Out of petrol on a level road.

I think the last sentence says it all,

The car is frictionless and is not affected by wind resistance etc.

if this is truly the case, then he should give the car a small shove and jump in for the ride because:

any body in motion will stay in motion until an outside force effects or changes the motion. So, if the car is truly frictionless and not effected by wind or other outside effects, then it will stay in motion until it reaches the petro station.

Put up a sail (or the hood/bonnet) prevailing winds will be in the right direction at those latitudes (I theeenk but you can check with a wet finger etc).

Harness the lion and let him pull you!

What happened to carrying a full petrol can in the boot when travelling in remote places. I suppose this thing is also weightless or does gravity not affect it or do we have to take the momentum of the rotation of the earth into account. If so what is the latitude?

If the road is completely level with the mid point 1Km past centre towards the east then because of the curvature of the earth the road will actually rise at both ends. If he is in the east and he has 51km of going downhill then he will be able to coast up the other 49km so all he has to do is let the handbrake off and keep the car in a straight line.

Agree!

Theoretical engineering again.

I left out some rules. #1,2 & 3 are all correct.

Del get 3rd prize - 3 weeks in Zimbabwe - A tissue and 2 tooth pics would have done for a sail.

LaybyGuy - get 2nd prize - 2 weeks in Zimbabwe - why all the trouble?

Maca - earned first prize - 1 week in Zimbabwe

Now for the final question for the grand prize - for any correct answer - you don't have to go to Zimbabwe.

1 if the one endpoint is placed on 26n ,14deg 30e and the other on 26n , 15deg 30e Where would the centre point be? (note it is slightly longer than 100km)

2 what would the height of the embankment at the ends be?

Alternative Questions

1 how many presidents did Zimbabwe had in the recent past?

2 Name them!

The centre point will be in the middle....

That's what me 'n the Lion reckon...

Can I donate my 3rd prize to my Mother in Law?

Not as easy as I thought This is the location if the road is built along the line of latitude (26° N)

If the road is built on a great circle the centre will be slightly north of this point.

Q2 Again the answer is (quite a lot) different for great circle:about 98 metres and strictly East/West: about 109 metres.

Incidentally did you know that i.) Robert came from Yorkshire: his name backwards is E Ba Gum.

ii.) A frictionless journey along any great circle chord (no forces other than gravity) takes the same amount of time: about 45 minutes I think.

iii.) Inflation is running at such a high rate in Zimbabwe at the moment that golfers buy their drinks before they start their game.

Hey that's a great golfing inovation...I must try that.

The height at the ends of the embankment would be roughly 1.56 km.

Don't know the answer to question 1.

For the alternative question, does Mugabe count? I suspect none cos he is a bloody loony.

I re-calculated and got 196 metres and 218 metres (I forgot to divide the earth diameter in two to get the radius). One of us is still wrong?

I cheated. On the net it says the radius of the earth is 6378.1 km. I drew it on autocad and snapped a 100km line to the top quadrant then took a list reading vertically down to the apparent intersect. I know this isn't the true height the road would be because that length is the hypotinuse and i should have take the length of the line running from the center of the earth to the tip of the road then taken away the radius of the earth but i couldn't be bothered (the adjacent line). Give me a second and I'll do it again.

Just done it again on autocad using the proper line and I get 1.0028 km. Maybe I cocked up the first time but I'm still getting higher readings than you. How are you doing it?

OK, I will play along. I did basically the same thing as you, based on your 6378.1km earth radius, except that I made one line 51 km and the other 49km, and used a SolidWorks sketch. The answers I got were 204m (51km end) and 188m (49km end). I also dropped a 90 degree line from the ends and got no significant difference (less than one meter, actually only about 13 mm at the 51km end).

Can anyone else confirm?

I must have been doing something wrong. Don't have time at the moment to try again but this little exersice may have proved useful in making me aware of some mistake I'm making on autocad. Can't think for the life of me what it is and I'm not going to tell my boss that I can't draw a circle with a line at a tangent to it.

Anyone else out there done the same thing and got different answers or the same answer and can see my mistake please let me know.

Zimbabwe mate! Don't go there it's at level 6 on the Genocide Watch list and they've already started the killing.

"Alternative Questions

1 how many presidents did Zimbabwe had in the recent past?

2 Name them!"

Hey, no one has tried to answer these "Alternative Questions".

Previous to the present form of government, with Robert Mugabe as Executive President (since 1987), Zimbabwe did have a figurehead President, Canaan Banana, from 1980-1987 with Mugabe as the executive Prime Minister.

