Bulldozing for fun and profit

[fishbait]

I was watching a guy push some dirt around with a bulldozer the other day and noticed something that puzzles me.

The bulldozer has two continuos tracks, one on each side. Each track consists of several links which are all connected and move necessarily in unison.

Here's what puzzles me: If the bulldozer was raised up with no contact with the ground then the entire track will move at a constant speed, that is, the top part of the track that is moving forward will move at the same speed as the bottom part of the track that is moving rearward. In other words, if we look at one link in the track, it will move at a continuos constant speed regardless of where it is relative to the whole track. Since they are all connected, if one link moves at 5 MPH then they all move at 5 MPH.

Now, place the bulldozer on the ground and start it moving. The link we are watching is on the top part of the track moving forward at 5 MPH. It continues at 5 MPH until it moves around the front sprocket and, upon coming into contact with the ground it stops instantly! ALL the links in contact with the ground are at a dead stop! The links not in ground contact continue on at 5 MPH until they come into ground contact at which point they stop instantly. As our 'test' link is taken up by the rear sprocket, it instantly resumes a speed of 5 MPH!

Now, the qustion that I could not answer clearly is this: If all the links are connected and the sprockets are driving the track at 5MPH, how could some links be moving at 5 MPH and others at a dead stop? It makes intuitive sense when I don't think about it, but when I try to explain why it is this way I am baffled.

 

[rwald]

Simple. As you noted, when the bulldozer is in the air, all of the links are moving at 5 MPH with respect to the bulldozer. And this remains true when the bulldozer is on the ground. However, when the bulldozer is on the ground, the bulldozer itself is moving with respect to the ground. Specifically, it is moving at 5 MPH forward. So, if a rock is just sitting on the ground, and the bulldozer is moving at 5 MPH forward, than the rock is going backwards at 5 MPH with respect to the bulldozer. Likewise, the track on the ground, though they go at 0 MPH with respect to the ground, go backwards at 5 MPH with respect to the bulldozer.

A side note: Do you think that the links on the top of the bulldozer are still going at 5 MPH when the bulldozer is on the ground? If the bulldozer is moving forward at 5 MPH with respect to the ground, and the links are moving forwards at 5 MPH with respect to the bulldozer, than the links are moving forwards at 5 MPH with respect to the ground. So, in a funny way, motion is conserved: Even though the links on the ground are stopped, the links on the top go twice as fast.

 

[Zep]

Because the links all stretch at 5mph when they on the ground.

No, this is purely a matter of relativity.

ONLY IF YOU STOOD ON THE BULLDOZER would the links be doing 5mph forward on the top and 5mph backwards on the bottom, regardless of whether the track is on the ground or not. Their RELATIVE difference is 10mph.

But you are standing off the bulldozer, and you will see the treads going forwards at 10mph on the top, the bulldozer moving forwards at 5mph, and the treads at zero mph on the bottom, thus maintaining the RELATIVE speed difference.

So...what would be the view if you were one of the tread links???

Zep

 

[fishbait]

Because the links all stretch at 5mph when they on the ground.

No, this is purely a matter of relativity.

ONLY IF YOU STOOD ON THE BULLDOZER would the links be doing 5mph forward on the top and 5mph backwards on the bottom, regardless of whether the track is on the ground or not. Their RELATIVE difference is 10mph.

But you are standing off the bulldozer, and you will see the treads going forwards at 10mph on the top, the bulldozer moving forwards at 5mph, and the treads at zero mph on the bottom, thus maintaining the RELATIVE speed difference.

So...what would be the view if you were one of the tread links???

That was my next question. I'm sitting here trying to do a 'though experiment" of riding on the track. I'm riding on one link and the dozer is off the ground. Around and around I go at a constant speed. The dozer is then placed on the ground and all of a sudden I stop then start then stop....

 

[rwald]

Well, if you were one of the links, than you never move. You're always stationary. It just looks like things move around you.

To whit: When the tractor is in the air, you would see the tractor moving around you. Nothing else. When the tractor is on the ground, you would see the tractor moving forwards at 5 MPH as the ground stays stationary, then the tractor and ground would start going down (and the ground would go backwards a bit), then the tractor would start going backward at 5 MPH while the ground is going backwards at 10 MPH, and then the tractor and ground would both drop down (and the ground would go backwards a bit).

That clarify things?

 

[fishbait]

Well, if you were one of the links, than you never move. You're always stationary. It just looks like things move around you.

To whit: When the tractor is in the air, you would see the tractor moving around you. Nothing else. When the tractor is on the ground, you would see the tractor moving forwards at 5 MPH as the ground stays stationary, then the tractor and ground would start going down (and the ground would go backwards a bit), then the tractor would start going backward at 5 MPH while the ground is going backwards at 10 MPH, and then the tractor and ground would both drop down (and the ground would go backwards a bit).

That clarify things?

Well, I always did have a grasp of the relative relationship of track, dozer, and ground. What bugs me is that it just seems so weird when you look at the thing in operation. I do appreciate your explaination though. Yours has more clarity than mine.

 

[xouper]

Another point that maybe needs clarifying:

fishbait: Now, place the bulldozer on the ground and start it moving. The link we are watching is on the top part of the track moving forward at 5 MPH. It continues at 5 MPH until it moves around the front sprocket and, upon coming into contact with the ground <span style="background-color: #ffa">it stops instantly</span>! ALL the links in contact with the ground are at a dead stop! The links not in ground contact continue on at 5 MPH until they come into ground contact at which point they stop instantly. As our 'test' link is taken up by the rear sprocket, it <span style="background-color: #ffa">instantly resumes a speed of 5 MPH</span>!

The change in link speed is not instantaneous. It only appears to be instantaneous because you are changing the frame of reference at those instances. If you keep to one frame of reference, the speed does not jump instantaneously. For example, as previously noted, if the reference is the ground, then the link makes a smooth transition from 0 mph to 10 mph and vice versa. Also already noted, if the reference is the dozer, the speed of a link is a constant 5 mph. it's only when you switch back and forth between these two references that the speed seems to "jump" instantaneously. If that was already clear, then never mind.

Another example, put a red dot on a bicycle tire and compare the relative motion of the red dot using the ground as a frame of reference, and also from the axle as a reference. For more on this and to see an animation of the red dot:

http://mathworld.wolfram.com/Cycloid.html

The motion of the red dot is called a cycloid. But the accelleration of the red dot is a sine curve (not shown).

 

[fishbait]

Thanks for your post and the site reference.

I do understand that the stop and start is not instant but only appears that way. I should have been clearer in my first post. (And should have read Moby Dick with greater attention!)