## The Rolling Cart

A forum for good logic/math puzzles.

Moderators: jestingrabbit, Moderators General, Prelates

jessebob
Posts: 64
Joined: Sat Sep 01, 2007 9:53 pm UTC
Location: Singapore, Singapore, Singapore

### The Rolling Cart

So, there is a cart with an endless track, next to a person walking. The cart is made so that it moves 2 inches for every 1 inch the man walks. So if the man is running at a specific speed, the cart would be going twice as fast.

BUT! What happens if the man jumps into the cart?
We could say the man is now moving at 4 inches per second, which means the cart is moving at 8 inches per second. Which now means the man is moving at 8 inches per second.

Does the cart eventually accelerate to the speed of light? or beyond?

I thought of it in bed this morning. I dont know the answer. Help me?
Huh? Did you say something? I couldn't hear you all the way over here!

There is a monkey in your pyjamas! Be Careful!

Exotria
Posts: 206
Joined: Fri Mar 28, 2008 10:41 pm UTC
Location: MA
Contact:

### Re: The Rolling Cart

Trick question. He's no longer walking.
Elvish Pillager wrote:
niolosoiale wrote:So which side of the fence would you say I'm on? Why?

The confusing one. I think you should pick a different fence.

fyjham
Posts: 240
Joined: Wed Nov 21, 2007 1:16 am UTC

### Re: The Rolling Cart

Wouldn't the cart evade him because as he tried to step in it'd run away twice as fast?

yohanleafheart
Posts: 349
Joined: Fri Dec 05, 2008 12:37 pm UTC
Location: São Paulo, Brazil
Contact:

### Re: The Rolling Cart

Spoiler:
Yeah, that's what I was thinking. He wouldn't be able to jump into the cart, unless the cart was long enough and he jumped early enough. Even than, he is no longer walking, or we can define that he walks at speed 0 m/s which will make the cart stop.
"When you gotta do something wrong, you gotta do it right." - Fighter - 8-bit Theatre
"Life is a bitch. But it is my bitch." - Slick - Sinfest
Avatars courtesy of Sinfest

Blatm
Posts: 638
Joined: Mon Jun 04, 2007 1:43 am UTC

### Re: The Rolling Cart

Spoiler:
v = 2v has one solution: v = 0.

jessebob
Posts: 64
Joined: Sat Sep 01, 2007 9:53 pm UTC
Location: Singapore, Singapore, Singapore

### Re: The Rolling Cart

ok lets say he can run. he doesn't have to be walking.

also, he could reach out and grab it, no? if he grabs onto the side after he has moved 2 inches, the cart is 2 inches in front of him. if he grabs hold, then jumps in, what happens?
Huh? Did you say something? I couldn't hear you all the way over here!

There is a monkey in your pyjamas! Be Careful!

yohanleafheart
Posts: 349
Joined: Fri Dec 05, 2008 12:37 pm UTC
Location: São Paulo, Brazil
Contact:

### Re: The Rolling Cart

Spoiler:
Same thing. The cart's movement is based on the relativity velocity between them. The moment he gets into the cart, that dV goes to 0, and the cart will stop.
"When you gotta do something wrong, you gotta do it right." - Fighter - 8-bit Theatre
"Life is a bitch. But it is my bitch." - Slick - Sinfest
Avatars courtesy of Sinfest

thc
Posts: 643
Joined: Fri Feb 08, 2008 6:01 am UTC

### Re: The Rolling Cart

I don't think that that the speed goes to zero instantaneously. When the guy jumps into the cart, the cart imparts dV speed on the passenger through momentum, which causes 2dV increase in speed to the cart through an unknown mechanism, which causes 2dV increase in speed to the passenger, which causes 4dV to the cart, and so on. What this looks like is the passenger becomes extruded through the back of the cart.

Very reminiscent of the airplane on treadmill question.

quintopia
Posts: 2906
Joined: Fri Nov 17, 2006 2:53 am UTC
Location: atlanta, ga

### Re: The Rolling Cart

let's assume the cart is infinitely long and can be walked on. the speed the man is walking is his speed relative to the cart once he is on it. since the cart is moving relative to the track at twice this speed.

