Physics question (I guess):Less energy expended near top of incline?

[Chessic_Sense]

@David42

as I pointed out, his buddy is not correct if the question is framed the last 10-20 feet is easier than any of the previous 180-190 feet because the 186th foot needs less energy than the 185th, but not the 187th. and framing the question this way allows us to do that, point out that 187th and 185th are both “any of the previous 180-190 feet.”

That’s true. It’s also not what the OP says:

less energy would be expended at about the last 10-20 feet than would be expended in any 10-20 foot stretch in the **previous **180-190 feet

You can’t compare the 187th to the 186th foot because they’re not 10-20 foot stretches of track.

[TokyoBayer]

@handsomeharry

So, it seems that the original statement is correct, in that gravity and momentum is a factor, if I am reading everybody correctly. Other than these factors, tho, it is incorrect…did I make a good interpretation on the facts?

Momentum is not a factor once you get up to speed. Climbing a hill is “blind” so there isn’t any way for the energy to know you are in the final 10 - 20 feet. As others have said, the difference in gravity over this type of distance is so negligible that you wouldn’t be able to measure it.

So, for practical purposes, your friend is wrong unless there is more to the story.

[doorhinge]

Sine A = a / c

Sine A for 45 deg = .70711
c = 200 ft
200 x .70711 = 141.42

The 200 ft mark would be 141.42 ft above the base.
The 180 ft mark would be 127.28 ft.
The 20 ft mark would be 14.14 ft.
And the 0 ft mark would be 0 ft.

Is less energy expended to cover the final 20 ft than the first 20 ft?

Assuming no head or tail winds because those could be real energy killers if they’re strong enough.

Also assuming no change in tempurature between 0 ft and 180 ft. Warm air is less dense that cold air.

There would be an ever soooo slight reduction in gravitaional force raising something from 127.28 ft to 141.42 ft compared to raising something from 0 ft to 14.14 ft. but nothing we could notice without very delicate instuments.

INHO, of course.

[handsomeharry]

I’m a thankin’ ye all!

[Earl_Snake-Hips_Tucker]

By the same reasoning, you weigh more when you inhale, and less when you break wind or belch–because of the additional air molecules in your body, or being expelled, respectively. As you noted, you didn’t care much about math, and “some kind of formula” leaves a lot of latitude for what he might have had in mind.

[CC]

As the OP frames the question, it starts out as a hill and becomes a pyramid. Apparently, he doesn’t really remember which. If it’s a pyramid, a lot of the babble above can apply. If it’s a hill, it would take less energy to go the last, say, 20 feet than any previous segments of 20 feet because you are not lifting yourself away from the earth as much, since the hill is flattening out. The work you do, and the energy expended, relates mainly to how high you’re lifting the body, not how far forward you’re moving it.

[Doubticus]

I was merely thinking you accelerate in the first 20 feet and coast to a stop the last 20 feet, thus the difference in energy exerted.