Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
Mass spectrometry the time they take to reach the detector. If the particles all have the same charge, the kinetic energies tends to be identical, and their velocities, in this case, will depend only on their masses. Ions with a lower mass will reach the detector first. However, in reality, even particles with the same m/z can arrive at different times at the detector, because they have different initial velocities. The initial velocity is not dependent on the mass of the ion what becomes a problem for the TOF-MS. The difference in initial velocity turns into difference in the final velocity. In