lift-off. It is generated by the burning of fuel and the release of hot gases out of the rocket's engine. This force is responsible for overcoming the force of gravity and allowing the rocket to take off.

## How do scientists calculate the reactive force of a rocket?

To calculate the reactive force of a rocket, scientists use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This means that the force generated by the burning fuel and the release of gases downwards is equal to the reactive force pushing the rocket upwards.

## What factors affect the fuel burn rate of a rocket?

The fuel burn rate of a rocket can be affected by various factors such as the type and composition of the fuel, the design of the rocket engine, the atmospheric conditions, and the weight of the rocket. These factors can impact the amount of fuel burned and the resulting reactive force.

## Why is it important to determine the fuel burn rate of a rocket?

The fuel burn rate of a rocket is crucial in determining the performance and trajectory of the rocket during lift-off. It helps scientists understand the amount of thrust generated and the time it takes for the rocket to reach its desired altitude. This information is essential in designing and optimizing future rocket launches.

## How do scientists measure the fuel burn rate of a rocket?

Scientists use various methods to measure the fuel burn rate of a rocket, including using sensors and cameras to record the rocket's performance during lift-off, analyzing the rocket's exhaust plume, and conducting ground tests to measure the amount of fuel burned per unit time. These methods help scientists accurately determine the fuel burn rate of a rocket and its resulting reactive force.

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