(Answered, thanks yall) Basically I have three competing understandings: potential energy with respect to height is linear AND gravity is constant in force applied per time (right?) AND at the end of falls you are losing height faster because greater speed.
So with these three things being my understanding I don’t understand how at the end of a fall (some arbitrary speed) you can lose more height and thus PE per second but be accelerated at the same force. I don’t see how you could expend more PE but not be putting in more energy to acceleration… Where does that extra PE lost by higher speed go? Does it take more energy to accelerate when moving faster? It shouldn’t I think ignoring fancy energy momentum stuff that doesn’t apply at 10 mph lol.
So yeah, I don’t get it. I’d be very grateful is someone could solve this for me. I know I must be missing something but don’t know what. This is a question i’ve argued with my brother about a little and tried to look up a few times but the forum posts I’ve found aren’t exactly my issue I think. I also tried asking some ai and it didn’t see my problem I think. For the record I’m in school for chemistry so not a lay person per se but not well read at all either.
In: Physics
Other comments talked about how the formulas are constructed or try to explain it in other terms. But what I want to do is ask a different question – what if indeed the energy depended on time.
So based on our observations, we know how fast an object will hit a ground based on a certain height. But it doesn’t have to be a straight path. If we take a ball and release it on a ramp from the same height, it’ll reach the same speed only horizontally. But in doing that, we can make the path from highest point to lowest point as long as we want. If the energy was dependent on time, then it would keep increasing and the longer the ramp, the faster it’ll exit. The path can be also squiggly or zigzag and because we increased the path, time increases and therefore the overall energy.
But it doesn’t work like that. Apparently the only thing that matters is the starting height and the end height. So time doesn’t factor in it.
We also have a great example of a very very very long path to fall – satellites. Satellites are constantly “falling” to earth, just in the longest path possible. If time was a factor in their energy, then the energy released when they hit the ground would be enormous. But it doesn’t. So our initial observation of only the beginning height and end height matters (barring any external force and friction).
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