Weird physics question for physics-minded people

[jinxmchue]

I have a weird physics question I'd like answered.

Say you have a car with a couple of small rockets strong enough to propel it attached to the back.  Here is my question: does it matter when each of the rockets are fired in regards to the distance the car will travel?  Three examples:

1. Both rockets fired at the same time
2. One rocket fired initially with the second fired immediately when the first one is depleted
3. One rocket fired initially with the second fired after the car coasts to a stop

My thinking is that the car will go the same distance no matter what.

[thundley4]

Theoretically, I think it would travel the same distance, but I don't remember the equations  involved to prove it.

[Happy Fun Ball]

I'm guessing 2 would probably go the farthest, beating 3 only slightly.

For 1, you have a big burst of force over a short time, and once it's over, air resistance and friction from the ground will take over. Also, I'm not entirely sure if two rockets will make it go twice as fast as one. Another thing is, two rockets (presumably side by side) have a much greater chance of malfunctioning than with just one. Both rockets have to fire at the exact same moment, and the rockets much have exactly the same amount of thrust, or that car is going to go off course rather quickly. Of course, the question is assuming that this is all true, so...

For 3, the second rocket fires when the car is stopped. Once that second rocket fires, it will have to overcome a bit of static friction. While negligible, it might still have an effect on distance.

[Lord Undies]

I think it depends on the traffic.

[Chump]

I'm gonna go with the first situation.

You have greater initial force and acceleration, greater maximum velocity, less time to reach to reach that maximum velocity, and thus a greater distance traveled.  I don't remember all the equations either, but a basic one is F = ma.  In this case, the reduction in mass as the rockets burn faster than in the other two scenarios is negligible compared to the massive increase in acceleration, and thus maximum velocity.

Good question.  I hope someone answers it with numbers and stuff.

[NHSparky]

Actually, as any physics student will tell you, it takes more energy to place something into motion as opposed to keeping it in motion.  This is why in a multi-stage rocket, the larger stages are used first to overcome friction from the atmosphere and gravity.  Similarly, on the ground, wind and rolling friction must be overcome in order to move the vehicle forward.

If either rocket is large enough to move the car on its own, the smartest thing to do would be to light off ONE rocket, then light off the second as the first expires to provide a longer period of acceleration, which results in a greater final acceleration (dv/dt) and therefore velocity.  And kinetic energy is a function of the SQUARE of velocity, meaning the greater velocity, the greater the travel distance.  

IOW, better to have a longer, more sustained thrust than one quick thrust.

[Mike220]

IOW, better to have a longer, more sustained thrust than one quick thrust.

Too easy...

[Chump]

IOW, better to have a longer, more sustained thrust than one quick thrust.

 

[Lord Undies]

I'm gonna go with the first situation.

You have greater initial force and acceleration, greater maximum velocity, less time to reach to reach that maximum velocity, and thus a greater distance traveled.  I don't remember all the equations either, but a basic one is F = ma.  In this case, the reduction in mass as the rockets burn faster than in the other two scenarios is negligible compared to the massive increase in acceleration, and thus maximum velocity.

Good question.  I hope someone answers it with numbers and stuff.

Try it with two fire extinguishers and a rolling desk chair in a hallway.

[Chump]

Try it with two fire extinguishers and a rolling desk chair in a hallway.

So I can find out that none of the scenarios matter at all when they each end up with smashing face first into a wall...

[youtube=425,350]http://www.youtube.com/watch?v=iktE77jGP3c&feature=related[/youtube]

[Doc]

Well....since physics is my field, I'll answer that there is too much information left out of your initial description to give you an accurate response.......the first question that I would ask is:  Are each of the rockets capable of producing enough thrust to move the vehicle to terminal velocity on their own?  

Assuming yes, then #2 would be the best answer (discounting asymmetric thrust losses).......assuming no, #1 would be the correct answer.......

Further assuming that this experiment is conducted here on earth (and not in the vacuum of space), you must understand that the amount of thrust needed to overcome the various forces acting on the vehicle will increase logarithmically with the increase in velocity, until terminal velocity is reached (which is determined by the thrust applied, and the relative mass of the vehicle, opposed by the rolling resistance, and the airflow resistance, after overcoming the initial inertia of the start).

All that said, answer #2 is the reason that vehicles that are designed for orbital and beyond type of missions are multistage instead of being single staged........as the vehicle is launched, its mass is gigantic, and therefore requires tremendous thrust to overcome the inertia of the launch.....as velocity increases, and the heavy launch stages are jettisoned, lessening the overall mass, the  next series of boosters are smaller, and produce less thrust to continue the same rate of change (Delta) of the velocity.......and the process continues to whatever point the mission requires.

Option #3 is a non-starter, as it would require overcoming the startup inertia twice, consuming fuel that could be used to expand the distance travelled otherwise

I am grotesquely oversimplifying......however I think that you should get the idea......the equations required to "prove" this type of experiment here on the ground would fill several pages........and require much more detailed data.

doc

[Lord Undies]

So I can find out that none of the scenarios matter at all when they each end up with smashing face first into a wall...

It's all good.  It's for science!

[jinxmchue]

I think it depends on the traffic.

 

[jinxmchue]

Actually, as any physics student will tell you, it takes more energy to place something into motion as opposed to keeping it in motion.

Ah.  I think I knew that at one time.

IOW, better to have a longer, more sustained thrust than one quick thrust.

You know, there's a sex joke in there...

[jinxmchue]

Well....since physics is my field, I'll answer that there is too much information left out of your initial description to give you an accurate response.......the first question that I would ask is:  Are each of the rockets capable of producing enough thrust to move the vehicle to terminal velocity on their own?  

Assuming yes, then #2 would be the best answer (discounting asymmetric thrust losses).......assuming no, #1 would be the correct answer.......

Further assuming that this experiment is conducted here on earth (and not in the vacuum of space), you must understand that the amount of thrust needed to overcome the various forces acting on the vehicle will increase logarithmically with the increase in velocity, until terminal velocity is reached (which is determined by the thrust applied, and the relative mass of the vehicle, opposed by the rolling resistance, and the airflow resistance, after overcoming the initial inertia of the start).

All that said, answer #2 is the reason that vehicles that are designed for orbital and beyond type of missions are multistage instead of being single staged........as the vehicle is launched, its mass is gigantic, and therefore requires tremendous thrust to overcome the inertia of the launch.....as velocity increases, and the heavy launch stages are jettisoned, lessening the overall mass, the  next series of boosters are smaller, and produce less thrust to continue the same rate of change (Delta) of the velocity.......and the process continues to whatever point the mission requires.

Option #3 is a non-starter, as it would require overcoming the startup inertia twice, consuming fuel that could be used to expand the distance travelled otherwise

I am grotesquely oversimplifying......however I think that you should get the idea......the equations required to "prove" this type of experiment here on the ground would fill several pages........and require much more detailed data.

doc

Cool.  Yeah, man.  Thanks!     Of course, as easy as your answer was to understand, it still reminds me why I failed physics in high school.  I dropped out of the class (an elective) to save my GPA.

[Chris_]

Cool.  Yeah, man.  Thanks!     Of course, as easy as your answer was to understand, it still reminds me why I failed physics in high school.  I dropped out of the class (an elective) to save my GPA.

Well....if you really wanted to make the answer challenging you could have added......."assuming two of the scenarios result in the same distance travelled, which one would have arrived first......"

doc

[DumbAss Tanker]

Theoretically no, in a frictionless environment.  Practially yes, it very much would.  Firing both at the same time would not double the speed because the air resistance increases in a nonlinear way, and is really the dominant factor here.  I'm not sure how the rolling resistance would play out, especially between the second and third case, but I'm pretty sure it would be a different distance.

[NHSparky]

I am grotesquely oversimplifying......however I think that you should get the idea......the equations required to "prove" this type of experiment here on the ground would fill several pages........and require much more detailed data.

doc

Thanks, I really didn't consider the increase in resistance as the car sped up.  D'OH!  But nice to see I still got it more or less right, for a dumbass nuke.

[Chris_]

Thanks, I really didn't consider the increase in resistance as the car sped up.  D'OH!  But nice to see I still got it more or less right, for a dumbass nuke.

Well....there is nothing dumbass about being a "nuke".......friend of mine is shift supervisor for the MU research reactor, and he came out of the "boomer" service (enlisted)......extremely bright guy.  He and I recently had a heated debate about the benefits (or lack thereof) of the quaint concept of liquid sodium-cooled reactors.......he won.....

doc

[NHSparky]

Well....there is nothing dumbass about being a "nuke".......friend of mine is shift supervisor for the MU research reactor, and he came out of the "boomer" service (enlisted)......extremely bright guy.  He and I recently had a heated debate about the benefits (or lack thereof) of the quaint concept of liquid sodium-cooled reactors.......he won.....

doc

I would hope he won.  We heard a few things from the old Soviet Union--they didn't call the Alfa the "Golden Fish" for nothing.

[Chris_]

I would hope he won.  We heard a few things from the old Soviet Union--they didn't call the Alfa the "Golden Fish" for nothing.

Yeah.......I based my argument on the far-superior heat transfer charastics of LS, and the overall reduced size of the reactor package (efficiency in kW/ton of powerplant weight), compared to high-pressure water, I kinda forgot about what you had to do about all of that radioactive "plumbing".......not to mention what happens if the coolant comes into contact with.......water.....

doc

[JohnnyReb]

It's the little things that kill you.

In my business...no...In my line of work, rolling resistance was and is a factor in moving dirt or ore. For those HUGE earthmoving jobs (and open pit mines) where the bidding is very competitive there are a lot of factors to be considered in the type of equipment to use, soil conditions, moisture content of soil, compaction of haul roads, tire size and even wheather the tires are inflated with dry Nitrogen or compressed air......99% of my work was short haul and small yardage so all that wasn't much of a factor.....thank goodness.

When you have large, heavy loads involved, the ground flexes .... you can envision it as a "wave" of dirt (or pavement) in front of the tire and the height of that wave determines the % of grade or steepness of an imaginary hill that the machine is trying to climb and thus the amount rolling resistance and the amount of horse power required to overcome it and maintain speed "X" with load "Y".  

So when you see those giant trucks and shovels working in an open pit mine somewhere, remember there is a nerd in the back office somewhere crunching the numbers and pulling his hair out trying to find a cheaper, faster, better, more profitable way of doing it.... because if he don't we could all wind up with a socialistic way of life and we'd all have a job at the mine.....carrying ore out by the 5 gallon buckets full.

[NHSparky]

Yeah.......I based my argument on the far-superior heat transfer charastics of LS, and the overall reduced size of the reactor package (efficiency in kW/ton of powerplant weight), compared to high-pressure water, I kinda forgot about what you had to do about all of that radioactive "plumbing".......not to mention what happens if the coolant comes into contact with.......water.....

doc

Rumor had it that to refuel an Alfa wasn't an easy process because the sodium was radioactive as hell, but obviously you couldn't let it solidify.  Even inport the Alfas had to run because shore steam simply wasn't enough to keep the sodium from solidifying and destroying the reactor.

Also, while not an Alfa, there was a report that there was a prompt criticality at a Soviet shipyard that really crapped up the place.  I wish I could find it on Google, but I know there was an obscure reference to it somewhere in the dark recesses of NavSea lore.

[Wineslob]

I like thrusting.

[Rebel]

I agree.