The numerator
This is a variable seperable right?
so you take the N(500-N) to the left side, split the dN and the dt to get:
int[ 1/{N(500-N)} ] dN = int[ 1/5000 ] dt
Now by chain rule (I think), if the differential is on the top of the fraction you can just say it is the log of the...
This is out of a P3 (OCR) textbook so it should be dead easy but I just can't see the answer. I know it is not a simple ln(N(500-N)) because the differential is not on top. Anyway here it is:
(5000)dN/dt=N(500-N)
they also say when N = 100, dN/dt = 8 (which is obvious)
the answer in...
I think I get it now. Newton only put it negatively inversely proportional to the radius (squared in force equation) because that is the rate it increases at. So if you plot -1/r (for symplicity) for PE as well as a 1/r for KE and translate PE up by an infinate amount so both graphs are in the...
I unterstand that potential energy is negative but I thought that was just convention. The size of the number is decreasing as you move away from a planet. So is the energy still not getting less as you move away?
If a particle is launched with kinetic energy as it gets further from the mass (eg a planet) the kinetic energy decreases. However Potential Energy GMm/r also decreases the further you get from the mass. Where does all this energy go? :confused:
Granted, the calculation U + K = 0 does give...