Prior to that Zimbabwe (also known at times as Southern Rhodesia, Rhodesia, and Zimbabwe-Rhodesia) had the status of a British colony, then becoming an unrecognized, white minority governed independent state, and later, under a black majority government, a member of the British Commonwealth, at all times Pledging allegiance to Queen Elizabeth II. During these times the executive powers were held by the Prime Minister. These Prime Ministers were:

1. Ian Smith, leader of the white minority separatist government. (1965-1979)

2. Abel Muzorewa, nominal prime minister under an internal power-sharing agreement that left most of the control in the hands of whites. (1979-1980)

3. Robert Mugabe, who won free elections under British supervision after the country reverted temporarily to colony status in 1980. He changed the constitution in 1987 to make himself President and has won every election since then.

During the separatist period under Smith as PM there were several Presidents as well, although the Queen was still considered the Head of State.

Today, Mugabe continues as President, having won the most recent election in 2002 by 56% versus 42% for his opponent.

Also in 2002, Zimbabwe was suspended from the British Commonwealth on charges of human rights violations and election tampering!

By the way, in high school I took Speech and Debate classes. While participating in a Model United Nations in the 1970's, I was chosen to represent (not necessarily my own views) the very same separatist white government of Rhodesia (as an observer nation, not a UN member). Of course I acted the part with zeal, just like any actor who enjoys playing the villain or a debater who takes the opposition, as in a Devil's Advocate.

During the Model UN we had a system of pages who were runners to carry messages between delegates. Boy, did I get a lot of hate mail and death threats , mostly anonymous! The next year, I was asked to represent the "Apartheid" government of South Africa. Again, same story, same hate mail. I guess I played my parts a little too well.

I decided not to participate the following year!

Blimey...you are really trying to win that GOOZ card!

Maybe it's that last one you need for the full set?

Smart move Smiley (face)

I think you should get the GOOZ card STL. You earned it.

Oh, oh, oh, YEEEEES!

"Bishop Abel Muzorewa" is an anagram for "Oops, I rule Zimbabwe!"

At last!

He should get in the car, select neutral and release the brakes. The car will roll to the petrol station. Seeing as the road was built under the constrain that it will follow 1 meter below the laser beam, and the beam will follow a straight line and not the curvature of the earth, the car will effectively be sitting on top of a 51km downhill ramp. As there is no friction or air resistance the car will have enough kinetic energy upon reaching the 51km mark to make it up the 49km uphill ramp to the petrol station.

Another exercise in M.M. for the unwary and uninformed.

As Alfred E.Newman is said to have said, "What? Me worry?"

51 Km downhill, & 49 Km uphill with the same slope should get the contractor to the "gas" station with plenty momentum to spare

If the workers follow the guidlines exactly he will eventually make it to the end. My question is how did he get up the ramp and how long is it???

Children, children... <shaking head>

What fun it is to live in a fantasy world where highways are constructed so they follow a laser beam with an ever increasing height above sea level! (1.56km high embankments, indeed!) In the real world that most engineers and construction contractors live in, that 51km point will simply be the starting point for a series of laser measurements, so that basically the road becomes a series of chords that approximate the curvature of the earth. In this case, as Labyguy said, your frictionless car would need a small push, or else put up Del's sail and wait for a strong enough breeze to get you started, overcoming the inertia of the automobile's mass. Note: frictionless does not mean inertia-less! MACA would probably still be waiting and miss his flight to Zimbabwe!

Funny that this is titled, "Out of petrol on a level road". I guess it depends on your definition of level, but if I go to either end on your "level" road that has a 1.56km high embankment on one end, and place a bubble level (most laser levels have one!) so that it follows the line of the road surface, pointing (literally and figuratively) down the road, it would surely indicate a non-level, sloping surface. How else would your frictionless car travel without a push or a sail? It has to be by gravity, and that would require a slope, not a "level" road! Therefore your entire question is bogus!

Note the question was a level road relative to the laser line and the question is obviously just to make you think along a different train of thought. Most of these question are utter nonsense and not to be taken seriously.

As for my trip to Zimbabwe, I have no intention on taking it as my mother was born there and escaped in the 70's. It was bad then and I believe it just continued going down hill. All 51km of it.

The laser would also be affected by the earths gravitational gield and would be bent as well. So... the road would be neither level (except at the 51 Km mark) nor would it be straight; it would only be a close approximation of stright. If you want to know the "exact" amount it would be out of straight, submit the question to Jorrie.