Spoiler:
Thus, the man's speed relative to the track is three times the speed he is walking.

If you rephrased it such that the cart went twice as fast as the man's speed relative to the track, then the only real solution is that neither are moving.

jessebob
Posts: 64
Joined: Sat Sep 01, 2007 9:53 pm UTC
Location: Singapore, Singapore, Singapore

### Re: The Rolling Cart

but what if the speed was relative to the starting point? or the ground. for each inch the man passes on the ground, etc.
Huh? Did you say something? I couldn't hear you all the way over here!

There is a monkey in your pyjamas! Be Careful!

quintopia
Posts: 2906
Joined: Fri Nov 17, 2006 2:53 am UTC
Location: atlanta, ga

### Re: The Rolling Cart

jessebob wrote:but what if the speed was relative to the starting point? or the ground. for each inch the man passes on the ground, etc.

read the last sentence in my post.

thc
Posts: 643
Joined: Fri Feb 08, 2008 6:01 am UTC

### Re: The Rolling Cart

quintopia wrote:If you rephrased it such that the cart went twice as fast as the man's speed relative to the track, then the only real solution is that neither are moving.

That's not true. Just because he is on the cart, doesn't mean he is going as fast as the cart.

fyjham
Posts: 240
Joined: Wed Nov 21, 2007 1:16 am UTC

### Re: The Rolling Cart

thc wrote:
quintopia wrote:If you rephrased it such that the cart went twice as fast as the man's speed relative to the track, then the only real solution is that neither are moving.

That's not true. Just because he is on the cart, doesn't mean he is going as fast as the cart.

If measured relative to the same point of reference as each-other and assuming he's not moving inside the cart, sure it does...

quintopia
Posts: 2906
Joined: Fri Nov 17, 2006 2:53 am UTC
Location: atlanta, ga

### Re: The Rolling Cart

thc wrote:
quintopia wrote:If you rephrased it such that the cart went twice as fast as the man's speed relative to the track, then the only real solution is that neither are moving.

That's not true. Just because he is on the cart, doesn't mean he is going as fast as the cart.

Good point. If he walks in the opposite direction of the cart, then every speed at which he walks is a correct solution under this interpretation. While the spirit of the OP's question was that they were moving in the same direction, under this interpretation, that is an impossible situation. So I amend my earlier statement:

If you rephrased it such that the cart went twice as fast as the man's speed relative to the track, then the man is stopped wrt the cart or moving in the opposite direction of the cart relative to the cart.

Kamikkels
Posts: 36
Joined: Fri Dec 26, 2008 2:07 pm UTC

### Re: The Rolling Cart

Ignoring the standard givens allows for two answers, and due to the ambiguity of the question it would seem logical, both can either be at rest (0 motion in reference to a given point of measure) or moving at a infinite velocity (again in reference to that point)

acidcj
Posts: 18
Joined: Tue Jan 06, 2009 9:27 pm UTC

### Re: The Rolling Cart

I say
Spoiler:
Either

A) He falls on his face as he tries to get in
B) If he does get in, the cart stops.
C) He breaks through the back of the cart

Luppoewagan
Posts: 523
Joined: Wed Apr 18, 2007 7:56 pm UTC
Location: Up a creek without a paddle
Contact:

### Re: The Rolling Cart

He could walk backwards until the cart catches up to him, then get in.

Hatter
Posts: 8
Joined: Sat Jan 10, 2009 6:23 pm UTC

### Re: The Rolling Cart

He would walk backwards untill the cart was behind him, stand on the track and run forwards, the cart would hit him. Assuming the man is able to get on without being run over then thats solved.

Maurog
Posts: 842
Joined: Tue Jul 10, 2007 7:58 am UTC

### Re: The Rolling Cart

He can't get to the cart due to Zeno's paradox in the first place.
Slay the living! Raise the dead! Paint the sky in crimson red!

uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

### Re: The Rolling Cart

If he gets in the cart, it'll come to rest immediately, like you stuck a pin between two sprockets with different gear ratios

There's one solution to v = 2v and it isn't infinity; it's zero.
I don't know what to do for you

scikidus
Posts: 792
Joined: Wed Nov 26, 2008 9:34 pm UTC
Location: New York, NY
Contact:

### Re: The Rolling Cart

Let's ignore the whole concept of walking for the moment and simply say that if the man is moving at x m/s relative to the ground in a horizontal direction, then the cart will automatically accelerate itself to 2x m/s (relative to the ground int he same direction).

