my father swears that a tank tread travels twice as fast on the top as it does on the bottom due to the fact that it is not moving on the ground. can anyone please help solve this .

Couple things to ponder regarding this one. First, does a tire spin faster at the top than the bottom since the bottom is touching the ground? Also, does the tread get all bunched up at the end of its top run or is there a large accumulator like at a printing plant that allows the changing of rolls without stopping the line? Think about those and the answer should materialize.

Starting multiple threads on the same topic is frowned upon... and won't change my answer.

my bad, I just wanted to make sure I had it in the correct forum

It would break if that was true.

It depends on your point of view.

If you are on the tank then the top and bottom are moving at the same speed but opposite direction.

If you are on the ground as the tank goes by, the bottom is stationary and the top is moving in the same direction as the tank but at twice the speed.

The tank tread doesn't care what your point of view is. It's really no different than considering a wheel. The whole wheel is moving at the same rpm. Saying the free side is moving faster than the traction side relative to the ground or the vehicle is misleading and can cause confusion.

It shouldn't. hawkmage's statement is correct, as is nonmythicaldragon's. If people cannot understand the relatively simple concept of relative velocity then they should learn about it, especially if you are going to be posting on a page whose title is "Science and Myth Questions".

In RPM, yes, they are moving the same speed...but not in relative speed to the ground. The bottom is technically moving far, far slower than the top, relative to the ground. this is true of tires as well.

quote:

The whole wheel is moving at the same rpm.

rotation is not the same as travel speed. A wheel can rotate and not travel at all, by spinning in place. Any individual portion of the wheel examined is traveling (albeit in a circle), and the wheel as a whole is stationary but spinning.
It may help to think of a tank tread as composed of many individual links composing a belt, similar to a chain composing a loop. Some links (those on the top of the belt) are moving forward twice as fast as the tank itself. Some links (those touching the ground) are stationary. (We use the ground as the reference for "speed", else it makes no sense to even talk about how fast the tank is traveling.)

Another example might be race cars running around a closed track. The race as a whole takes place in a specific location and certainly does not move. The individual cars do move, though within the bounds of the track.

Taken as a whole the tank tread is moving at the same speed as the tank relative to the ground. The top of the tank tread doesn't get 40 miles down the road any faster than the bottom.

quote:

Originally posted by srmarti:
The tank tread doesn't care what your point of view is. It's really no different than considering a wheel. The whole wheel is moving at the same rpm. Saying the free side is moving faster than the traction side relative to the ground or the vehicle is misleading and can cause confusion.

All motion and measurement of speed and velocity is relative so your point of view matters. What is the speed of the tread with respect to a person in a jet flying over head at 500MPH or someone standing on the moon. What about with respect to an ant on the tread?

If you look your example of a wheel the part of the wheel that is in contact with the road is not moving.

quote:

Originally posted by srmarti:
Taken as a whole the tank tread is moving at the same speed as the tank relative to the ground. The top of the tank tread doesn't get 40 miles down the road any faster than the bottom.

Your reference point is the ground. That is because from your reference point about half the time a section of the tread it traveling at twice the speed of the tank and the other half it is stationary averaging out to the same speed of the tank.

I understand what you're getting at. But the top of the track doesn't travel a mile along the reference ground in half the time the bottom does. It's all one track.

That's only true when the distance traveled is a multiplier of the total length of the tread.

If the tread has a circumference of 10 ft(to make this easy) and the tank moves 2 feet, the top has moved 4 feet and the bottom hasn't moved(the exception is the small part that became the side).

If the tank moves 10 feet, then half the time the top is moving twice as fast and then the other half the time it becomes the bottom and doesn't move at all, so they average.

If the tank moves fifteen feet, then one part of the tread has moved 20 feet, the other part has moved 10....another five feet and they are averaged out again....Basically every time the tank moves half the tread circumference, the top of the tread moves that distance AND the distance from the back of the tread to the front(thus doubling the distance travelled)

It's a lot like a game of leapfrog...the overall speed of the pair is half that of what the individuals move when they jump, but half the time they stop moving at all.

NOT TRUE hee hee

My god, I can't believe what I am reading, Thank you srmarti and smorpy for not making this any more difficult than necc. It is all travelling at the same speed, period.

you are WRONG. The question is "does the top of the tank tread move twice as fast as the bottom"

the simple answer is NO. the slightly less simple, but still correct answer, is "No, it moves twice as fast as the tank, the bottom doesn't move at all" when relative to the ground.

