- #36
Doc Al
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I did. Of course you must realize for the exercise that these are point masses, not macroscopic objects.schroder said:I think it would be even wiser to stick with the problem as stated : two 1 kg masses starting out (stationary) at a distance of 1 meter.
All measures of PE depend upon a reference point. When talking about the gravitational PE between two point masses (or astronomical bodies), the natural reference point is to take PE = 0 when they are infinitely far apart. You earlier agreed that the gravitational PE between two bodies is given by -GMm/R; that relationship assumes a reference point at infinity.The PE and indeed the total energy they possesses is based on that distance and not on infinity.
Not generally, because you are talking about Earth gravity and you are only concerned about small changes in position compared to the distance to the Earth's center. But if you were to move that rock to a height equal to the Earth's radius, you'd certainly use the more general expression. Or perhaps you want to calculate the escape velocity of that rock, again you'd use the more general expression.When you calculate the PE of a rock held at 1 meter above the ground, you do not reference it to infinity?
In raising the rock a mere 1 m above the Earth's surface, you are only changing the distance to the Earth's center by 1 part in about 6,400,000. That's a realm where you can treat the force of gravity as being constant. Not so when the bodies are going from 1m to "contact". Just to get to within a mm of each other changes the distance between them by a factor of 1000!
Nope. As explained above, over this range the force is wildly nonlinear.The linearization I am using here is valid for a distance of 1 meter.
Again, you are confusing your common sense experience with ordinary objects with this exercise in Newtonian gravity involving point masses.It takes about 27 hours for them to cover 1 meter. Do you really think their velocity is approaching infinity? When that tool bag floated away from the astronaut in space, would it have come back to her at infinite velocity and infinite energy? I am not the one talking nonsense here!