I DDWFTTW: Looking for the least confusing explanation

[jbriggs444]

Thanks for your time; it must have been frustrating.It's all down to having a consistent definition of work. I won't waste more of your time looking for 'loopholes'. It makes more and more sense now.

In my post I used a definition of "work" in terms of the dot product of a particular force times the displacement of the material of the target object at the interface where that force is applied.

It is also possible to define "work" in terms of the dot product of the net force on the target object times the displacement of the target object as a whole.

The former may be called "mechanical work". The latter is called "net work". Mechanical work is the one that is properly suited to tracking mechanical energy flows.

The distinction between the two is crucial when contemplating scenarios involving tires on road or wire on winches. Or, for that matter, Black Birds on lake beds.

If one is dealing purely with rigid non-rotating bodies then the distinction between the two sorts of work is pretty well nil. I managed to skate through school without ever worrying about it.

 

[A.T.]

It makes more and more sense now.

But does it make enough sense to you to answer the orignal question?:

In case A2 (rest frame of the cable), since the motor cannot power the torpedo via a static cable, where does the energy from the motor go to?

Note that I basically gave the answer away when I pointed you to the question:

But in frames where the Earth is moving, the work done on the Earth is not negligible, compared to the work done on the much smaller object. See for example my question about the Brennan torpedo:

You then started out very well:

The ground is moving (in the cable frame).

You also got additional hints:

Think about the forces exerted by the whole motor assembly on other objects. Aside of the wire, what is the motor assembly exerting forces on? Are those forces doing work?

All you have to do is to apply the definition of work:

Work is the vector dot product of the force across an interface and the displacement of the material of the target object at the interface.

 

[rcgldr]

And here is a question to ponder: In case A2 (rest frame of the cable), since the motor cannot power the torpedo via a static cable, where does the energy from the motor go to?

The energy goes into accelerating (rotating) the earth forwards and increasing the earth's kinetic energy (with respect to the cable). Since the earth has a huge mass, the rate of acceleration is very tiny. Prior posts already mention work done on earth equals force applied by motor times distance the earth rotates. This work shows up as an increase in kinetic energy of the earth (with respect to the cable). Consider the motor as part of the earth since it is attached to the earth.

I posted about the 1877 Brennan Torpedo in one of the earlier threads (2011) also noting that if the wires were attached to posts, the torpedo would move downstream faster than the stream.

https://www.physicsforums.com/threa...dressing-common-questions.562993/post-3690588

I posted essentially the same thing in a later thread in 2012:

https://www.physicsforums.com/threa...dressing-common-questions.562993/post-3883574

 

[A.T.]

We are looking at energy flows, not causation chains or information flows. They are not at all the same thing.

Conflating causation with energy flow is indeed one of the most common mistakes, that leads people to get the DDWFTTW brain teaser wrong, and conclude it's impossible or some sort of perpetuum mobile. Instead of simply applying the definition of work, they go in circles trying to determine what causes what in a mechanical feedback loop.

 

[A.T.]

Steve Mould made a great video on the Brennan torpedo, the probably first practical guided missile, which used a propulsion system based on the same principle as the DDWFTTW carts.

Here a great 3D animation with details of the actual Brennan Torpedo. A lot of additional engineering was needed to make it work as intended: