1. The problem statement, all variables and given/known data I am trying to derive an equation for the net force, or thrust, acting upon a rocket. The equation I get is different from the standard equation given in most textbooks, so I want to know where I am going wrong. 2. Relevant equations [itex] F = d(mv)/dt [/itex] I also make use of the principle of conservation of momentum. 3. The attempt at a solution I will deal with the scenario whereby the only force acting upon the rocket is due to the ejected exhaust. At time t=0, let the rocket have mass m and velocity v with respect to an inertial reference frame. At this instant, its momentum, p1 is given by p1 = mv Let the ejected exhaust have a speed v e with respect to the rocket. Since the exhaust is ejected opposite to the direction of motion, its relative velocity is –ve. Let vf be the velocity of the exhaust relative to the inertial reference frame. Then, vf =v – ve After an infinitesimal amount of time, dt, let the mass of the rocket be m – dm. So, the mass of the ejected exhaust is dm. Also, the rocket’s velocity becomes v + dv. The total momentum of the system p2 is given by p 2 = (m - dm)(v +dv) + (dm)( vf) = (m – dm)(v+ dv) + (dm)( v – ve) = mv + mdv – (ve)(dm) The change in momentum of the system, dp, is given by dp = mdv – (ve)(dm) =0 Hence, mdv = (ve)(dm) The change in momentum of the rocket is given by [itex] (m – dm)(v+ dv) – mv = mdv – vdm [/itex] The rate of change of momentum of the rocket, or net force, Fnet is given by Fnet = (m)(dv/dt) – v(dm/dt) = ((ve) – v)(dm/dt) = (-vf)(dm/dt) However, most textbooks simply define the net force to be (m)(dv/dt). How can this expression be used to find the force on the rocket if its mass is changing? And what is wrong with my derivation? I would appreciate if someone could clarify. Thanks in advance.