What is the formula for variable mass systems and rockets?

In summary, the conversation is about studying variable mass systems and rockets, and the formula v=u*ln M0/M is introduced, where v is the velocity of the rocket, M0 is the initial mass, M is the mass after a certain time, and u is the velocity of the ejected gas. The mass is being lost at a constant rate and the person is asking for help with the derivation of this equation. They mention they are just starting to learn integration and are having trouble with the integrand.
  • #1
UchihaClan13
145
12
Okay guys
I am studying variable mass systems and rockets,as such
I was introduced to the formula v=u*ln M0/M
where v is the velocity of the rocket after a time t
M0is the initial mass of the rocket,M is the mass of the rocket after time t
u is the velocity of the ejected gas w.r.t to the rocket
The mass is being lost(in the form of fuel being used up to propel the rocket and provide it the required upward force) at a constant rate r=-dM/dt
Could any of you guys help me with the derivation of this "useful" equation?
I just started learning integration
Hence i can't figure out the integrand so easily
Thanks in advance!:)
UchihaClan13
 
Physics news on Phys.org
  • #2
UchihaClan13 said:
Could any of you guys help me with the derivation of this "useful" equation?
If you give us a link to a specific derivation and tell us exactly where you get "stuck", someone can probably help you.
 
  • #3
Okay I will
Thank you:)
 

Related to What is the formula for variable mass systems and rockets?

1. What is rocket propulsion?

Rocket propulsion is the process of generating thrust to move a rocket through space. This is typically achieved by expelling high-velocity exhaust gases from the rear of the rocket.

2. How do rockets overcome the Earth's gravity?

Rockets overcome the Earth's gravity by achieving escape velocity, which is the speed required to break free from the pull of the Earth's gravity. This is typically around 25,000 mph for rockets launched from Earth's surface.

3. What are the different types of rocket engines?

There are two main types of rocket engines: liquid-fueled and solid-fueled. Liquid-fueled engines use liquid propellants, such as liquid hydrogen and liquid oxygen, while solid-fueled engines use solid propellants, such as solid rocket boosters.

4. How do rockets change direction and speed in space?

Rockets change direction and speed in space by using thrusters. These thrusters can be placed at different points on the rocket to provide control and maneuverability. They work by expelling gas in a specific direction, which creates a force in the opposite direction and allows the rocket to change its course.

5. What is the role of rocket staging in space travel?

Rocket staging is the process of separating parts of the rocket as it ascends into space. This allows the rocket to shed excess weight and increase its efficiency. Typically, rockets have multiple stages, with each one providing enough thrust to reach a certain altitude before being discarded.

Similar threads

I Meaning of the terms in the formula of the net external force
    • Mechanics
Replies
17
Views
1K
Insights How to Apply Newton’s Second Law to Variable Mass Systems
    • Mechanics
Replies
0
Views
1K
Conservation of energy in Gravitation
    • Mechanics
Replies
4
Views
794
I Doubt about variable mass systems
    • Mechanics
Replies
30
Views
1K
I Modeling a Bottle Rocket: Analyzing the Maximum Altitude
    • Mechanics
Replies
4
Views
2K
How to calculate velocity of infinite-stage rocket?
    • Introductory Physics Homework Help
Replies
2
Views
371
100% energy efficient, constant power rocket
    • Mechanics
Replies
25
Views
3K
Relative velocity of exhaust in Ideal Rocket Equation
    • Mechanics
Replies
1
Views
1K
Derivation of Rocket Equation Using Relative Velocity
    • Mechanics
Replies
1
Views
2K
How Does Rocket Ejection Mass Affect Its Velocity in Space?
    • Introductory Physics Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top