Humber,
The "closing speed" is used in various areas to discuss the idea of how fast it appears that the relative speed between two objects is changing.
A reference, if you please. There is no closing velocity in this context.
Like Sol and Spork you are confusing a constantly changing distance with a constant speed.
This is a semantics issue and not an issue in understanding.
No, it is black and white.
So even though the cars pass at 120 mph, the instantaneous distance between them is not increasing or decreasing at that point so the "closing speed" is 0mph.
The distance is zero.
On Collision courses the closing speed always is the relative velocity of the two objects.
Try looking that up.
On non-collision courses between two objects, the closing speed is a function of velocity of the objects and the path they are on and are not numerically equal except at infinity so this was why Spork made his comment to highlight this subtlety.
It was nonsense disguised as erudition, and tarted up with talk of dimensions, which makes no sense anyway. One dimensional cars. Might be difficult to measure that distance.
With regards to this issue, I think you missed the point of Spork's video in the car. For a NB balloon, the balloon occupies a space that air would normally have occupied.
So, rises because the denser air replaces it.
The air weighs the exact same as the balloon that is occupying the space.
The balloon is less dense, so has less gravitational force for the same volume.
That's how a ship floats.
This is why it is neutrally buoyant. Once this is understood the issue becomes clear: It's an old Jedi mind trick of one's own brain.
More like Imperial Stormtrooper.
This is why the balloon in the car demonstrated the "torque effects" illustrated.
And after I pointed out that balloons may have lift due to the Magnus effect.
A face-saver.
So, the point was that the NB Balloon is behaving just like the air that would normally occupy the same volume except for the mass property effects shown.
No, even air takes time to accelerate. There are several means of calculating the horizontal velocity of a weather balloon, assuming it can be coaxed to fly horizontally without rising. The simplest, I would expect is to use Rayliegh's drag formula and then use the mass of the balloon to provide the time-constant t. Something like this: Vb = Vw - e-t/tau
The balloon will rise exponentially to Vw (but not reach it) and the time t will be related to the acceleration. That is because the driving force falls as the balloon approaches WS, so the acceleration will fall too.
The balloon nor the air in the car reacted instantaneously but it reacted at the same speed as the medium which I believe to be the speed of sound in the media. But since it reacts at the exact same speed of the media in bulk, for the purposes of the discussion, it reacts immediately-same as the surrounding media. This does not imply infinite force contrary to what you stated. This was the subtlety of Spork's video and I'm sure it was hoped by the presenters that "bright" students watching this would observe all these effects and learn something. I can't make the claim to be "bright" but I sure learned something.
All these "subtle" nuances....sure. A brute force and silly show provided by an office manager.
Those "tests" become forced when mathematical and theoretical skill are absent.
With regards to potential energy, the NB balloon has no potential energy with respect to the ground because it occupies a volume containing the equivalent mass of air as the balloon.
PE = m*g*h. A stationary NB balloon has a buoyancy force that is equal to the force of gravity upon it. For an object on top of a ladder, the ladder provides the opposing force. That object still has PE, and so does the balloon.
This is the subtlety that we didn't want to bludgeon most readers with as it is normally assumed it is understood. When questions are asked, it makes sense to explain-or as the phrase goes "Otherwise we'll be here all day!" Sheesh-we sure exceeded that one so maybe its worthwhile after all being initially concise-lesson learned on my part.
How about you didn't think about it until I mentioned it, and Spork put his foot in it?
Rhett has corrected you regarding the KE. Stand corrected, rather than fall over yourself with contradictory exudes, Windgrins.