The discussion centers on the implications of setting the distance variable \( r \) to zero in the gravitational formula \( F = \frac{(k)mm}{r^2} \). It is established that mathematically, this leads to a singularity where force \( F \) approaches infinity. However, in practical terms, two masses cannot occupy the same space, making the formula inapplicable at \( r = 0 \). Instead, as \( r \) approaches zero, \( F \) grows without bound, but real-world constraints and quantum mechanics must be considered for very small distances.
PREREQUISITESStudents of physics, mathematicians, and anyone interested in the intersection of classical mechanics and quantum physics will benefit from this discussion.
But In reality i can have two mass put in r=0.000001mBvU said:That's what happens with the formula. In reality you can't have two masses in exactly one place, so the formula isn't endlessly applicable...
Mathematically you have a singularity.
garylau said:What happen if i put r=0 into the formula F=(k)mm/r^2then F= infinite large in mathematical sense?
is that statement correct to say F is infinitely large?
Well, the masses become smaller too for such small particles. One micron diameter with a reasonable density gives a very small mass !garylau said:But In reality i can have two mass put in r=0.000001m
So the force still become very large?
is it possible that the mass is very large but the r is very small?BvU said:Well, the masses become smaller too for such small particles. One micron diameter with a reasonable density gives a very small mass !
On even smaller scales still other things happen. Protons, for example have a mass of only 1.67 10-31 kg and a diameter of 0.88 10-15 m. At such small scales other kinds of forces are much stronger.
Yes. Moreover, in quantum physics mass is, in a certain sense, proportional to ##1/r##.garylau said:is it possible that the mass is very large but the r is very small?
Yes, then you get a very large force. But it is always finite. And if you want to put the masses too close, you have to consider quantum mechanics where the simple approach with a well-defined distance fails.garylau said:is it possible that the mass is very large but the r is very small?