So the man is walking along, very slowly, at 0.125 m/s. The cart's moving along side him at 0.25 m/s. At this speed, he can easily reach out, grab the cart, and attempt to jump in. However, the cart will be slightly ahead of him at this point, so he need to move faster to catch up tot he cart, which accelerates the cart. Therefore, the man cannot get into the cart.

If, however, we do wish for the man to be able to get into the cart, then we require another condition: the cart must start off behind the man. Again, walking along at 0.125 m/s, the cart catches up to him, moving at 0.25 m/s. He jumps in sideways while maintaining the 0.125 m/s, and (assuming no friction in the cart) slides to the back of the cart, still moving at 0.125 m/s. When he hits the back of the cart, however, he is accelerated to the speed of the cart, which is 0.25 m/s.

Here's where things get messy. The cart keeps tryign to accelerate to twice the man's speed, but the man is in the cart. This results in an exponential increase in speed.
jessebob wrote:Does the cart eventually accelerate to the speed of light? or beyond?

Le tme rephrase that: an exponential increase in speed, until relativistic speeds are reached. Goign at speeds comparable to the speed of light causes time to slow down for the cart and the man, meanign that what "m/s" means becomes fuzzy. Also, it takes more and more energy to accelerate the cart: to hit the light barrier, it would take an infinite amount of energy. However, at this point, the cart (and man) have other problems. They are moving so fast that Fitzgerald contraction is shrinking their lengths in the direction of motion, while the energy being applied to their motion is hopping on as mass more and more. An increasing mass and a decreasing volume mean that their density is skyrocketing. At some point the man and the cart will collapse into a black hole.

So no, they won't break the light barrier.
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

### Re: The Rolling Cart

scikidus wrote:Here's where things get messy. The cart keeps tryign to accelerate to twice the man's speed, but the man is in the cart. This results in an exponential increase in speed.
Why would it do that as opposed to simply stopping? Again, the only solution to V=2V is V=0. Therefore when the man gets in the cart, both their velocities immediately become 0. There's no reason for the cart to "try" to outrun the man by accelerating, because it never satisfies, or could satisfy, the supposed design of the cart.
I don't know what to do for you

fyjham
Posts: 240
Joined: Wed Nov 21, 2007 1:16 am UTC

### Re: The Rolling Cart

I'm going to start with a simple statement: I assume this cart obeys the laws of thermodynamics (Significantly the ones that contradict perpetual motion).

With that said, it has to be being powered by something, and hence that item is increasing it's power output to try to achieve the requested results. At which point the question you're asking becomes "Can we propel a cart at the speed of light?" and the answer is "No". Such a motor could never achieve V=2V unless V=0, if it tried it would be constantly trying to reach an impossible target until it eventually peaked out or broke itself somehow which would occur well before the speed of light in all modern technologies.

If the laws of thermodynamics don't apply to our cart, the means it uses to do that most likely render the majority of our laws of physics flawed when applied to it, so I'm going to suggest that if this happened it would spontaneously turn into a walrus and hence is freed from it's need to outpace the man because it's no longer a cart (With the laws of physics discarded it's as logical to believe as anything else ).

scikidus
Posts: 792
Joined: Wed Nov 26, 2008 9:34 pm UTC
Location: New York, NY
Contact:

### Re: The Rolling Cart

uncivlengr wrote:
scikidus wrote:Here's where things get messy. The cart keeps tryign to accelerate to twice the man's speed, but the man is in the cart. This results in an exponential increase in speed.
Why would it do that as opposed to simply stopping? Again, the only solution to V=2V is V=0. Therefore when the man gets in the cart, both their velocities immediately become 0. There's no reason for the cart to "try" to outrun the man by accelerating, because it never satisfies, or could satisfy, the supposed design of the cart.

