1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rocket Burning fuel causing change in mass

  1. Mar 19, 2013 #1
    I made up a scenario: Let's say I have a rocket at rest in space. The rocket initially weighs 100 kg, 50 kg of which is fuel. If the fuel burns at a constant rate of 1 kg/s and produces a thrust of 100 N out the back of the rocket, what will the rocket's velocity be after it runs out of fuel?

    From F=ma and V=v0+at, I derived V=Ft/m. The force is 100 N, and it would take 50 s to burn 50 kg of fuel at 1 kg/s, so it would be V=100*50/m.

    My question is: What would I use for the mass, since it is changing at the fuel burns? When I assumed that it was just the average mass, 75 kg, I got the final velocity ≈ 66.7 m/s. Am I supposed to just use the average mass since the fuel is burned at a constant rate? Does rocket fuel in the real world burn at a constant rate, or exponentially? If it was exponential, could I just use calculus to find the average mass and then plug it in?
  2. jcsd
  3. Mar 19, 2013 #2


    User Avatar

    Staff: Mentor

    What you are asking about is known as the "Rocket Equation". Here is a tutorial from NASA:


  4. Mar 19, 2013 #3
    You need to use ## 50 + 50 ( 1 - \frac{t}{50} ) ##. Because the acceleration is not constant, you cannot use V=v0+at or work with an average mass though: you need to integrate a differential equation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook