# Thread: Help me explain this...

1. Me and a friend had an argument this morning about speed and resistance. Scenario is 2 identicle cars are driving single file, 5 feet apart, at a constant rate of 60 mph with a head wind of 45 mph. My friend says that the car in the back will run into the car ahead of it. I explain that the cars are moving the same speed so they will never hit unless the front car runs out of fuel because that is the only difference that the wind resistance would make.

First, someone please tell me if I'm wrong because I don't think I am. Second, I need a better way to explain this to him and a way to prove that if 2 objects are moving at a constant rate of speed, one with resistance and one without, they are going to cover the same distance in the same time.

2.

3. His confusion results from the fact that the second car is getting better mileage because the air resistance is lower.

4. I tried for almost an hour to make him understand but he is stuck in the belief that the resistance would somehow slow the front vehicle without changing its speed. Maybe I'm just not smart enough to explain it to him.

5. Originally Posted by svenrawr
I tried for almost an hour to make him understand but he is stuck in the belief that the resistance would somehow slow the front vehicle without changing its speed. Maybe I'm just not smart enough to explain it to him.
Speed has nothing to do with resistance. If both of them are moving uniformely at constant speed, then the distance between them will never change. The only thing that happens is that the front car will likely run out of fuel before the car at the back does, because it needs more fuel to maintain its 60mph.
The confusion stems from SPEED vs FUEL CONSUMPTION. They are not the same things.

6. The forces acting on each car are not the same.

The cars will hit each other.

7. Originally Posted by Geo
The forces acting on each car are not the same.

The cars will hit each other.
The OP did not say anything about forces; it was made clear that their speeds are the same. Therefore their relative positions will not change.

8. To put it another way, if the fuel consumption of the two cars was fixed to be the same then the front car would go slower.

9. Exactly. If both cars were tested individually to run at 60mph in the same gear with the acceleration pedal depressed the same amount, then if you run one behind the other in the same way, the second one will exceed 60mph and crash into the first one. But as long as their speeds stay the same they won't.

This is similar to how someone maintained that if you have two identical cars, except that one has a more powerfull engine and both have the same max rpm, that the car with the bigger engine would have a higher top speed, even when running at the same rpm. It doesn't make sense and betrays a deficient understanding of basic physics and mechanics.

10. It is simple really. If both cars are travelling at the same speed, they will remain the same distance apart. If the car in front punches a hole in the air it is passing through, causing less pressure behind it, the rear car will speed up to more than 60 mph due to something known in motorsports as drafting, or "getting a tow". The rear car will now be moving faster than the front car, so they will not both be travelling at the same speed any more. If the rear car lifts a little on the throttle however, they can remain at 60mph and keep the distance between the two cars constant, and use less energy to travel at the same speed as the car in front.

11. As you write it, the cars will actually impact at some point. True, both cars are driving at the same speed, 60 mph. The car in the back is driving behind the front car which causes the car in the back to have less air to "press through". The front car will run out of fuel first because it needs more fuel to maintain the speed.
If a brick were placed on each acceleration pedal then they would also impact due to drafting which have been explained above

- Niclas

As you write it, the cars will actually impact at some point.
Yup, and this is known as "bump drafting", which also temporarily increases the speed of the car in front to faster than 60mph. This then temporarily increases the "tow" on the car behind, so this technique gives both cars a temporary speed boost.

The question in the OP is too vaguely defined. For both cars to remain at 60mph and thus remain a constant distance apart, both cars will have to modulate their throttle inputs in order to maintain a constant speed. If both cars maintain a constant throttle input, they will hit each other, because both cars will not be travelling at 60 mph any more.

They cannot both travel at 60mph and hit each other. Perhaps the friend in the OP meant to say they maintain the same throttle input, rather than the same speed.

13. Two cars driving at same speed describes a situation of constant distance between the cars. This is given as the premisse situation.
When this premisse changes into ; "two cars drive behind each other and distance decreases". Then it has other situation, other premisse.
It can,t be both of these situations or some combination with two cars.

In case of same speed (Op,s premisse situation) say 100 miles an hour, they don,t just use different amount of gasoline each mile and for the hundred miles. Also for each second and for the hour.

This could be the problem for the discusion :
If the milage use is different but Op's friend assumes the use of gasoline to time stays the same the premisse becomes impossible so he sees the distance shrink in his mind. The discussion then follows of the term mileage-use. In the thinking process he forgets the time and leaves the premisse.

Or in the discussion one thinks from gasoline/hour and other gasoline/time both without keeping reckon that both ratio,s change.

When they had the same distance from starting to drive and also when they stop (constantly same) the two events run simulaneous in time.
Gasoline to time is the same then.

If they use the road as a one dimensional space (with same origin x=0) they start and end at different position.
If the origin is at where the front car starts (or elsewhere, euclidean space has one defined origin) the car in the back has to drive from a negative position to the origin first. Same as marathon of New-York where it can take a while before even the starting line is reached.

This can occur (Example):

Mutual distance 100 meter time simultaneous. First hundred meter is travelled in one second.
Passing the origin of the one dimensional space delta,s are 0 - - 100 (backcar) and 100 - 0 (frontcar). No problem, both travel(led) positively (- - = + ) hundred meter.

But the difference between the delta,s for both cars : (100 - 0) - (0--100)= 0. Bump....that,s a problem if this difference between delta,s is confused with delta S to the road.

This confusion can happen if the origin of the space is not kept at the road somewhere but regarded as travelling with the front car (or other).
Both cars are no longer inertial frames to the road as defining the space then. The front car would carry the origin and define the space. Onle the the backcar a classic inertial frame.

In that case dS for both cars would be zero ; they don,t drive then. Front car stays at the origin and back car at fixed position to that.

14. I think the car in front has greater airspeed and will gradually pull further ahead.

15. I think a very simple scenario is made unnecessarily complicated. The OP clearly states

Scenario is 2 identicle cars are driving single file, 5 feet apart, at a constant rate of 60mph
therefore the two cars will not hit each other, and neither does the wind speed have any effect on this outcome. The conclusion reached was

they are going to cover the same distance in the same time.
which is of course correct.
And that is all there is to it.

16. Do you propose to take the air as space instead of the road ? That,s a flexible and complex space then, molecule distances are not set, all move different so it needs a particular molecule to be able to use air for space.

Assumed a paper blows with the wind I suggest you use a paper blowing in the wind somewhere to be able to do that and define x=0 for air as space.
Then we can see the different airspeeds clearly.

As a third objekt to a space defined by the road air is useless (all molecules move different).

There is another reason why it is misleading then just turmoil. Air density is higher in front of the front car but also in it,s back (it profits also from a car driving in it,s back). The density difference between front and back is therefor not that much higher.
The higher air resistance is also from the overall higher density for the front car then just from density difference (between back and front and then between the two cars). The car in the back drives more or less in a vacuum.

The higher density means same speed for the cars has the frontcar has a stronger drag also (from car to air).

The drageffect slows the windspeed (to the road) at the flanks coming from the pressure difference. Compensating the higher density difference...in effect it,s zero or near zero.
Maybe when they stick their head out a window it feels as more wind (make it all seem obvious) but denser air can have similar effect as more wind.

17. Originally Posted by Ghrasp
Do you propose to take the air as space instead of the road ? That,s a flexible and complex space then, molecule distances are not set, all move different so it needs a particular molecule to be able to use air for space.

Assumed a paper blows with the wind I suggest you use a paper blowing in the wind somewhere to be able to do that and define x=0 for air as space.
Then we can see the different airspeeds clearly.

As a third objekt to a space defined by the road air is useless (all molecules move different).

There is another reason why it is misleading then just turmoil. Air density is higher in front of the front car but also in it,s back (it profits also from a car driving in it,s back). The density difference between front and back is therefor not that much higher.
The higher air resistance is also from the overall higher density for the front car then just from density difference (between back and front and then between the two cars). The car in the back drives more or less in a vacuum.

The higher density means same speed for the cars has the frontcar has a stronger drag also (from car to air).

The drageffect slows the windspeed (to the road) at the flanks coming from the pressure difference. Compensating the higher density difference...in effect it,s zero or near zero.
Maybe when they stick their head out a window it feels as more wind (make it all seem obvious) but denser air can have similar effect as more wind.
So what ? All this is completely meaningless, because the OP stated that both cars travel at a constant 60mph. That's all that counts.

18. Right. And sixty miles an hour to what ? Not to the road or it must be airplanes. Their tires keep touching the floor is what I presume. Is that strange presumption ?

So where from is this speed ? Did they depart simultaneous in time or does it start from one moment (while they drive) ? That,s different position then. Or does the op mean from same position at different times. The cars can,t be at same place same time (Op and his friend understand this both). It,s different time same place or vice versa.

If Op and his friend argue from these two it can give exactly this type of discussion. If that,s meaningless for you it,s not my problem. It,s you,re problem not seeing the problem then.

I,m not mistaken velocity and speed here. Speed in Newtonian sense also uses a defined origin for the space. In the sense of clasic fysics A speedmeter in a cars uses the car as space and meassures the speed of the road not vice versa.

Two cars means not just two speedmeters also two euclidean spaces then. Something to keep reckon with I think.

19. I think what the OP means is that the identical cars start at rest, 5 feet apart. They then accelarate uniformly at the same rate, until they both reach 60mph as measured by their speedometers; they then maintain that speed. The point is that the relative speed between the two is exactly zero. Therefore they will not collide.

20. It's really pretty simple as Markus states. The OP presumtion is that the two cars are traveling at the same speed, therefore, the distance between them will never change. This ain't rocket science

21. Ah, that would make a clever trick question for a high school physics class.

But yeah, since the situation implies that both speeds are equal and absolutely fixed, they can't collide, no matter what... even if fuel consumption was the same and air resistance inequal. But practically, yes, the first car would need more energy by using more fuel to make up for the speed lost to air resistance.

22. Offcourse this is the premisse and within the premisse it seems simple.
But it,s not part of it that the measurements correspond with real scenario.

Same speed for measuring but will it be for real ? That,s more how I read the question.

23. Lol...
d= v*t
If time is 10 second & speed is (CONSTANT) 10 meter per second, then distance will be 100 meter. If speed is constant then the distance travelled will be same! Why soo much confusion LOL.

If the car has acceleration then use this formula:
d= v*t + (a*t*t)/2 ...where "a" is acceleration.

This describe 100% of all type of linear motion... no exception. Just use this and world will be saved.

24. How do you know it,s constant ? I can,t see two cars from here. The two don,t see two cars - while they discuss - have constant distance either. The meassurements are assumed constant distance. It,s a theoretic experiment more that needs to be verified.
Testing could show when meassurements are identic that distance doesn,t stay constant.

Op just doesn,t mention it explicitly that it,s about same measurements. Maybe he forgot to mention it here but from the friends point of view I assume this as the case.

I have more hope for op,s friend not to be a complete moron or fool then others here it seems.

It,s too foolish to discuss otherwise. As if discussing in a bus between two people in the back and front ; one argues the back is catching up on the front.

Also it has the frontal wind. The friend could argue that this means both cars can,t drive with same accelleration.
One car,s engine has to make more turns or use more fuell each turn. That keeps the speed constant both speed and accelleration are relative. Relative wind affects accelleration. So front car has to accellerate more then.

Different accelleration same speed but far from linear. Linear speed has no accelleration not relative, none. It,s a theoretic idea ; no accelleration means no change of speed. This logic is not reversible to : constant speed means no accelleration. They could turn of the engine and then bump.
Friend can reason ok so linear speed it has no force or engine working then relative the back car must accellerate to approach the front car.

Wind is relativistic somewhat comparable with gravity in an elevator for this. Except in horizontal plane and different for both cars.

To keep the analogy thinking further on it ; It would mean that the back car is at much higher altitude then the front car for the analogy.

25. Originally Posted by Ghrasp
How do you know it,s constant ?
Because the OP says so...?

26. True, if svenrawr's said the speed is constant then "the speed is constant". There's no need to make any new assumption.

27. I have a feeling Ghrasp would be easier to understand if he mimed what he wanted to say, instead of talking.

28. Originally Posted by Markus Hanke
Originally Posted by Ghrasp
How do you know it,s constant ?
Because the OP says so...?

In this case it could very well be meant as "reading speedmeters is the same, can the distance change then under this circumstances".

And I still think from classic speedmeters in cars. Don,t know what Op and his friend had in mind for this.

With such meters I allready mentioned different airdensity as possible complication. Back car drives in relative vacuum compared to front car.
Could this affect tirediameter ? Minimal I guess but maybe a little.

Other complication : more driving force to the road could make the asfalt stretch in front of the driving wheel.
Does this stretch mean the front car meassures higher speed then it has ? I think so, also a little maybe but still.

Does the higher driving force make the tire smaller diameter for the front car ? Front car would also meassure more distance to time from this then it really makes.

All these things together count up for the same effect : the distance decreases with meters showing same speed.

Then read the starting topic again it,s maybe not that simple.

Interesting aspect : all cars in this universe seem to have same speed for all observers.

Speed to what ? Vacuum ? The road ? The road could be endless who knows. As long as the road has no coordinates they do drive in vacuum.

29. The stipulation is the speed of the cars, not the measured speed of the cars. Stop making it complex where it isn't.

Much of the rest of what you are writing displays a strong inability to be practical. Do you often venture out on to actual roads without an attendant?

30. Originally Posted by Ghrasp
Don,t know what Op and his friend had in mind for this.
What they had in mind were two cars with the exact same speed, i.e. zero relative speed. The OP was quite clear to anyone who can read English.
You are trying very hard to proof a point that just isn't there.
Complete waste of time.

31. It is patently obvious that the question is about how air resistance has an effect on speed, and how the car behind is subject to less air resistance than the car in front. That is why the OP's friend says the car behind will hit the car in front. I described the scenario completely, in posts #9 and #11.

The problem here is that the question is ill posed.

32. How many times can we repeat this. IF THE SPEEDS OF THE CARS ARE THE SAME, THE DISTANCE BETWEEN THEM WILL NOT CHANGE!

33. Yup, as I said in both posts #9 and #11.

34. And as many of us have repeatedly stated. This is like arguing with a piece of granite.

It seems to be that it's the "chimers in" that can't read and understand the original post.

35. The speeds of the cars are not the same.

If they both start out at 60Mph, car B will be going faster. Final minus initial.

Car B speeds up due to a lack of drag. It hits car A.

36. Geo the conditions are stipulated that the cars are travelling at the same speed. As several other posters have pointed out this can be achieved with a lower fuel consumption on the part of the trailing car. But if they are travelling at the same speed then they are travelling at the same speed.

This is not frigging rocket science. It's basic English comprehension and some of you are failing abyssmally.

37. How can they be travelling at the same speed?

Picture a force vector diagram of each car?

The original question implies a force imbalance.

If the net force on a body equals zero it has a constant velocity, which could be zero.

38. Originally Posted by Geo
How can they be travelling at the same speed?
Because that is what the OP says. Yes, if both travel at 60mph and the back one moves in behind the other one without adjusting throttle, he will hit it. BUT, that is not what the OP said. He said they are moving at 60mph, one behind the other.

39. Originally Posted by Geo
How can they be travelling at the same speed?

Picture a force vector diagram of each car?
Speed is not force.

The original question implies a force imbalance.
It also said they are travelling at the same speed. So, presumably one must be consuming more fuel to account for the force imbalance.

Scenario is 2 identicle cars are driving single file, 5 feet apart, at a constant rate of 60 mph with a head wind of 45 mph.
Really, how hard is it.

40.

41. It sounds like a confusion over the energy required to move both vehicals with their respective velocities. 60 miles per hour, both vehecles having the same mass. The front car requires more energy than the car behind it. Both traviling the same speed staying equal distance apart. The front care requires more energy than the car behind it.

We understand this. How to get your friend to get him to understand this, may require some questions. Like why do you thinkg the front car will be hit by the rear car? Listen to his answer, it might give you a clue as to why he thinks this. And then maybe you can come up with another question to get him to clarify his undersanding. And just maybe give you a clue as to what you need to ask him, to help him understand what you were saying.

42. All nice but when I read "two cars have same speed" I suspect this is a meassured value on two different speedmeters that can deflect between each other for distance to the same time for several reasons as I mentioned a few. Otherwise the op would have formulated as "two cars keep same distance to each other".

43. Why do you have a problem ghrasping this concept. If their actual speed is the same, the distance between them will NEVER change.

44. If it is but how do they know or does anyone know ? This is a scienceforum it needs provabillity not say so from two people reading two different meters in two different cars giving them the same number. Nowhere in the initial post it says the word actual. I don't know where they got the idea from that the two cars drive same speed.

45. Cars usually use a speedometer, which measures their speed relative to the road through the rotation of their wheels. That is the speed that both the speed limits and speed records for cars relate to, so it is the obvious choice here.

There is a 45 mph headwind, so the car in front will need to press hard on the gas to reach 60mph and then release the gas some, in order to maintain that constant speed. The car behind, if he starts out 5 feet behind the front car and sets off at the same time, will need to press slightly less hard on the gas, in order to accelerate to 60mph in the same time, and thus remain a constant 5 feet from the other car, due to the car in front cutting a "hole" in the headwind, and will have to use slightly less gas than the front car in order to maintain a constant speed of 60mph.

2 identicle cars are driving single file, 5 feet apart, at a constant rate of 60 mph with a head wind of 45 mph.
They will not hit each other.

46. If they are both going 60 mph, THEY WILL REMAIN EXACTLY THE SAME DISTANCE APART!!!!!

47. Maybe air speed is being confused with ground speed.

48. Air speed is irrelevant in the orginal post. It clearly states: "at a constant rate of 60 mph". That's miles per hour relative to the ground. The headwind is mentioned, but it does not change the groundspeed. The airspeed is different, and with a headwind of 45 mph is close to 105 mph, but varies with the exact position relative to the two cars. That depends on aerodynamic airflow, and turbulence and can change greatly within a distance of a quarter of an inch, and from instant to instant. The only constant is the specified 60 mph. Since the airspeed is close to 105 mph, this is obviously not what is being asked.

49. These are not cars pulled by horses. Internal driven motorvehicles.

A fuell engine constantly accellerates a car and decellerates it (compressionstroke) from within itself. Newtons laws have a perspective from a driving force from outside more. A horse or human or wind pulling or pushing something. A stone thrown aso.

The driving energy coming from inside makes the horse part of the car, the stone become a plane aso. Newton was unfamiliar with that. The engine can,t be regarded seperated from the car staying behind or be at rest.

Therefor I,m tending to see the engine more as the better origin for setting the - specific - space (x=0 moving with the car) and all other things as reference spaces or objekts moving to it. At least for newton mechanics more close (for how cardriving can feel also) then having a point on the road and constantly switch to a next point (making unitsteps of speed). Or maybe combine the two ?

The cars are for instance not the same for this ; they can be the same before they start but front car would use more fuell. That on itself makes them different cars ; using fuell is part of a driving car and these cars are supposed to be driving (or have or will). The frontcar will be lighter also after a while ; more exhaust looses gasoline.

These cars wheels are both different from transmitting a drivingforce and opposite force for compression stroke (through a fly wheel but still) at certain frequency. When the frequency is the same for the engines both the compressionstroke and workingstroke are more powerfull for the front car. They affect the road different, their driving wheels different.
All things together can make ten meter to start with become nine meter after half an hour or less.

For difference in speed that may seem nothing (speedmeters won,t meassure it) but for distance I find that significant. Take a tire from a car affects the diameter also ; speed is very high then on the meter but the car drives slow. Rubber deforms with different driving force more or less...that affects diameter also.

If these differences are not significant I want to know how much or little.

And maybe that,s also why Op's friend persists from intuition. So I enjoy taking the role of the friend here for the further discussion...I,m not convinced yet and this was the question : how can Op convince his friend ?

50. I imagine the OP has backed away slowly, relieved that his friend isn't as mad as some of the people here.

And the friend has probably said, "I was just kidding, have a beer, of course they stay the same distance apart. But those science forum guys, jeezus..."

51. Ghrasp,

52. Originally Posted by Ghrasp
If these differences are not significant I want to know how much or little.
These differences are not relevant because:
a) You you have invented them, they are not part of the original question.
b) The original post stated the cars were "identical"
c) The original post stated the cars were travelling at the same speed.

You make up as many irrelevant extra facts as you want but they are not part of the original question. Which has a very, very, very simple answer.

53. For those of you who are still in school, this why you instructors toss in irrelavant details like "head wind'. It looks like something significant but is just a distraction to tempt you into overthinking the problem.

54. svenrawr,

.....2 identical cars are driving single file, 5 feet apart, at a constant rate of 60 mph with a head wind of 45 mph.......
This is the scenario that you proposed. First, the head-wind does not matter conserning this question. The gas pedals of the drivers would compensate for the headwind. The second car, would have less head wind and wind resistance because the first car would clear much of it away. Secondly, even a constant or changing speed relative to the ground would not even be relevant if they must always remain 5 feet apart. Your friend or anyone else should realize that it would be impossible for the second car to ever hit the first car if they must always remain 5 feet apart, as in your proposal I don't think it takes a great deal of smarts to realize this -- and I think this point (5 feet apart) is the point that you should emphasize if you really need to explain it to your friend again. If he still wishes to argue the point after this explanation then I think you should change the subject, since intellect is obviously not his strong suit

55. A wheel doensn,t move to a road to me as having a speed. It stays at same distance. Mowing a lawn when the lawn mower has a change of distance to the lawn the lawn becomes uneven. If a barber,s scissor has a speed to my head I,m probably severely hurt or the scissor is cutting air.

Is that strange or weird ? Maybe that,s why I don,t have that much friends ?

56. Sorry this post just makes no sense. Slow down and try again. The wheel moves " down the road" or "over the lawn" That is what the speed of the vehicle (car or lawn mower) is, not the distance to the surface (road or lawn).

57. I wonder where these cars are by now.

58. If they were driving straight, in the ocean by now

59. It was a joke but I assumed the road would be horizontal not straight.

If they drove a straight road starting from ninety degree angle to gravitational direktion (vertical) that angle has deflected significantly by now. They could angle the cars for that but then the cars would drive in an impossible direction for cars.

When they landed in the ocean it must have been a high fall back after running out of gas.

Or maybe they started at a different angle then zero following a road digged straight through a horizontal landscape directing to the ocean.

But "just straigth" one dimensional has no angle whatsover to anything so they can be anywhere by now.

60. As the OP has not made a reappearance, and the initial question more than answered, there is no reason to keep this thread open any further.

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