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!

Changing mass

  1. Jan 31, 2013 #1
    hi,

    I want to calculate how is acceleration changing if I have changing mass, but constant trust i.e. :

    T = m*a

    a = T / m

    (I know it has to be calculus).
    Then again I also wan't to be able to calculate displacement and velocities etc..
    Trying to find somewhere on the internet a tutorial on equations of motion when the acceleration is varying.. but most of the time I find equations for constant-acceleration.
    Do you have a good tutorial ? (don't point me to wikipedia, it is good as reference but not as tutorial)
    I would like also to have some simple Exersises, so I can figure out how it is done in general.

    thank you
     
  2. jcsd
  3. Jan 31, 2013 #2

    jbriggs444

    User Avatar
    Science Advisor

    You are on the right track. a = T/m and it takes calculus.

    The derivitive of 1/m with respect to m is -1/m2

    So for constant T, the derivitive of T/m with respect to m is -T/m2

    The minus sign indicates that as m increases the quotient T/m decreases.
     
  4. Jan 31, 2013 #3
    Nice.. ok now how can I calculate displacement or time taken to cross specific distans having this acceleration...
    I suppose I can't use :

    d = x + v*t + 1/2 a*t^2

    because this is only valid for constant acceleration ?
     
  5. Feb 1, 2013 #4

    jbriggs444

    User Avatar
    Science Advisor

    You are correct. For a non-constant acceleration instead of computing the change in velocity by simply multiplying acceleration by time, you have to compute it by integrating acceleration over time using calculus.

    Similarly, for a non-constant velocity you compute change in position by integrating velocity over time rather than simply multiplying velocity by time.

    You end up with a double integral.

    The first integration to compute velocity as a function of time results in:

    http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
     
  6. Feb 1, 2013 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Conservation of momentum, mv, leads to (mv)'= m'v+ mv'= 0 (the ' indicates the derivative) if there is no external force. If there is a force, then we do not have conservartion of momentum but have (mv)'= m'v+ mv'= F.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook