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The question is as follow:

"a spacecraft of X mass moving at Z velocity in striaght line, the rocket fuel explodes, causing the spacecraft to split in two parts one part speeds up and one part slows down

apparently, it shows that momentum has been reserved as a piece speeded up and another slowed down, but, as I thought the explosion could have caused a gain in KE and thus momentum should increse, so is it what I am thinking true or not?

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  • $\begingroup$ Questions for the student: Is momentum a vector or a scalar? Is energy a vector or a scalar? Why do the answers to those questions matter? Supplemental question: Can kinetic energy be negative? Why or why not? $\endgroup$ – dmckee --- ex-moderator kitten Jul 9 '17 at 21:05
  • $\begingroup$ Is this a test? I know which is scalar and vector, but why does it matter? $\endgroup$ – phenolicdeath Jul 9 '17 at 21:06
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    $\begingroup$ This is a very bad example of momentum conservation. A rocket simply breaking apart would be illustrative - for example by hitting a space fragment - but having fuel exploding will drastically add energy as well as momentum to the situation. You can have a stationary rocket with fuel tanks on the left side that suddenly explode, and the whole rocket flies in pieces rightwards at high speed. When an extra energy source such as a fuel tank is included and released, the situation is not good to show conservation laws. $\endgroup$ – Steeven Jul 9 '17 at 21:09
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    $\begingroup$ @Steeven a fuel explosion might add momentum to the the superstructure but it doesn't add any to the system. In that respect there is no difference between an explosion and a controlled burn. $\endgroup$ – dmckee --- ex-moderator kitten Jul 9 '17 at 22:24
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    $\begingroup$ It might help to look at the explosion as the reverse of a purely inelastic collision. An inelastic collision conserves momentum but decreases kinetic energy. Reversing this, an explosion sill conserves momentum but it increases kinetic energy. $\endgroup$ – David Hammen Jul 9 '17 at 23:29
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It depends on the conditions of the question and what assumptions you are expected to make.

For a system as a whole, momentum is always conserved if there are no external forces, even though kinetic energy has increased. (Chemical energy has been converted into kinetic energy.) However, if the mass of "the system" changes then total momentum might change also.

If the spacecraft breaks up into only two parts, the total momentum of those two parts will be conserved in the explosion. The total mass of the system is the same. This assumes either that the mass of the fuel can be neglected compared with that of the two parts of the spacecraft, or that the fuel somehow remains stuck to one or both of the two parts.

However, if the fuel is expelled as in a rocket and it has significant mass, then effectively the spacecraft has broken into 3 or more parts. The total momentum of the 3 or more parts is conserved. But if you ignore the ejected fuel and consider only the momenta of the 2 main parts then momentum is not necessarily conserved. In this case the mass of the system has changed.

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  • $\begingroup$ However, if the mass of "the system" changes then total momentum might change also. Isn't it otherwise? Ie: Total momentum conserves, and if mass changes, the velocity of the center of mass of the system will also change, as to conserve the total momentum. $\endgroup$ – Physicist137 Jul 16 '17 at 14:41
  • $\begingroup$ @Physicist137 see my final paragraph. For a rocket, mass changes and momentum changes. $\endgroup$ – sammy gerbil Jul 16 '17 at 18:09

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