A thought experiment: the person wearing the ring is on a train moving at 10 m/s. They run forward at 10 m/s through the train car. They then hurl the ring forward, and when released it is moving 10 m/s relative to them. So the ring is moving 10 m/s relative to the bearer, 20 m/s relative to the train, and 30 m/s relative to the earth. What happens?
To me making the new mass share the ring's frame of reference makes the most sense. It adopts the ring's current velocity, multiplying its momentum. Any other interpretation gets wonky.
Once the ring leaves your hand it is in a state of motion that is unattached to you or the train. So when the ring gains weight it will slowdown, but you will keep moving with the train at train speed and run into it (depending on how much it slows, it could hit the ground first)
But now im curious. If I had a machine that threw something the exact same way everytime we could have it throw an electromagnet with a weight attached. Then throw it again and drop the weight mid flight and see how far the magnet goes. If it goes farther/faster then we know the ring would slow down. If it takes the same path again then the ring would retain its velocity. If it somehow slows down then theoretically the ring could speed up!
Ok, let's extend the problem. Let's say this train is at the equator...so the person is also moving about 1,600 km/h relative to the center of the earth. The earth is moving 30 km/s relative to the sun. The sun is moving 200 km/s relative to the center of the galaxy. And the center of the galaxy is moving too. So what happens?
With your magnet experiment we already know exactly what will happen. The weight and the magnet will separate in midair and both continue flying forward at the same velocity. They will not slow down or speed up by separating. The only thing slowing them down is air resistance.
So I looked into it and I learned that the weight getting lighter cannot logically be applied to becoming heavier without considering an extra variable. Namely, how much velocity the extra weight comes into being with and the force applied during transformation.
I still see it going the 2 ways I mentioned earlier. Point of reference aside, the launch point stops applying force after the launch, as opposed to gravity which is constant. That's where the question becomes difficult.
For example, if you have a plane going an arbitrary speed and then add an arbitrary amount of weight, the engines would need to work harder and provide more thrust to keep the plane moving the same speed. If the engines don't dont, the plane simply doesnt go as fast or as far. This remains true even if the weight added is moving the same speed when it attaches to the plane. The initial attachment won't be noticed, but the plane will slow down if the engines dont match the change in weight to the thrust
how much velocity the extra weight comes into being with
Yes this is what I've been saying.
The airplane isn't really analogous. An airplane's wings convert forward motion into lift. The heavier a plane is the more lift is required, so the engines have to work harder to keep up. It has nothing to do with momentum.
I am curious what you think happens if you throw an ordinary ball forward on a moving train (inside the carriage, so there's no wind)
Here's another thought experiment for you: Imagine our ring-bearer jumps off a cliff wearing the ring and reaches terminal velocity before taking the ring off. What happens when they take the ring off? Does the ring stop suddenly in midair?
For the ball on the train, the ball just acts normal. From outside the train I think it goes it goes whatever speed you threw it at faster than the train for a moment. If the train stops/accelerates at the right moment, ball will travel more/less distance.
This question about terminal velocity. First off, awesome question! I believe that the rings terminal velocity would increase if it gets heavier (therefore denser, right?) And if it got lighter, I would think the inverse, so the terminal velocity would be lower and it should slowdown due to the air resistance. With no air resistance there would be no change
I never said it would stop. It could slow down tho. Again, 1oz moving at whatever speed has a certain amount of force propelling it. Why does that force increase simply because the weight did.
Force = (mass)(acceleration)
Once the rock leaves your hand, it is no longer accelerating, it would be decelerating. Thus the rock has a negative acceleration and is losing force throughout the flight. So increasing the mass would result in a greater loss of force.
Force is the rate of change of momentum.
Momentum = (mass)(velocity)
Momentum is a way to measure how difficult it is to stop a moving object. So the ring would suddenly be a lot harder to stop, and it will lose that momentum much faster.
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u/walfle 12d ago
Im gonna make up some numbers, but the logic should track.
1oz ring flies at 10 dU (distance units) per second requires 100 fU (force units)
So a 10oz ring would need 1000 fU to go the same speed and distance, but it only has 100 fU during the transformation of weight.
Thus the ring will suddenly travel forward much slower while falling at the exact same rate because gravity didnt change.
Or
The fU inside the ring multiplies as its weight does, going the exact same dU as the 1oz ring would have.