# Grade 12 Rocket propulsion Question

• rock33y
In summary, the conversation is about determining the amount of fuel and oxidizer needed for a rocket to achieve a speed of 10000m/s with an exhaust velocity of 2000m/s. The ideal rocket equation is used to calculate the amount of fuel needed based on the initial and final masses of the rocket. If the exhaust velocity is increased to 5000m/s, the amount of fuel and oxidizer needed would also change.

## Homework Statement

A rocket for use in deep space is to have the capability of boosting a pay load ( plus the rocket frame and engine) of 3 metric tonnes to an achieved speed of 10000m/s with an engine and fuel designed to produce an exhaust velocity of 2000m/s.
a) How much fuel and oxidizer is req'd, b)and if a diff fuel and engine design could give an exhaust velocity of 5000m/s, what amount of fuel and oxzidier would be req'd?

P=P'

## The Attempt at a Solution

m1 = 3000 kg, v1= 0, v1' = 10 000m/s
m2 = ? kg, v2 = 0, v2' = 2000m/s

m1v1 + m2v2 = m1v1' + m2v2'
0 = m1v1' + m2v2'
-m1v1' / v2'= m2

-15 000 kg = m2

How is the mass negative :S
the answer at the back says "442 x 10^3 kg"

so I know I'm off by a lot... Our fizzicks teacher didn't teach us how to solve these problems, but I assumed it was a momentum problem.

Any help would be greatly appreciated. :)

Can someone please assist me anyway possible.

I'm sorry if it's a stupid question.

You are assuming that the 15000 kg are ejected all at once at 2000 m/sec. That is not how the rocket works, however. The rocket fuel burns over a period of time during which the rocket + fuel is accelerated in the other direction. So a lot of the rocket fuel is used to accelerate the rocket fuel still on board the rocket. You also have to take gravity into account if the rocket is moving away from the earth.

This is a hard question if they are expecting you to solve it from first principles. I think they are expecting you to use an equation such as the ideal rocket equation:

$$\Delta v = v_{engine}\ln{m_i/m_f}$$

where the left side is the final payload speed, m_i is the initial mass, m_f is the final mass (payload), v_engine is the speed of the gases exiting the engine (ln is the natural logarithm). Do you see this equation anywhere in your materials?

$$m_fe^{\Delta v/v_{engine}} = m_i$$

Since the fuel mass is mi-mf you can calculate the amount of fuel used.

AM

## 1. How does rocket propulsion work?

Rocket propulsion works by using a propellant, typically a mixture of fuel and oxidizer, to create a controlled explosion in the rocket's combustion chamber. This explosion creates hot gases that are directed out of the back of the rocket, creating thrust that propels the rocket forward.

## 2. What type of propellant is used in rocket propulsion?

There are various types of propellants used in rocket propulsion, including liquid propellants (such as liquid hydrogen and liquid oxygen) and solid propellants (such as solid rocket fuel). The choice of propellant depends on factors such as cost, performance, and safety.

## 3. How does rocket propulsion differ from other forms of propulsion?

Rocket propulsion differs from other forms of propulsion, such as jet engines or propeller engines, in that it does not require air or oxygen from the surrounding environment to function. This makes it ideal for use in space where there is no atmosphere.

## 4. What are the main components of a rocket propulsion system?

The main components of a rocket propulsion system include the rocket engine (combustion chamber, nozzle, and propellant), the fuel and oxidizer tanks, and the guidance and control systems. These components work together to generate thrust and control the direction of the rocket.

## 5. What are some challenges in designing and implementing rocket propulsion systems?

Some challenges in designing and implementing rocket propulsion systems include managing the extreme temperatures and pressures generated by the combustion process, ensuring the stability and control of the rocket during flight, and optimizing the efficiency and performance of the propulsion system. Safety is also a critical concern in the design and implementation of rocket propulsion systems.