Rocket launches up starting from zero, conservation momentum

Click For Summary

Homework Help Overview

The discussion revolves around a rocket problem involving conservation of momentum and energy. The original poster presents a scenario where a rocket ejects exhaust to achieve acceleration, with specific parameters for initial and final mass, as well as exhaust velocity. The problem includes both theoretical and practical aspects of rocket propulsion, particularly in relation to achieving relativistic speeds.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of conservation laws, with the original poster attempting to derive the rocket's final velocity using momentum principles. Some participants suggest looking up established equations, while others express the need to differentiate the equations due to changing mass and velocity. There is also mention of using the center of mass frame for momentum calculations.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the conservation laws and how they apply to the rocket problem. Some guidance has been offered regarding established equations, but there is no explicit consensus on the approach or solution yet.

Contextual Notes

Participants note the constraints of the problem, including the requirement to use conservation laws as outlined in their textbook. There is also a mention of the need to estimate the mass required for a specific payload to reach a significant fraction of the speed of light, which introduces additional complexity to the discussion.

ex81
Messages
73
Reaction score
0

Homework Statement



A rocket ejects exhaust with an velocity of u. The rate at which the exhaust mass is used (mass per unit time) is b. We assume that the rocket accelerates in a straight line starting initial mass (fuel plus the body and payload) be mi, and mf be its final mass, after all the fuel is used up. (a) Find the rocket's final velocity, v, in terms of u, mi, mf. (b) A typical exhaust velocity for chemical rocket engines is 4000m/s. Estimate the initial mass of a rocket that could accelerate a one-ton payload to 10% of the speed of light, and show that this design won't work. (ignore the mass of the fuel tanks.)


Homework Equations



Kinetic Energy = 1/2 mv^2
momentum = mv
work = f*d
f=ma

The Attempt at a Solution



I started out with the conservation of energy, and then switched to the conservation of momentum.

The rocket starts out at rest. so mi*vi = 0

0 = mf*v +(mi-mf)*u
which makes sense since the rocket's momentum will be opposite to the exhaust velocity, and the two momentum will cancel.

Now is the part where I am stuck.
 
Physics news on Phys.org
Look up the ideal rocket equation. Although it is basically a Newton's third law momentum problem, it is not that simple to develop it on your own.

AM
 
It is in the conservation section of the book. Ergo I have to use the conservation law :-(
I do realize that I need to differentiate the equation but I am pretty sure I need to tweak my current equation. Due to the change in mass vs velocity.
 
ex81 said:
It is in the conservation section of the book. Ergo I have to use the conservation law :-(
I do realize that I need to differentiate the equation but I am pretty sure I need to tweak my current equation. Due to the change in mass vs velocity.
Ok. You can do a rough estimate using conservation of momentum.

Use the centre of mass frame - the earth. Initial momentum is 0. In order for you to get 1000kg moving at .9c how much mass moving at 4000 m/sec in the opposite direction will you need so that the total momentum is 0?

AM
 
I think I am on the right track just from looking at NASA's ideal rocket equation
0 = mf*v +(mi-mf)*u

now NASA has dm * u/dt= v * d(mass propellant)/dt. Cancel out their dt, and their equation is dm *u=v*d(mass propellant)

So based on the above my equation needs to change a little, and needs to be derived.
 
P.S. my u, and v is switched from NASA's
 

Similar threads

How Does Rocket Ejection Mass Affect Its Velocity in Space?
  • · Replies 1 ·
Replies
1
Views
2K
How Does the Relativistic Rocket Equation Describe Velocity?
  • · Replies 2 ·
Replies
2
Views
2K
How to calculate velocity of infinite-stage rocket?
  • · Replies 2 ·
Replies
2
Views
1K
Distance between rocket and object
  • · Replies 30 ·
2
Replies
30
Views
3K
Conservation of Momentum With Changing Mass
  • · Replies 6 ·
Replies
6
Views
2K
Why is the thrust equation same under gravitational force?
  • · Replies 10 ·
Replies
10
Views
2K
How long does it take for a rocket to lift off the ground?
  • · Replies 7 ·
Replies
7
Views
2K
Force and acceleration of a rocket
  • · Replies 3 ·
Replies
3
Views
2K
Rocket acceleration problem: confused about Newton's 2nd Law
  • · Replies 42 ·
2
Replies
42
Views
6K
A rocket on a spring, related to potential/kinetic energy
  • · Replies 3 ·
Replies
3
Views
2K