Yes, Brian-M !
Works both ways, all points. The problem is not with the principle, or my understanding, but with interpretation and its consequences.
I'm going to make one last attempt at explaining the frames of reference thing to you. If you still don't get it after this, I just don't care any more. You're on your own.
Yes, I have appreciated your effort. No problems engaging with you.
There is no such thing as absolute velocity.
There is no such thing as zero velocity either.
Velocity only exists relative to something else.
When we measure velocity, we have to choose what velocity we want to call zero when measuring the velocities of other objects. Normally we choose to call the velocity of our local environment zero, for convenience. On the ground, we use the velocity of the surface of the earth. In a plane, we use the velocity of the plane. In a train, we use the velocity of the train.
<snip>
Agreed. This argument is for the "principle of equivalent relative velocities". I have no problem with that.
Situation A:
A skateboarder is standing stationary to the road on his skateboard. A West-bound car is headed toward him at 60 mph. Because the skateboarder is moving at 0 mph relative to the road, we'll set our frame of reference to 0 mph relative to the road (reference A).
Situation B:
A skateboarder is travelling 60 mph East on his skateboard, heading toward a stationary car. Because the Skateboarder is moving at 60 mph East relative to the road, we'll set our frame of reference to 60 mph East, relative to the road (reference B).
In situation A from reference A, the skateboarder appears to be stationary and a car appears to be travelling West at 60 mph toward him. In situation B from reference B, the skateboarder appears to be stationary and a car appears to be travelling West at 60 mph toward him.
In situation A from reference A, the skateboarder is struck by the car, which imparts exactly enough kinetic energy into him so that he is now travelling West at 60 mph. In situation B from reference B, the skateboarder is struck by the car, which imparts exactly enough kinetic energy into him so that he is now travelling West at 60 mph.
You'll notice that in both situations, using a frame of reference equal to the skateboarder's initial velocity, the exact same thing happens, and the exact same amount of energy is imparted to the skateboarder from the car.
You'll also notice that in situation B, when the skateboarder struck the car, the frame of reference continued to move at the skateboarder's initial velocity. A frame of reference does not change velocity, even if the object it was originally based on does.
Newton's laws of motion are symmetrical. No matter what frame of reference you look at an event, the results are always the same.
Your idea that a car colliding with a person is somehow different from a person colliding with a car, or that a ball colliding with a house is somehow different from a house colliding with a ball, violates the symmetry of these laws.Newton's laws of physics work the same no matter what frame of reference you are using, and identical situations produce identical results.
If a cart is moving downwind at wind speed in a 10 mph Westerly wind, using 10 mph West relative to the ground as your frame of reference: the air is motionless, the cart is motionless and the ground is moving 10 mph East. If a cart is stationary on an indoor treadmill with a belt moving 10 mph East, using 0 mph relative to the ground as your frame of reference: the air is motionless, the cart is motionless and the ground is moving 10 mph East.
The situations are identical and the results will be identical.
This is where we differ.
Of course I agree that Newton's laws apply in both cases, and from the view of relative velocities, A hits B is the same as B hits A, but not any A hitting any B.
A large mass hitting a smaller mass is not the same as a smaller mass hitting a larger one. The difference in momentum alone means that the outcome will be different.
1.With respect to their relative velocities, when a person hits a car, each has an equivalant view.
2.With respect to their relative velocities, when a car hits a person, each has an equivalant view.
But not that (1.) and (2.) are equivalent. They are different events.
This appears to be the problem. The conclusion seems to be 'If two objects have equivalant velocities, they are equivalent in all properties'.
Other poster's opinions;
Roadside observer and driver may claim to have "equivalent relative velocities", but that does not mean that the driver can insist that his
velocity is zero, and the ground is moving beneath at 60mph, because the car would have to be capable of rotating the entire planet.
"Equivalancy" means that the car is bound to the Earth, by the same means and forces, as the Earth is bound to the car. Our participants will
also agree that the Earth is a planet, a car is car, and that a road is not a treadmill.
"Two things may be relative to each other but common to a third, and at the same time"
Practically though, the problem is not about "frames of reference" but of the accuracy and completeness of the model.
Other treadmills:
A dyno does not consider or model the car's kinetic energy. It is recognised that it is excluded from the model (frame?). The only concern is the engine's power, so it is a valid simplification to dissipate the engine's power as heat, while the car is at rest. But it does model a realistic load.
In aerodynamic tests, the vehicle is tied down, so the engine's power and the vehicle's kinetic energy are not modelled. This too is a valid simplification, because the only concern is airflow over the body. The tunnel may not completely emulate wind, and have boundary conditions, but these innacuracies are minimimized or accountable. But it does model air flow over a car. (F1 car designers are after the tiniest improvements, so they may well run their aerodynamic tests on a dyno at the same time.)
This treadmill is quite different, so where was the math, the structure that validates the simplification? However, it really did turn out to be the simple arithmetic subraction of V_wind.!
What exactly does the treadmill demonstrate, then?
The thought experiments;
The treadmill is in a van travelling at windspeed. See, it predicts the correct behaviour.
What would indicate a failure, and how would it be explained?
I have said it N times. The cart on the treadmill is no a model of the real cart, even in principle, because there is no wind, and it cannot be inferred to exist.
The treadmill;
If you are still not convinced, then perhaps the difference is best described as a phylosophical.
But what effect does that have on the treadmill? It causes you to come to the wrong conclusion regarding the working of the cart.
(One of the first questions asked by new posters "Which way do the prop/wheels turn?")
It is not possible to conduct a valid test without kinetic interaction with the wind. A real wind.
I can show you why.
Both you and Myriad, think that I am deceiving you in some way with my force balance idea. Well, no.
How does is move up the belt? Here's one way.
Thrust 2n <-- X --> Drag 12n
\
\
---------------
| Gears |
---------------
0 0
-------------------------------------------------
Belt <---------- 10n (friction)
(The wheel/prop forces are locked int opposition, due to the gears.
I divided the prop force into two forces this time; "more drag" alone qualifies, perhaps clearer this way)
The cart is in balance. Now, reduce the friction with the belt. Now the "thrust" component of the propeller's output can push the cart to the right. But if the wheels are not providing power, where does the thrust come from? The prop will continue to turn from momentum ( as seen on the video) and that is more than enough.
The cart moves up, friction is regained and lost momentum restored, until the next time. There is no "next time", because the process is essentially continuous. You can see that the cart is barely in contact with the belt. It's floating on friction, and the laminar flow of the air close to the belt surface. (The bigger one is similar, but its mass makes a difference in how it behaves in detail.)
Because of the relation between friction and available (useful) torque, I would expect the cart would move faster on a steeper slope because the load is greater. If that results in a bigger residual imbalance, then it would go faster. If you want a complete force-by-force analysis, then that would be complex analytical task, and more data would be needed...by someone else.
Perhaps you agree, or think that is OK, because the prop does provide thrust. Yes, but it is limited. The treadmill tries to maintain the driving force at a minimum, obviously (hopefully) not like the real cart.
Do another 'experiment'. Place your finger on the prop shaft to generate a little friction, so as to do some work. Now, the power to meet that work will come from the belt. The forces within the transmission and at the wheels will rise, but all of the power taken from the belt does work only at the finger, so the car should not move. Generally, the only forces within the cart's transmission are due to residual frictions and drag.
Why is this happening? I implied that the only source for the work done on the finger comes from the treadmill, but it shouldn't be; I should be able to get it from the wind, but it just isn't there.