That's right. Light is bent by any gravitational field. Or do I remember correctly that space time is distorted by gravity and light traveling in a straight line through it actually follows the curvature of the space time it travels in. I have no idea how much a laser beam over 100km would be bent in an arc when on earth. Someone who knows Jorrie please invite him to give us the details. I studied applied physics and this kind of thing was never discussed cos as other posters have said you would never do something like this in real life.

Look forward to hearing Jorries comments.

Don't confuse the terms "level" and "straight". The road was level only at the point where the instrument was placed, 51 km from the eastern end of the road. It was straight for its entire length.

I tried to visualize this. It would be a trench,though I am not sure how deep said trench would be in the centre. My rule of thumb is 2 meters over 5 kilometers, but maybe you guys who do surveys would know better.

" It would be a trench,though I am not sure how deep said trench would be in the centre."

From the OP "He took a laser level and set it up on the 51km mark from the east. and gave instructions for the road surface to be to be exactly 1m below the beam (in both directions)."

It appears to me that there is no concern about the depth at the 50 km marker, only at the begining, 51 km marker and the end of the road. Assuming the laser is on the surface of the sand the cut and finished surface of the road would be 1 meter down.

Why would you assume the laser is on the surface of the sand? Common practice would be to place it on a tripod, which could easily be exactly 1m above the sand, hence, at least at the 51km mark, the road level would be EXACTLY the same as the sand, 1m down from the laser line!

Also, I just worked out the math, by the Pythagorean Theorem, using 6378.1km mean earth radius, the 51km end would be about 204m above the sand, which matches my graphic solution using a SolidWorks sketch.

What then is the situation at the 100 km marker 49 km from the 51 km marker?

A steep drop off depending on angle of repose of the Sahara sand?

Even, or especially, if the Sahara sand is flat (and not duned up against the end of the roadway), my graphic solution gave 188 meters in height for the other end.

As I see it, in order to comply with the ridiculous request, if it is so interpreted, the contractor would have to build, essentially, two "bridges to nowhere", one at each end, 188 and 204m high at each end, starting wherever it became impractical to continue the grade using available materials. Now, how ridiculous is that?

Lots of sand to make concrete, but where would one get all the Portland cement and other aggregate, not to mention the rebar or steel piers needed to be sunk into the sand to support the extremely long bridge halves! Perhaps our roadbed would need to be asphalt concrete, or bitumen (made with asphalt "tar" from the Arab oil fields with a sand filler?), although it might not make the best roadway surface in the hot Sahara sun....

I wonder how frictionless a car will be on a soft / sticky molten road surface.

I hate to be this way but if we have waived wind resistance for the auto how does Del the Cat's sail operate..................selective resistance?. Sorry.

Jeez I must be bored...

The Car is unaffected by wind resistance.

I said put up a sail.....The Q doesn't mention the wind resistance of any addons...

I s'pose if You really wanted you could construct a sail made of holes tied together with sting.

For my part I would try and use something which did have wind resistance. Maybe your pants? or I'd strip the seat covers...or whatever... I just can't be arsed with this anymore.

It's getting like the old pantomime Q..how do you get out of the cell...no door ..no windows..just a table?

"It's getting like the old pantomime Q..how do you get out of the cell...no door ..no windows..just a table?"

I'd call a cat to get me out!

Maybe a net would make a good sail in this hypohypohypohypothetical absurdity!

"It's getting like the old pantomime Q..how do you get out of the cell...no door ..no windows..just a table?"

I haven't heard this one. How do you get out?

It's a good old child pleaser...oh no it isn't...oh yes it is..etc..here goes...

Rub your finger on the wall until it's 'sore'...

Take the 'saw' cut the table in half... two halves make a 'whole'

Climb through the 'hole'...shout until you are 'hoarse'

Jump on the 'horse' and ride away....!

Sorry about that...dunno if you have panto' in the States?

It's a great Christmas tradition over here....lots of audience participation ..

Oh no there isn't..oh yes there is etc....

And the villain always creeps up behind the hero and all the little kids in the audience have to shout ..'look out he's behind you!'

Oh no it isn't !

Oh, yes it is!

Sounds like great fun. The little ditty would never go over here though because no American would pronounce "saw" the same as "sore", although I certainly understand how a Brit would. Reminds me of the great Mike Meyers character (way before Austin Powers) he used to do on Saturday Night Live, who was, I think 5 years-old and played in a park in London, very funny stuff.

We would say "saw" as rhyming with "paw" or "claw", although some New Englanders would pronounce "car" as rhyming with it (like "caw pawk").

