Friday, 21 September 2007 - 3:43 PM EDT

Look Matt, It's a pulley. The two weights are equal so they will always be at the same level because they pull with an equal amount of force. The amount of rope doesn't matter becaues if x meters of rope pass through the guy's hands, than x/2 meters will be lost from either side. It's a pulley, Matt. The two will always be at the same level.

Friday, 21 September 2007 - 3:46 PM EDT

Hey all,

For this question, I'm not only looking for a response, but I want you to really justify your answer and continue the discussion as much as possible.  Thanks and have a good weekend.

Friday, 21 September 2007 - 3:50 PM EDT

Just drawing a free body diagram makes this answer obvious.  It is clear that there is a net upward force on the person and the sack equal to the force applied to the rope minus the weight.  Both objects have a net upward force, and should therefore accelerate upward.  As far as I see it, as the athlete reaches for the rope above him, whatever distance upward he reaches, half of it will be pulled onto his side from the other side.  So he will advance upward a distance which is half of that "reach distance."

Friday, 21 September 2007 - 7:35 PM EDT

Ladies & Gentlemen,A A

Saturday, 22 September 2007 - 11:45 AM EDT

Hi all,

Now you all have to understand that my argument was that the movement of the 'man and sand' with respect to the rope is different than the movement of the 'man and sand' with respect to the ground. 

As Giovanna clearly explained, when x meters of rope move through the man's hand, x/2 meters is removed from each side.  Mr. Celona also explained this by saying that if the man reaches x meters, than both he and the sand will rise half the 'reach distance' or x/2 meters.  Now these are both correct statements and I agree with them.  So there was no need to be nasty Giovanna because you were not addressing my theory.  Once again, my theory is that the movement of the 'man and sand' with respect to the rope is different than the movement of the 'man and sand' with respect to the ground. 

Now, my case has already been made for me by Giovanna and Mr. Celona.  When the man reaches x meters and pulls himself up x meters, he has move x meters with respect to the rope.  But, the man and the sand only move up half of the 'reach distance' or x/2 meters.  Thus, with respect to the ground, the man has only moved x/2 meters, which is clearly not equal to x meters.  So we can conclude that the movement of the man with respect to the rope (x meters) is not equal to his movement with respect to the ground (x/2 meters). 

This can be illustrated in a slightly different manner also.  We have all agreed that, with respect to the ground, the man and sand move upward at the same rate.  This means that when the sand rises x meters, the man, (with respect to the ground) also rises x meters.  No please follow closely (I am using x to describe the displacement from the original position, not how far the man has climbed.

Let us divide the rope down the middle.  Each half of the rope is y-meter long, giving a total length of 2y meters.  Now, when the sand has rises x meters, the length of rope on the sand side is y-x meters.  This also means that when the sand has risen x meters, x meters of rope has traveled to the other side of the pulley.  Since conservation of rope is vitally important here, there must still be 2y meters of rope.  So...if one side equals y-x, the other side must equal y+x.  These two added together yield a total length of 2y.  Thank goodness we didn’t lose any rope!!!  Now, once again we have all agreed that the man and sand rise (with respect to the ground) at the same rate.  This means that if the sand's location is y-x than the man's location must also be y-x.  However, remember that the rope on the man's side is y+x.  This means, that for the man and sand to be at the same height, the man has climbed 2x meters!  So now we see that, even though the man and sand have risen the same distance from the ground, the man has climbed twice as much rope as the sand! This is constant with Mr. Celona's argument.  The man clime 2x meters for every x meters that he and the sand rise!!  Thus, is it not terribly obvious that the movement of the man with respect to the rope is different than his movement with respect to the ground?

I want to apologize if my argument in class was not this clear, but with Mr. Celona hanging from the ceiling, everyone laughing and Giovanna yelling in my ear, it was difficult to get my points across.  I hope we have settled this minor issue and we can all move forward in the wonderful world of Newton's laws and begin to understand the confusion that comes with relativistic motion. 

Saturday, 22 September 2007 - 4:27 PM EDT

Wow Special Relativity, whoever you are, you really made a good argument.  I will have to think about this before I post my official answer. 

Sunday, 23 September 2007 - 7:58 PM EDT

If you have two objects that are the same mass they will NOT always end up at the same height.  Two objects that are the same mass wil find a point where they are pulling on each other with the same amount of force.  Thats point isn't always necessarily where the two objects are even in height.  When the athlete pulls on the rope he is exerting a foce upon both the rope and the sack of sand. This creates a tension in the rope that is greater than gravity.  On the sack this force cause the tension force in the rope to become greater than gravity, therefore pulling the sack of sand into the air.  On the person, they are pulling down towards the ground, therefore the force is not counteracting gravity.  Therefore the athlete would stay in place while the sack of sand would rise.  And if the man were to stop pulling on the rope, the two objects would remain where they are because both are exerting an equal force on the other.

Sunday, 23 September 2007 - 8:39 PM EDT

I agree with Mr. Celona and Mr.Folmar's conclusion to this question. What they are saying seems to make more sense to me then Special Relativity’s explanation. I remember the discussion we had during class and I even listen to Matt when he continued to try and explain it after class and I still wasn’t convinced. So I am going to stick with my original answer of they both accelerated upward and are at the same level.  When I think about how Newton’s Second and Third law apply to this situation it only seem to confirm my answer. Since they both are the same weight and they have the same forces acting on them. We can say according to Newton’s second that they will accelerate at the same rate and will accelerate upward in this situation.  Now when I think about how Newton’s third law applies to this situation we know that when the man pulls on the rope and the sandbag will an exert equal force in the opposite direction.  So it only makes sense that they would be at equal levels on the rope as the man climbes the rope since they have equal forces acting on them.  I just want to say that special relativity’s argument was very well thought out but, it just seems like he or she is over complicating this problem with their thought process. I think that he or she is reading too much into the fact that there is a pulley in the problem.

Sunday, 23 September 2007 - 8:50 PM EDT

I honestly don't think there is going to be an end to this argument until it can be replicated on a scale level. The guy ascends say 10 meters and by doing so the bag also ascends 10 meters from the extra force required for the man to lift his body weight. The rope on his side moves down 10 meters and the bag on the other side moves up 10 meters but by moving up 10 meters the rope on the bag side is now 10 meters shorter than it was in the beginning. That extra rope has gone over the pully to the side with the man on it and has caused the man to go back down the amount that he climbed up to begin with. I can somewhat understand the way it works from a free body perspective, but once you factor in that extra rope going over the pully it makes the free body diagrams logic seem more hazy. And that's all i'm saying.

Sunday, 23 September 2007 - 8:56 PM EDT

Hi all,

I would just like to clearify, once again that I agree with Mr. Celona's answer, although he and I did not originally understand this.  We were arguing two different points.  My point has to do with the relative motion, which is pretty much an unecessary element to the problem.  However, I am sure those clear thinkers out there will understand and appreciate my point.  Why just think about a situation on the basic level?  If we all did that, science would never advance (although I still admit it wasn't necessary to answer the problem).

Sunday, 23 September 2007 - 9:04 PM EDT

You're wrong about the tension. As the athlete pulls he creates more tension on the bag causing it to rise. Because  the tension on his side of the rope increases, the tension on the other side increases as well. Because there is extra (and equal) force on both and less rope, they should boh rise by the same amount.

Sunday, 23 September 2007 - 9:40 PM EDT

First and foremost, we absolutely need to test out this situation to be one hundred percent sure on the answer.  Anyway, it is hard to look past Chris' argument citing Newton's Second Law, which concluded with both objects accelerating at the same rate.  Now, since the question does indeed ask for a discussion of the motion relative to both the ground and the rope, that must be discussed as well.  In this case, I do believe that the athlete and the sack of sand will accelerate at the same rate relative to the rope, however, I do not believe that they will accelerate at the same rate relative to the ground.  In fact, relative to the ground, I don't think the athlete will move at all.  My evidence for this comes mainly from special relativity's argument as well as a diagram of the the situation that was shown to me by special relativity.

Sunday, 23 September 2007 - 9:58 PM EDT

In the argument of the bag and athlete's position with respects to the ground I don't believe they will be the same height. If the sand bag is pulled on with enough force to make it move x meters then the bag will be x meters above the ground and that x meters of rope will be moved to the other side of the pulley because thats how much force was acted on the bag. Therefore I disagree with theory that the x meters of rope will be distributed equally on either side of the pulley. So for the athlete to be in the same position as the sandbag with respects to the ground the athlete would have to climb the initial x meters and the x meters that was shifted over to the other side of the pully meaning they would be moving at two different speeds to maintain the same position with respects to the ground.

Sunday, 23 September 2007 - 10:02 PM EDT

Im going to be completely honest Mr. Celona im very very confused by the question. But to my understanding i agree the most with joe, because once the x meters of rope goes over the one side it transfers to the other side with the athlete so relative to the ground he will not have the same acceleration as the bag relative to the ground.

Sunday, 23 September 2007 - 10:20 PM EDT

I think that mathematically, Mr. Cellona's answer makes sense.  If they have the same amount of force and the same mass than both the bag and the person would accelerate equally in relation to the rope.  However, I also think that the person wouldn't move relative to the ground.  Logically it just doesnt make sense to me that they would be able to stay equal with one another.  So I guess I agree most with Correnti.

Monday, 24 September 2007 - 9:10 AM EDT

i completely agree with correnti's proof to why the athlete and the bag would not rise at the same time respectively to the ground.  this is beacause the athlete who is pulling on the rope is bringing that that slack over from the other side of the pulley which means that they would not levetate equally.

Monday, 24 September 2007 - 10:08 AM EDT

sup celoun