# Homework Help: Velocity change by running engine for 1 year

1. Feb 18, 2012

### pridet8

1. The problem statement, all variables and given/known data

A rocket engine has an exhaust velocity of 20,000 m/sec. The mass flow (dm/dt) rate is 1 milligram per second.
a) What is the thrust produced by the engine?
b) The engine propels a 200 kg space craft. What change in velocity is achievable by running the engine continuously for one solid year?
note1: assume a constant mass for the system.
note2: One year = 31.56 x 10^6 seconds.

2. Relevant equations
Thrust = -Ve*(dm/dt)

Change in velocity = V - Vo = Ve*(ln Mo/M)

3. The attempt at a solution
a) Thrust = 20000m/s *(.000001kg/s) = .02N

b) 20000*(ln 200kg/31.56kg) = 36928.6 m/s^2

My question: Part A I believe is right but part b I am having trouble believing. Should I just keep it simple since the mass is constant at 200 kg? Thus giving a new equation which would be
a = (Thrust - W)/M

which is (.02N - (200kg*9.8m/s2))/200kg = 9.79m/s^2

2. Feb 18, 2012

### willem2

in V - Vo = Ve * ln(Mo/M), Mo is the initial mass of the rocket including propellant, and M is the final mass of the rocket including leftover propellant.

There's no mention in the problem that you should account for the gravity of a planet or start, so you can use a = (Thrust)/M. You still have to compute the velocity change from the accelerations and the duration.

The assumption that the mass is constant won't give an accurate solution, since more than 30 kg of the 200 kg will disappear.

3. Feb 18, 2012

### pridet8

So then the velocity change will be:

a= Thrust/M

Where Thrust = .02 N and M = 200kg
= .0001 m/s^2

Velocity @ 3.156 x 10^6 seconds = (.0001m/s^2)*500s = 315.6m/s

Then the velocity change will be from 20,000m/s - 315.6m/s = 19684.4 m/s

4. Feb 18, 2012

### pridet8

******Velocity @ 3.156 x 10^6 seconds = (.0001m/s^2)*500s = 315.6m/s********

I meant (.0001m/s^2)*3.156 x 10^6

5. Feb 19, 2012

### willem2

It's actually 31.56 x 10^6 second.

I don't understand why you subtracted the velocity change from 20000 m/s. What is wanted is just the velocity change.

6. Feb 19, 2012

### pridet8

So which one should I use then?

The ln with mass ratio which gave me an answer of: 3411.02 m/s

Or the a = f/m which gave me a change of : 3156 m/s

7. Feb 19, 2012

### willem2

As I said: The assumption that the mass is constant won't give an accurate solution, since more than 30 kg of the 200 kg will disappear.