# Changing Mass and Impulse

1. Aug 29, 2015

### Alameen Damer

1. The problem statement, all variables and given/known data
A 1990 kg rocket is loaded with 102 kg of propellant. It exhausts the propellant in a burn of 25s. The rocket starts at rest, and moves with a speed of 240 m/s after the burn. Determine the impulse.

2. Relevant equations
Impulse (p) = m1vf-m1vi

3. The attempt at a solution
How would one calculate the impulse given that the mass changes because of the loaded propellant which is used up by the time the mass hits the final velocity.

2. Aug 29, 2015

### haruspex

The question seems ambiguous. Is it the total impulse generated by the fuel that's wanted, or the effective impulse on the rocket? The second is quite easy.

3. Aug 29, 2015

### Alameen Damer

I would assume the effective impulse on the rocket, given that they talk about it speeding up, etc. If this is the case, using (p) = m1vf-m1vi, do I include the 102 kg propellant as part of the mass?

4. Aug 29, 2015

### haruspex

The description speaks of rocket and fuel as distinct, so no, it would not include the 102kg. That's what makes the question easy. If yiu had to include the 102kg you would not know what to put for final velocity. Relative to the ground, fuel expelled early would have a different velocity from that expelled later.

5. Aug 29, 2015

### HallsofIvy

Staff Emeritus
The basic rule is that force equals the derivative of momentum. If the mass is constant, that is "mass times the acceleration" but if mass is not constant, it is (mv)'= m'v+ mv'.

Last edited by a moderator: Aug 29, 2015
6. Aug 29, 2015

### haruspex

Halls, I'm not alone in regarding that formulation as misleading. It treats mass as an arbitrary variable, as though a moving object can acquire mass out of nowhere. In reality, the mass must come from or go to somewhere else. For the equation to work, that mass must not bring in or take out any momentum, i.e. when not part of the object it must be at rest in the reference frame. I wrote a homily on this in section 6 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-momentum-impacts/.

Anyway, if I'm reading the question correctly, there is no need to get tangled up with that. The information regarding the mass of fuel is redundant. (But maybe there are more parts to the question.)

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