Kinetic Energy Paradox: What Went Wrong?

[Gokul43201]

Were you never at school when they said "simplify be ignoring friction losses"? Come on, you're playing dumb now. You know full well they tell you to ignore it to make it easier.

I'm absolutely not playing dumb. There is a very clear distinction between ignoring losses due to friction (which is what we should do in this problem) and ignoring friction itself (which we can not do). In a pure rolling friction there is no dissipation (much like static friction), so by assuming a rolling friction without any kinetic component, we are indeed ignoring losses due to friction without actually ignoring the rather important role that friction does play.

Why don't you answer my earlier question: if there is no friction, where in your free body diagram is the external force that causes the car to accelerate?

 

[JaredJames]

I'm absolutely not playing dumb. There is a very clear distinction between ignoring losses due to friction (which is what we should do in this problem) and ignoring friction itself (which we can not do). In a pure rolling friction there is no dissipation (much like static friction), so by assuming a rolling friction without any kinetic component, we are indeed ignoring losses due to friction without actually ignoring the rather important role that friction does play.

Why don't you answer my earlier question: if there is no friction, where in your free body diagram is the external force that causes the car to accelerate?

Ah I see, I thought you meant friction loses.

 

[rcgldr]

Trying to get this thread back on track. If the road itself is used as a frame of reference, then there is no perceived change in the kinetic energy of the earth, and all of it goes into the car. Also the application of force to accelerate the car is occurring between the tires and the road, so the road is the appropriate frame of reference.

If a frame of reference with a speed relative to the road is used, the the energy change of the road/earth needs to be taken into account for the total change in kinetic energy of Earth and car to equal the chemical or electrial potential energy of the fuel converted into kinetic energy by the engine.

This same subject has been brought up twice recently. Take a look at post #3 of this thread:

https://www.physicsforums.com/showthread.php?t=464859

 

[JaredJames]

Perfect rcgldr.

I think we're all on the same track now.

So yeah, you have to take into account the train - as demonstrated in post 3 (of that thread) there I believe.

Perhaps you could bring your first post there over because that would answer this nicely.

 

[rcgldr]

So yeah, you have to take into account the train - as demonstrated in post 3 (of that thread) there I believe.

Not so much the train itself, but the trains frame of reference, since it's speed relative to the road and surface of the Earth is non-zero. The mass of the train can be be ignored when considering the total mass of the earth, since it's such a relatively tiny component of the total mass.

 

[JaredJames]

Not so much the train itself, but the trains frame of reference, since it's speed relative to the road and surface of the Earth is non-zero. The mass of the train can be be ignored when considering the total mass of the earth, since it's such a relatively tiny component of the total mass.

Trust me, my wording may not be clear but I do understand. You only have to read back through my posts and you'll see I'm discussing the trains frame of reference - it's speed relative to the car has to be taken into account etc etc.

I think this has been answered well enough now.

 

[Dale]

It doesn't, which is the point.

If the train is doing 100 and you ignore this - as paul did - then it appears the car has gone 200 to 300, which from the trains perspective it may have. But we're talking about the fuel used by the car, and the car hasn't used the fuel to get to 300. It used the fuel to get to 200. Any additional apparent speed is down to the trains motion.

If you took the car to be traveling at 300 from the trains view, then yes it would have the relevant KE. But, again we're not talking about that.

The question is regarding the cars fuel use in stage 2. So we're looking at things from the cars point of view and any effects the train grants to the car are irrelevant so far as the cars fuel use goes - so you must allow for any effects the train has.

The car during stage 2 is traveling at 200 from it's point of view. It's fuel got it to that point. Now, the fuel did not get it to 300 - which means you can't work out the energy requirement to 300 and claim its the fuel required for stage 2. The fuel requirement to go from 100 to 200 =/= 200 to 300 so Paul working out the latter is not correct for how much fuel is required by the car for stage 2. He is ignoring the fact the train is allowing the car to travel at 300 - not the fuel of the car.

You are missing the point of the question. The point is that Newton's laws are invariant under Galilean boosts, this is known as Galilean relativity. You can do the analysis just fine in the train's reference frame, you do not need to do the analysis in the ground's reference frame. The physics is the same. The only difference is the KE of the ground and the speed of the car.

The KE of the train is not relevant because the train does not interact with the car at all, consider a super-massive train and a super-light train it does not change the problem at all. Now, consider a super-massive ground (normal) and a super-light ground, the problem changes significantly because the car interacts with the ground.

The car gains more energy in the train's frame than in the ground's frame. That additional energy comes from the KE of the earth.

EDIT: never mind, I see we all agree from the intervening posts

 

[JaredJames]

DaleSpam,

The car's fuel use is the same in either case correct? Of course.

In which case, no matter which method you use (correctly) you will end up with the same required fuel for the car. Do we have that? No.

I'd point out that in the quote you used from me I note there would be a difference in KE of the car for the relevant speeds.

 

[Dale]

In which case, no matter which method you use (correctly) you will end up with the same required fuel for the car. Do we have that? No.

Correct. My point was only that the reason is because Paul negelcted the KE of the earth, not because Paul neglected the KE of the train. The KE of the train is irrelevant.