Conservation of momentum continous mass flow freight cart.

BareFootKing

1. The problem statement, all variables and given/known data
I am having difficulty understanding why in 2.1 Worked Example Coal Car on page 3 One can use the initial time as time = 0, but 2.2 Worked example on page 4 they start the initial time at an arbitrary time t.


2. Relevant equations



3. The attempt at a solution

BareFootKing

because in the second example if you start with the initial time =0 then the initial momentum is zero because it is initially at rest and this simplifies the second example to a solutions similar to the first. But that is wrong.

haruspex

your two links point to the same page, and I can't see anything there that matches either description.

BareFootKing

Thank you I put up the wrong link. Here is the correct link:

haruspex

In each case they start at t=0. In 2.2 they also consider some arbitrary later time t and an interval δt from there. That is normal when deriving differential equations. In 2.1 they did not need to do that; they could solve the problem just by considering t=0 and t=t_f and applying conservation of momentum. Whether such an approach was available in 2.2 I've not tried to analyse.