Can you elaborate on the conditions you set for escape velocity? In particular, why would there have to be no kinetic energy (V=0) at the point where it's no longer effectively influenced by the gravitational field of m1?
Escape velocity relates to the minimum amount of kinetic energy you need in order to completely escape the gravitational pull of a mass. So, if you have JUST enough energy to get free, and none left over (no kinetic energy), that translates to your escape velocity. If you have more velocity than the escape velocity, after you've used up that kinetic energy to get free of the mass's GPE, you would still have some kinetic energy left over.
The - sign is there based on our arbitrary reference. If we set an arbitrary 0 point of gravitational potential energy at an infinite distance from any masses, then as you get closer to the masses, you are "held in" by the mass's gravity, therefore, you would need to add energy to the object that's being held in order to get free again, hence the negative sign.
Remember how F=-dU/dl? Then U=Integral(-Fdl). Integrate Newton's Law of Universal Gravitation from infinity (0 gravitational potential energy) to some distance r.
You can, but it wouldn't be my recommendation. I'd recommend coupling video lessons with lots of independent practice, group discussions, hands-on lab activities, deeper dives, etc. But others have done well with just the videos -- I would imagine they would be in the minority, however.
Dan: Thanks for the speedy and clear elaborations!
Grade saver!!!
Your videos are gonna help me to pass my AP test.
Thank you so much!
Your video is so helpful teacher. Thank you
Can you elaborate on the conditions you set for escape velocity? In particular, why would there have to be no kinetic energy (V=0) at the point where it's no longer effectively influenced by the gravitational field of m1?
Escape velocity relates to the minimum amount of kinetic energy you need in order to completely escape the gravitational pull of a mass. So, if you have JUST enough energy to get free, and none left over (no kinetic energy), that translates to your escape velocity. If you have more velocity than the escape velocity, after you've used up that kinetic energy to get free of the mass's GPE, you would still have some kinetic energy left over.
Starting at 5:45, can you explain the signs used for potential energy--why is there a minus sign there?
The - sign is there based on our arbitrary reference. If we set an arbitrary 0 point of gravitational potential energy at an infinite distance from any masses, then as you get closer to the masses, you are "held in" by the mass's gravity, therefore, you would need to add energy to the object that's being held in order to get free again, hence the negative sign.
Can you explain how is potential energy = -Gm1m2/R?
Remember how F=-dU/dl? Then U=Integral(-Fdl). Integrate Newton's Law of Universal Gravitation from infinity (0 gravitational potential energy) to some distance r.
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Can I take Ap physics C test by watching your videos?
You can, but it wouldn't be my recommendation. I'd recommend coupling video lessons with lots of independent practice, group discussions, hands-on lab activities, deeper dives, etc. But others have done well with just the videos -- I would imagine they would be in the minority, however.