It would do that in my case because I initially specified that the man's speed was measured based on his speed relative to the ground. Imagine for a moment that the acceleration fo the cart is not instantaneous. The man is moving at 0.125 m/s, he hits the back wall of the cart moving at 0.25 m/s, the cart immediately begins accelerating to 0.5 m/s, but once it's at 0.5 m/s, it now must accelerate to 1 m/s, then to 2, 4, 8, 16, 32, etc. until it becomes a black hole.

However, in the original case where the man's speed is measured off of his walking speed, then yes, I agree, the cart would stop.
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

### Re: The Rolling Cart

scikidus wrote:It would do that in my case because I initially specified that the man's speed was measured based on his speed relative to the ground.
It would still be zero if you're measuring his speed and the cart's relative to the ground.

The man's speed is Vman, the cart's speed is Vcart. We are told that the two are related by Vcart = 2Vman, but when he jumps in the cart we have Vman = Vcart. The only way Vman = 2Vman is possible is if Vman (and subsequently Vcart) is zero. Anything else, including accelerating to the limits of the cart, would not satisfy these conditions.

The only possible scenario in which they both accelerate is if the hypothetical cart isn't designed to move at twice the speed of the man, but to track the man's motion via some sort of external camera, for example, and send that information to a computer, which adjusts the cart's speed accordingly after some finite amount of time. In that situation, the result acceleration is merely a flaw in the computer's ability to precisely monitor and respond to the person's motion.

The original scenerio is that the cart moves at twice the speed of the man, not that it meagerly attempts to do so.
I don't know what to do for you

MarshyMarsh
Posts: 140
Joined: Tue Aug 07, 2007 7:43 pm UTC
Location: UK
Contact:

### Re: The Rolling Cart

If the cart itself was of infinitly long length then this would be more interesting. If it was infinitely long then the man could jump into the cart and then rung along the length of the cart. If the cart itself then moves at 2dv he should accelerate beyond the speed of light. But an infinitly long cart cannot accelerate or travel at a speed as it is in all places at once, therefore it would have to be an infinitly long treadmill. In my eyes this is similar to the problem of shining a torch on concorde, the light appears to go faster than the speed of light from respect to the earth (the longest golf put). The problem with this problem is where you are measuring the velocity from, the ground or the start point.

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: The Rolling Cart

MarshyMarsh wrote:In my eyes this is similar to the problem of shining a torch on concorde, the light appears to go faster than the speed of light from respect to the earth (the longest golf put).

No, it doesn't. The whole point of special relativity, of time dilation and spatial dilation in particular, is to ensure that from every reference frame, every observation of the speed of any light in a vacuum is a constant.

I'm coming closer and closer to locking this thread.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

thc
Posts: 643
Joined: Fri Feb 08, 2008 6:01 am UTC

### Re: The Rolling Cart

but when he jumps in the cart we have Vman = Vcart.

No you don't. Momentum is the time integral of force, so Vman != Vcart unless you have a delta function of force from the cart onto the man, which clearly doesn't happen IRL.

uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

### Re: The Rolling Cart

thc wrote:
but when he jumps in the cart we have Vman = Vcart.

No you don't. Momentum is the time integral of force, so Vman != Vcart unless you have a delta function of force from the cart onto the man, which clearly doesn't happen IRL.
If he's sitting inside the cart, his motion is obviously governed by that of the cart. What else would you propose? That he's suspended in the air above the cart?
I don't know what to do for you

thc
Posts: 643
Joined: Fri Feb 08, 2008 6:01 am UTC

### Re: The Rolling Cart

uncivlengr wrote:
thc wrote:
but when he jumps in the cart we have Vman = Vcart.

No you don't. Momentum is the time integral of force, so Vman != Vcart unless you have a delta function of force from the cart onto the man, which clearly doesn't happen IRL.
If he's sitting inside the cart, his motion is obviously governed by that of the cart. What else would you propose? That he's suspended in the air above the cart?