And another thing!

I bet I can be more pedantic than you!..

A sail doesn't resist the wind!

I goes with it !!!

If the car is frictionless, how did it stop in the first place?

If the car is frictionless, how did it stop in the first place?

The car may be frictionless, but he never said the brakes weren't. Geez, this sounds like the same trouble that Del had with the sail!

Rolling wheels may be considered frictionless if they are mounted on frictionless bearings. That does not mean that if the wheels are stopped by a brake, that the wheels have NO friction with the road surface! Elementary my dear Guest!

Besides, even if it had no brakes, our frictionless car could still be stopped if a barrier is put in front of it, maybe pile up a couple dead camels or something.

Good handbrake!

Randall is awarded a get out of Zimbabwe card - (pass go and collect money)

the ±98 m (about 3') is about right. the ±198m as well.

It is increased to 2,4,8,16 and counting.

Golfers must use their own balls in Zim.

iF MACA keeps on applying the inflation rate he will be ok one of these days.

Del is awarded a pardon because of post 37.

DAVAH - I visited Zim when the roads were 2 strips. It was a beautiful promising country with a lot going for it. What is happening today is a crying shame.

About going there, I would not even recommend that to an enemy. (some politicians excluded)

"Randall is awarded a get out of Zimbabwe card - (pass go and collect money)

the ±98 m (about 3') is about right. the ±198m as well."

Wait one darn minute, Hendrik!

Randall gave the East/West end height as 196m, not 198m. I agree with that, IF the road was started at 50km mark. However, you stated very clearly in the beginning that the road was started and constructed both ways from the 51km mark, which would make it 51km long on one side and 49km long on the other. In this case the heights at each end using the equatorial earth radius of 6378.1m would be 188m and 204m for the 49m and 51m ends respectively, as I had posted previously!

Do I need to show my work, or do I get my GOOZ card as well?

Sorry STL_Engineer - Your answer is correct for the 49/51 split and you deserve your 64 stay out of Zim cards.

Typing with one hand (One arm in plaster) seems to influence my memory.

I am not sure where I got the 198 from. Maybe your 188.

My calculator (a ±1980 model HP71) was stolen recently and I am lost without it. For the second question I used the centre to avoid calculations.

I used a old program I did to check the figures. (based on Clark 1880) The results are however rather close.

As long as Randall doesn´t take the money out of the country, he should be OK!

If, while gravity and wind power were used, a painting wheel was mounted to the car which also was on frictionless bearings, how much paint would it take to paint the white line in the middle? (Just woken up from a siesta and my brain is a little doppy, sorry)

In Zim the white lines in the centre do not last. They roll it up for toilet paper.

Thinking of it - What did they use the rolled up road for?

Sod, for the Zimbabwe yard of the month!

Hey Hendrick, did you know that SOD is DOS spelled backward?

Metsys Gnitarepo Ksid - What does it mean? - Vista?

I forgot to mention - you are only allowed three sheets per go. (up, down, polish)

Temporary Special Event Flooring

If painted during a sand storm.

- The surface will be sand blasted clean.

- The quantity will have to be doubled for proper mixing with the sand.

- The thickness of the paint will be about 1"

- The paint nozzle Will be blocked.

==> 0 paint used

.

A 100 km long road that just goes on and on and on and never ends!

.

Maybe we can connect one end of it to the Gravina Island bridge (Alaska's "bridge to nowhere").

No silly, simply place a Stargate at each end. Just be sure to carry a mobile DHD and a GDO with you in the car or you might end up reconstituted as raw DNA and amino acid molecules splatted against the Iris in the SGC under Cheyenne Mountain!

Oh, and if you do end up coming back through the gate in the SGC, better make sure you hit the brakes as you come down the ramp in the Gate Room, or Walter will make you clean up the mess, provide your air bag deployed properly when you hit the back wall!

Hey, this is actually a pretty good idea. Put in a few on/off ramps and we could have a nice interstellar truck stop in the middle of the Sahara! Perhaps then the Vogons won't need to destroy the Earth to make way for a hyperspace bypass as noted in "The Hitchhiker's Guide to the Galaxy".

The engineering answer should be: He should get on his cell phone and call the service station to bring gas...

Nah!

The engineering solution would be...(assuming a flat rather than down hill road)

Take out the plugs hit the starter...off you go !

...gimme a GOOZ card !

Frictionless = NO BRAKES
Sorry hand brake guys.

I am concerned about the power to produce an accurate laser; strong enough to pin-point either 49 or 51 Km. I have used some very high powered units and they tend to flare at distance; making them utterly useless as a measure for more than 300 feet.

