# Velocity of the rocket with changing mass

• annie.hung
In summary, Annie recommends reading through a good online source for the derivation of the rocket equation, and then doing a problem similar to the one she provided.
annie.hung
I want to do something about the rocket. I have done the zero gravity point, escape velocity and the velocity of the rocket with constant mass. But I would like to expand it! PLEASE GIVE ME SOME IDEAS!
1) http://i53.photobucket.com/albums/g58/hunghoiyanl6/1.jpg"
2) http://i53.photobucket.com/albums/g58/hunghoiyanl6/2.jpg"
3) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3.jpg"
3.1) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3-1.jpg"
3.2) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3-2.jpg"
3.3) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3-3.jpg"

My physics teacher said that the mass (fuel) is changing only upto a point where the rocket passes the atmosphere. Afterwards, it will be a freefall process. If so, what other sort of ideas can I expand on it. Please give me some comments on this 'presentation', and give me some other recommandations on what else I can do.
Thank you very much.

Annie

Last edited by a moderator:
annie.hung said:
I want to do something about the rocket. I have done the zero gravity point, escape velocity and the velocity of the rocket with constant mass. But I would like to expand it! PLEASE GIVE ME SOME IDEAS!
1) http://i53.photobucket.com/albums/g58/hunghoiyanl6/1.jpg"
2) http://i53.photobucket.com/albums/g58/hunghoiyanl6/2.jpg"
3) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3.jpg"
3.1) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3-1.jpg"
3.2) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3-2.jpg"
3.3) http://i53.photobucket.com/albums/g58/hunghoiyanl6/3-3.jpg"

My physics teacher said that the mass (fuel) is changing only upto a point where the rocket passes the atmosphere. Afterwards, it will be a freefall process. If so, what other sort of ideas can I expand on it. Please give me some comments on this 'presentation', and give me some other recommandations on what else I can do.
Thank you very much.

Annie
There are numerous sources on the internet for the derivation of the rocket equation. Some of them are good, and some are not. One that I think does a very good job of setting up the equation in terms of conservation of momentum is found here

http://ed-thelen.org/rocket-eq.html

I think this approach is far superior to anything that involves F = d(M*V)/dt = V*dM/dt + M*dV/dt. This latter equation is only useful under special circumstances. For example, if fuel were being expelled out of both sides of the rocket perpendicular to its direction of motion dM/dt would be the rate of losing mass, but there would be no change in velocity and no net force.

I'm not sure the point your teacher was making about the mass changing only up to the point where the rocket passes the atmosphere. While in the atmosphere there is an effect related to the pressure of the exhausted gas helping to push the rocket. This effect is ignored in the derivation I posted, and it is not needed for the roicket to have thrust. Ships landed on the moon where there is no atmosphere and lifted off again. A rocket does not need atmosphere to accelerate.

Last edited by a moderator:

## 1. What is the relationship between rocket mass and velocity?

The velocity of a rocket is directly affected by its mass. As the mass of the rocket decreases, its velocity increases. This is due to the principle of conservation of momentum, which states that the total momentum of a system remains constant unless acted upon by an external force.

## 2. How does the changing mass of a rocket affect its acceleration?

The changing mass of a rocket does not directly affect its acceleration. However, as the rocket burns fuel and decreases in mass, the force of thrust remains constant, resulting in an increase in acceleration.

## 3. Why is it important to consider the mass of a rocket when calculating its velocity?

The mass of a rocket is a crucial factor in determining its velocity. In order to achieve a desired velocity, the mass of the rocket must be carefully controlled and managed. Too much or too little mass can greatly impact the rocket's performance and trajectory.

## 4. Can the velocity of a rocket with changing mass be accurately predicted?

Yes, the velocity of a rocket with changing mass can be accurately predicted using mathematical equations and principles such as Newton's laws of motion and the rocket equation. However, factors such as air resistance and external forces can also affect the velocity of a rocket in real-world scenarios.

## 5. How does the velocity of a rocket with changing mass impact its final destination?

The velocity of a rocket with changing mass greatly impacts its final destination. The higher the velocity, the further the rocket will travel and the greater the distance it can cover. This is why rockets are designed to reach high velocities in order to reach their intended destinations in space.

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