Rocket launches up starting from zero, conservation momentum

In summary, the conversation discusses the problem of finding the final velocity of a rocket based on the exhaust velocity and mass usage rate. It also explores the ideal rocket equation and how it can be used to estimate the initial mass of a rocket needed to accelerate a one-ton payload to 10% of the speed of light. The conversation concludes that this design is not feasible due to the high initial mass required.
  • #1
ex81
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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.
 
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  • #2
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
 
  • #3
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.
 
  • #4
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
 
  • #5
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.
 
  • #6
P.S. my u, and v is switched from NASA's
 

1. How does a rocket launch from a standstill?

A rocket launches from a standstill by igniting its engines to produce thrust. This thrust pushes against the ground and propels the rocket upwards.

2. What is conservation of momentum in relation to rocket launches?

Conservation of momentum is a fundamental principle in physics that states that the total momentum of a system remains constant unless acted upon by an external force. In the context of rocket launches, this means that the total momentum of the rocket and its propellant remains constant throughout the launch.

3. Why is conservation of momentum important in rocket launches?

Conservation of momentum is important in rocket launches because it allows for the efficient use of propellant. By conserving the momentum of the rocket and its propellant, the rocket is able to achieve greater speeds and heights.

4. How does a rocket maintain its momentum during launch?

A rocket maintains its momentum during launch by continuously burning its propellant and expelling it out of the engines at a high velocity. This action produces an equal and opposite reaction, propelling the rocket forward and maintaining its momentum.

5. What happens to the momentum of a rocket once it reaches space?

Once a rocket reaches space, it will continue to maintain its momentum unless acted upon by an external force. In the vacuum of space, there is no air resistance or friction to slow down the rocket, so it will continue to travel at a constant speed and direction until another force, such as gravity from a planet or moon, acts upon it.

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