I'm interested in how he traveled around the world in just over 80 days.

George Francis TRAIN, once said:

"Verne stole my thunder. I'm Phileas Fogg."

Verne replied:

"I have a great number of scientific odds and ends in my head. It was thus that, when, one day in a Paris café, I read in the Siècle that a man could travel around the world in eighty days, it immediately struck me that I could profit by a difference of meridian and make my traveller gain or lose a day in his journey. There was a dènouement [sic] ready found. The story was not written until long after. I carry ideas about in my head for years - ten, or fifteen years, sometimes - before giving them form." In his lecture of April 1873 "The Meridians and the Calendar"

(referenced from Wikkipedia; http://en.wikipedia.org/wiki/George_Francis_Train , and:

Our friend may have cheated time and beaten his car to the finish line...

Or maybe he had a railroad car and he wouldn't need any petrol whatsoever.

One may conclude the petrol for the electric generator, for the rail car; to be at one end or the other. He may have traveled on a "Center Beam" railroad car or an "Automated Beam Carried Traffic System". It does not matter.

He may be using steam or wind, solar electricity or any number of non-petrol related power sources to get to the other end of the rail-road. It doesn't matter.

According to: http://www.alaskarails.org/terminology/related-terms.html

Brake Beam

A cross-piece in the foundation brake gear for a pair of wheels to which the leverage delivers its force to be transmitted through the attached brake head and brake shoes to the tread of the wheels.

Therefore; the rail-road was to be laid 1 meter below the beam, or the "brake beam".

Even if this is what is referred to; again it does not matter.

No friction = a train without brakes.

This can be associated with a temperature sensor failure of the Ultrasonic Distance Measuring System, designed to monitor railroad car loads, (no matter what type of railroad car system, track, rail, beam, etc.). The ultrasonic BEAM would be adversely effected by the high temperatures of the desert air, causing faulty readings to the load management system, which in turn regulates BRAKING of the train, according to the weight adjusted load management system.

http://www.wipo.int/pctdb/en/wo.jsp?IA=WO2001069188&wo=2001069188&DISPLAY=DESC

Or the engineer may be dead at the controls and the Dead Man Switch is faulty or has been intentionally bypassed, (though this is unlikely, as the device should be double redundant or mechanically necessary for operation; as a "failsafe".)

Not effected by wind resistance would mean he is within an aerodynamically efficient shape, (to his utter horror).

... for now, leaving the thought aside where he cheated time and is actually at the end of his journey, we can assume he is on a Runaway Train.

Maybe he should jump for his life; as he will run off the tracks?

I wonder if this area of the world will now suffer from the dreaded "Palin Effect"?http://en.wikipedia.org/wiki/Michael_Palin (also directed "Around The World in 80 Days"-1989, and: "Great Railway Journeys Around The World" -1980

No! No! No! No one is concerned with stopping the car, all we want to do is move it along this "yellow brick road" that we've concocted.

If stopping turns out to be an issue then I'll do it this way:

I will attach one end of my 49km bungee cord to the front bumper of "the" car. Then I'll attach the other end to the steel hook we buried in the center point of the road (when we built it) at the 51km mark (pick either end and measure 51km). Now, since I'm a pretty strong guy, I'll push the frictionless car to the 51km end of the road. Next I'll carefully get in while holding the car in place with my "Fred Flintstone" shoe leather brake (I know, Fred didn't wear shoes but humor me). Now, when I lift my foot- Wheeeee! Off we go! The force of the bungee should just about get me to the other end of the road before the elasticity of the bungee takes hold and brings me slowly to a gentle stop. But then I must apply my foot brake, hold the car back then unhook the bungee. You folks back there watching and betting on me getting to the end better get outa the way cause there's a great big rubber band coming atcha. If for some reason I don't stop in time, who cares. I'm in the Twilight Zone anyway. Maybe Rod Serling will come along and scoop me up.

-John

"I am concerned about the power to produce an accurate laser; strong enough to pin-point either 49 or 51 Km. I have used some very high powered units and they tend to flare at distance; making them utterly useless as a measure for more than 300 feet."

Oh no, LASERS that tend to "flare out" at distance? Not usable past 300 ft. (91.4m) ? By that I assume you mean that their beams diverge, making a much bigger spot and becoming much less intense, right?

Well, maybe you can get one of those "higly collimated" non-divergent lasers from Blink, OK?

RE: Braking the "frictionless car" see my post#35 above.