The answer "Yes" or the answer "No, they move the same speed" are NOT correct when speaking relative to the ground.

The part of the tread on top will always be moving twice the speed of the tank, so long as the tread is actually moving the tank. When the piece rotates to the bottom, it is no longer "the top" and therefore is no longer moving twice as fast.

Imagine you were standing on the back of a tread that was ten feet long. the tank moves forward ten feet. You would then have moved ten feet for the movement of the tank, AND ten feet further forward on the tread. That means you'd have moved 20 feet, twice as far as the tank, in the same amount of time. By definition, that means you moved twice as fast.

We are not making it more complicated than necessary, we are answering the spirit of the myth. YOU are trying to oversimplify the question.

This is one of those cases where the big picture is different from the little picture:

when looking at the big picture, the tank track is moving at the same rate as the rest of the tank: the whole shebang gets where it is going at more or less the same time.

when looking at the little picture, the frame of reference becomes a factor: in the small picture, when referencing by ground speed, Gojan's leapfrog example becomes valid. each track tread "shoe" alternates between moving faster than the whole and moving slower than the whole, as the tank travels; to maintain the same average speed.

If you place a board on top of the tank tread, and drive the tank forward, the board will travel faster than the tank, until it falls off. then it will travel slower.

quote:

Originally posted by srmarti:
I understand what you're getting at. But the top of the track doesn't travel a mile along the reference ground in half the time the bottom does. It's all one track.

Actually from your response either you do not understand or you are being purposefully argumentative.

Lets make some assumptions, lets say that the tank tread has a length of 22 meters and a distance between the front and rear axle of the wheels that the tread is on is 10 meters and the wheels have a circumference of 2 meters.

Start by marking the ground where the front and rear axle are. Also mark the tread above the back axle and below the front axle you will get something like the first ASCII picture.

Picture #1

 0m       10m      20m
 |        |        |
 x_________
(          )
 ---------x

Move the tank forward 5 meters and you will get something like picture #2 where the two marks are one above the another. The mark on the top part of the tread is now 5 meters from the rear axle but is 10 meters from the mark on the ground where is started. The mark on the bottom part of the tread is now 5 meters from the front axle but is still right next to the mark on the ground where it started.

Picture #2

 
 0m       10m      20m
 |        |        |
     _____x____
    (          )
     -----x----

Move the tank forward another 5 meters and you will get something like picture #3 where the mark on the top of the tread is now above the front axle and the bottom one is under the rear axle.

So now the mark on the top of the tread is 10 meters from the rear axle and the rear axle is 10 meters from the mark where it started so the the mark on the top of the tread is now 20 meters from the mark on the ground where it started.

The mark on the bottom tread is now 10 meters behind the front axle but still next to the mark on the ground where the front axle started.

Picture #3

 
 0m       10m      20m
 |        |        |
          _________x
         (          )
          x---------

Looking at this from the marks on the ground. The tank moved 10 meters and mark on the top of the tread moved 20 meters in the same amount of time the top of the tread is moving at twice the speed of the tank. And the bottom of the track did not move at all.

Looking at this from either the from or rear axle each of the marks on the tread moved 10 meters but in the opposite direction so the speed of the top and bottom tread marks have the same speed but opposite direction.

So if you follow this to its conclusion once the tank moves another meter the whole process starts over again but what was the mark on the top tread becomes the one on the bottom. So that in the next 10 meters the mark that was on the originally on the bottom moves the 20 meters forward while the other is stationary.

If the tank is moving at 10 meters/second then while the mark is on the top it is moving at 20 meters/second and stationary when it is on the bottom so it is averaging 10 meters/second.

quote:

Originally posted by: GojanTorresque
you are WRONG. The question is "does the top of the tank tread move twice as fast as the bottom"

I agree that if you looks at the exact wording of the question you are correct no mater if you look at the situation from the perspective of the ground or the tank the top tread and bottom of the tread will not be traveling at twice the other.

It is true from the perspective of someone moving along the same direction of the tank but at 2/3 the speed of the tank. For example a tank moving at 30 m/s and a motorcyclist moving at 20 m/s the top of the tread would be moving at 40 m/s forward and the bottom would be moving at 20 m/s backwards.

So it does depend on your point of view.