It doesn't change the fact that the change in momentum can't be instantaneous, since that would require an infinite force. When the man gets in the cart, he feels a force from the cart onto him; kind of like when you step on the accelerator in a car. You don't immediately go as fast as the car, rather you are pushed back into the seat of your car before reaching the same speed as the car.

Axidos
Posts: 167
Joined: Tue Jan 20, 2009 12:02 pm UTC
Location: trapped in a profile factory please send help

### Re: The Rolling Cart

scikidus wrote:We are told that the two are related by Vcart = 2Vman, but when he jumps in the cart we have Vman = Vcart.

Not true at all. We are also told the man's path is beside the cart's path. Let's assume they're infinite and parallel, and they are one metre apart. The cart begins 2 metres further back on its path than the man is on his.

The man will jump 1 metre toward's the cart's path - sideways - in 1 second. In that second, the cart moves double that distance - 2 metres. The man lands on the cart (and does not fall off) and still possesses some momentum, which is passed on to the cart. Infinite speeding up begins.

scikidus
Posts: 792
Joined: Wed Nov 26, 2008 9:34 pm UTC
Location: New York, NY
Contact:

### Re: The Rolling Cart

uncivlengr wrote:
scikidus wrote:It would do that in my case because I initially specified that the man's speed was measured based on his speed relative to the ground.
It would still be zero if you're measuring his speed and the cart's relative to the ground.

The man's speed is Vman, the cart's speed is Vcart. We are told that the two are related by Vcart = 2Vman, but when he jumps in the cart we have Vman = Vcart. The only way Vman = 2Vman is possible is if Vman (and subsequently Vcart) is zero. Anything else, including accelerating to the limits of the cart, would not satisfy these conditions.

The only possible scenario in which they both accelerate is if the hypothetical cart isn't designed to move at twice the speed of the man, but to track the man's motion via some sort of external camera, for example, and send that information to a computer, which adjusts the cart's speed accordingly after some finite amount of time. In that situation, the result acceleration is merely a flaw in the computer's ability to precisely monitor and respond to the person's motion.

The original scenerio is that the cart moves at twice the speed of the man, not that it meagerly attempts to do so.

If the acceleration is instantaneous, then it's impossible to determine what happens, because you end up dividing by zero. You reach your conclusion that Vcart = 2Vcart because of this. Really, it's an expansion of the 1=2 "proof."

However, if acceleration takes some finite period of time, then the cart will accelerate more and more.
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

### Re: The Rolling Cart

scikidus wrote:If the acceleration is instantaneous, then it's impossible to determine what happens, because you end up dividing by zero. You reach your conclusion that Vcart = 2Vcart because of this. Really, it's an expansion of the 1=2 "proof."
No, that conclusion is a direct result of the information given in the problem. If the man in sitting in the cart then their velocities are equal. If the cart moves at twice the man's speed then it moves at twice the man's speed.

Let's actually propose a physical system by which the cart operates. A pulley system connects the box-shaped man and box-shaped cart that causes the cart to move at twice the speed of the man. As the cart passes the man, they link together.

This captures the essence of the problem described in the OP as simply as possible - it doesn't rely on motors or computers or cameras, merely a simple mechanical connection. What mechanism do you propose that would cause the cart to accelerate indefinitely after the point at which they connect, or how do you prove that my conclusion that they would both come to rest constitutes "dividing by zero"?

cartman.JPG (7.82 KiB) Viewed 4901 times
I don't know what to do for you

scikidus
Posts: 792
Joined: Wed Nov 26, 2008 9:34 pm UTC
Location: New York, NY
Contact:

### Re: The Rolling Cart

uncivlengr wrote:
scikidus wrote:If the acceleration is instantaneous, then it's impossible to determine what happens, because you end up dividing by zero. You reach your conclusion that Vcart = 2Vcart because of this. Really, it's an expansion of the 1=2 "proof."
No, that conclusion is a direct result of the information given in the problem. If the man in sitting in the cart then their velocities are equal. If the cart moves at twice the man's speed then it moves at twice the man's speed.

Let's actually propose a physical system by which the cart operates. A pulley system connects the box-shaped man and box-shaped cart that causes the cart to move at twice the speed of the man. As the cart passes the man, they link together.

