I would appreciate some help clarifying some ideas:
Consider a scale with sand falling in at a constant rate, say C kg/s. The reading on the scale as a function of time consists of two parts: the weight of the accumulated sand as a function of time + the rate of change of the sand's momentum, that is dp/dt. It is the dp/dt term in which I am interested.
dp/dt= d(mv)/dt = m(dv/dt) + v (dm/dt)
In all the treatments I have seen the first term is never included, so that the force from the sand is just v (usually sqrt(2gh) or some such thing) times dm/dt, or v*C. Is this because the only mass that is actually undergoing an acceleration is the timy bit of mass dm? In other words, is the first term zero because dv/dt = 0 for the m in the cart.
This seems obvious to me as I write, but strange that I have not seen it mentioned in any of the well known texts.
Thanks
Justin Parke
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.