Rockets and Energy Conservation
Most recent answer: 12/26/2013
- Mike (age 57)
Kirkland WA USA
The chemical energy from the fuel is converted into two main mechanical forms, in addition to some heat. These are the kinetic energy of the average backward motion of the exhaust and the kinetic energy of the forward motion of the vessel. As the vessel speeds up, the proportion of that mechanical energy that goes to the vessel goes up.
At first the backward speed of the exhaust is whatever the exhaust velocity is relative to the vessel. By the time the second rocket is done firing it's whatever the exhaust velocity is relative to the vessel - 60 mph. So initially the rocket is putting more kinetic energy into the exhaust. By the end it's putting less into the exhaust and more into the vessel.
p.s. If you look at the particular situation you describe, the second rocket adds 3x as much energy to the vessel as the first, not four times.
Mike W.
(published on 12/26/2013)
Follow-Up #1: Rockets and energy conservation
- Mike (age 57)
Kirkland WA USA
"So is it correct to say that half or the energy of each rocket (disregarding heat production) goes into pushing the vessel forward and its corresponding gain in kinetic energy, and the other half of the energy goes into the the kinetic energy of the exhaust going in the opposite direction? "
No, not even close. The proportion varies as the vessel's velocity changes, or depending on what reference frame you choose. If you pick a reference frame in which the vessel's initial velocity was backwards, the initial firing imparts a negative change in the vessel's kinetic energy.
Mike W.
(published on 12/28/2013)