Changing mass

  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. jbriggs444

    jbriggs444 2,225
    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. 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. jbriggs444

    jbriggs444 2,225
    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:
  6. HallsofIvy

    HallsofIvy 41,260
    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.
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