This captures the essence of the problem described in the OP as simply as possible - it doesn't rely on motors or computers or cameras, merely a simple mechanical connection. What mechanism do you propose that would cause the cart to accelerate indefinitely after the point at which they connect, or how do you prove that my conclusion that they would both come to rest constitutes "dividing by zero"?

cartman.JPG

Flash code I'm looking at [set at 5 frames per second]:

Code: Select all

`Stage.scaleMode="showAll";depth = 500;createEmptyMovieClip("vman",depth++);createEmptyMovieClip("vcart",depth++);vman.lineStyle(2,0xFF0000);vcart.lineStyle(2,0x00FF00);lineStyle(1);xx=0;yy=2;vman.moveTo(xx,1);vcart.moveTo(xx,yy);_root.onEnterFrame=function(){   if(xx<Stage.width){      moveTo(xx,0);      lineTo(xx,Stage.height);      moveTo(0,yy);      lineTo(Stage.width,yy);      xx+=Stage.width/9;      vman.lineTo(xx,yy);      yy*=2;      vcart.lineTo(xx,yy);   }}`

In the code, the cart takes one frame to accelerate to the man's speed.

I hope you realize that we're talking about different cases here. In your case, acceleration is instantaneous (e.g. the chains system you have), and I agree that the cart stops. I've been saying that if acceleration is not instantaneous, then the cart will accelerate and obliterate itself as a black hole.

I say that you're equations break down because acceleration is [imath]\Delta[/imath]v / [imath]\Delta[/imath]t. Since [imath]\Delta[/imath]t is 0 (you're saying that acceleration is instantaneous), you're dividing by zero. Sure, the cart might come to a stop, but the acceleration is undefined.

-----------------------

I made a quick Flash app which illustrates my point. Refresh the page to watch it again.
http://www.freewebs.com/scikidus/cartman.htm
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

jaap
Posts: 2094
Joined: Fri Jul 06, 2007 7:06 am UTC
Contact:

### Re: The Rolling Cart

scikidus wrote:I hope you realize that we're talking about different cases here. In your case, acceleration is instantaneous (e.g. the chains system you have), and I agree that the cart stops. I've been saying that if acceleration is not instantaneous, then the cart will accelerate and obliterate itself as a black hole.

Even with the chains, it need not be instantaneous. He jumps onto the cart, the momentum of the cart (and the rest of the system) keeps it travelling forward, but still at twice the speed of the man relative to the ground. The cart keeps travelling forward relative to the man, or rather the man is pulled backwards relative to the cart by his rope. If he can get enough grip on the ground before he falls off the back, he will slow himself and the cart down to a standstill.

What makes you think that when the man jumps into the cart, the cart will make the man go faster rather than the man making the cart go slower? And even if it were to speed up, how can the man possibly remain in the cart? The premise is that It is always going twice the speed of the man.

scikidus
Posts: 792
Joined: Wed Nov 26, 2008 9:34 pm UTC
Location: New York, NY
Contact:

### Re: The Rolling Cart

jaap wrote:Even with the chains, it need not be instantaneous. He jumps onto the cart, the momentum of the cart (and the rest of the system) keeps it travelling forward, but still at twice the speed of the man relative to the ground.

Except now the cart wants to move at twice the speed of the man inside of the cart, who is moving at the carts current speed. In other words, the cart now wants to continuously accelerate to twice its current speed.
The cart keeps travelling forward relative to the man, or rather the man is pulled backwards relative to the cart by his rope. If he can get enough grip on the ground before he falls off the back, he will slow himself and the cart down to a standstill.

What makes you think that when the man jumps into the cart, the cart will make the man go faster rather than the man making the cart go slower? And even if it were to speed up, how can the man possibly remain in the cart? The premise is that It is always going twice the speed of the man.

I am imagining a walled cart, not a flatbed. When you sit in a car and the car accelerates from 15 to 30 mph, you do not fall otu the back; instead, you accelerate with the car.

