- #1

- 1,421

- 5

## Main Question or Discussion Point

Hello,

I am reading section 3.2, concerning the analyzation of a moving rocket with a changing mass. (I couldn't find a preview of the book in google books, so hopefully someone out there has this textbook.) Here is an except from the book, but be warned that I am adding notes in brackets:

"At time t, the momentum [of the rocket] is P(t) = mv [m and v are the mass and velocity of the rocket at time t]. A short time later at t + dt, the rockets mass is (m + dm), where dm is negative, and its momentum is (m+dm)(v+dv). The fuel ejected in the time dt has mass (-dm) and velocity v - vex [v is the velocity of the rocket as viewed by some stationary person on earth, and vex is rate at which the fuel flows out, relative to the rocket]. Thus, the total momentum (rocket plus the fuel just ejected) at t + dt is

P(t+dt) = (m + dm)(v+dv) - dm(v - vex)."

As one might notice, as I did, they accounted for the momentum of the fuel at time t+dt, which is - dm(v - vex) (there's a negative because the momentum is in the opposite direction); but at time t, they did not, for the expression is P(t) = mv. Where is the momentum term for the fuel at time t?

I am reading section 3.2, concerning the analyzation of a moving rocket with a changing mass. (I couldn't find a preview of the book in google books, so hopefully someone out there has this textbook.) Here is an except from the book, but be warned that I am adding notes in brackets:

"At time t, the momentum [of the rocket] is P(t) = mv [m and v are the mass and velocity of the rocket at time t]. A short time later at t + dt, the rockets mass is (m + dm), where dm is negative, and its momentum is (m+dm)(v+dv). The fuel ejected in the time dt has mass (-dm) and velocity v - vex [v is the velocity of the rocket as viewed by some stationary person on earth, and vex is rate at which the fuel flows out, relative to the rocket]. Thus, the total momentum (rocket plus the fuel just ejected) at t + dt is

P(t+dt) = (m + dm)(v+dv) - dm(v - vex)."

As one might notice, as I did, they accounted for the momentum of the fuel at time t+dt, which is - dm(v - vex) (there's a negative because the momentum is in the opposite direction); but at time t, they did not, for the expression is P(t) = mv. Where is the momentum term for the fuel at time t?