A man moves at 1 m/s. The cart is moving at 2 m/s. When he jumps in the cart as it passes, he accelerates from 1 m/s to 2 m/s. For a moment, both the cart and the man move along at 2 m/s. Now the cart wants to accelerate to 4 m/s, but as soon as it accelerates, the man accelerates with it. Because of this, the cart is always tryign to accelerate to twice its current speed. Because the cart was not at a standstill when it started, it will continue to try to accelerate more and more, eventually creating a black hole.

Imagine you're sitting in your car. You're driving along at 2 m/s. Since you're stationary relative to the car, you now want to accelerate the car to 4 m/s. But as you start accelerating, you remain stationary relative to the car. By the time you're at 4 m/s, you now need to accelerate to 8 m/s. THis process repeats again and again until your car can no longer accelerate.
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: The Rolling Cart

So all I have to do is train a rat to jump on a cart as it moves past and set up a pretty simple pulley, and before I know it I'll have created a black hole? The work on my doomsday device is significantly progressed by this surprising discovery.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

### Re: The Rolling Cart

scikidus wrote:I hope you realize that we're talking about different cases here. In your case, acceleration is instantaneous (e.g. the chains system you have), and I agree that the cart stops. I've been saying that if acceleration is not instantaneous, then the cart will accelerate and obliterate itself as a black hole.

It certainly would not be "instantaneous" - the cart will put a significant amount of tension on the chains and come to a quick stop, and would probably be very unpleasant for the man, but it's not instantaneous. Even the act of pulling on the cable would not translate to an "instantaneous" response from the cart, assuming some elasticity in the cable. It is a mechanical system that models the concept as idealy as possible, would be easy to construct, and would prove that the system will stop, with or without ideal materials.

You, on the other hand, are proposing something that has no basis in reality - the fact that your conclusion is a cart with a man in it forming a black hole is indication enough of that. The problem never states "the cart attempts to travel at twice the speed that the man was travelling half a second ago" or anything of the sort.
I don't know what to do for you

fyjham
Posts: 240
Joined: Wed Nov 21, 2007 1:16 am UTC

### Re: The Rolling Cart

jestingrabbit wrote:So all I have to do is train a rat to jump on a cart as it moves past and set up a pretty simple pulley, and before I know it I'll have created a black hole? The work on my doomsday device is significantly progressed by this surprising discovery.

You will however have to produce a pully that has complete traction and a rope with zero elasticity so that the stop has to be completely instantaneous for it to stop... Those could be a bit harder to find (And if you found it I suspect when you test at a high enough speed you'll kill your rat ).

thc
Posts: 643
Joined: Fri Feb 08, 2008 6:01 am UTC

### Re: The Rolling Cart

There is a difference between your pulley system and the original problem in that you can slow the man down by slowing the cart down, even when they are not linked. In the original problem, the cart's speed is determined by the man's speed.

The cart becoming twice the speed of the man is not the same as the man becoming 1/2 the speed of the cart. In the first case, the cart will speed up indefinitely. In the second case, the cart comes to a stop. This is the true because momentum transfer from cart to man needs to occur before the mechanism that makes 2Vman = Vcart.

X = momentum transfer from cart to man
Y = mechanism that makes 2Vman = Vcart
Y' = mechanism that makes Vman = 1/2 Vcart

Case 1:
X accelerates man and makes him go V+dV; the cart is slowed by dV (assume they weigh the same for simplicity)
Y makes the cart then goes 2V+2dV.
Positive feedback occurs and the system blows up.

Case 2:
X accelerates man and makes him go V+dV; the cart is slowed to 2V-dV
Y' makes the man go back to 1/2(2v-dV), less than his original speed.
The system is damped out and comes to a halt.

Scikidus' conclusion has no basis in reality because the original problem has no basis in reality. Obviously it wont create a black hole, which was said tongue in cheek. Realistically, the cart will try to speed up until the system breaks.

edit: here is another system modelling the original problem. It's been a while since circuits, so it might be incorrect

opampcircuit.GIF (1.91 KiB) Viewed 4721 times

V+ represents the speed of the man, Vout is the speed of the cart. The gain is 2. In this case, I'm pretty sure V+ and Vout get railed.