When I was in high school, a friend of mine was taking aerodynamics and physics. I was taking music, so I didn’t care much about math, science, etc… I didn’t really care about music either, but, that’s neither here nor there.
At any rate, friend told me that given a hill, or let’s just say a pyramid, with the incline about 45 degrees, and approximately 200 feet long. He said that 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. I said that that was nonsense, and he proceeded to explain why it was correct. He then whipped out some kind of formula, which I looked at and nodded. End of subject. I, of course, didn’t believe him, but it seemed to me that he had more smarts in this area than I, so I could be wrong. I doubt it, tho. Is less energy expended in the final 10-20 feet?
Doesn’t gravitational strength drop off with the square of distance or some such? I haven’t seen them, but I’ve heard the Great Pyramids are really, really big.
I haven’t any more than freshamn level physics at college, and to tell the truth was never too much a higher math person myself. I do read a lot of physics, though, and have never heard this as you put it. I suspect the question is wrong.
it is true that the further an object is from the center of gravity of the earth the less the pull of gravity. Thus, as the object goes up the lighter it gets and the less energy needed to move it. An ordinary scale wouldn’t even register the difference with only 200 feet. So practically you won’t know the difference.
How the question is messed up is that it allows for less energy only in the last protion of the trip. As the object goes up, it constantly weighs less through the whole trip and not just the last segment. Not that you’d know over 200 feet.
That wouldn’t matter. It doesn’t say that the gravitational pull is a constant for the preceding 180 feet, only that it is less for the last section than any previous section. That would be the case however long the slope is and however long you decide to make your measurement sectors.
I think we’re misinterpreting the problem, but I don’t think that can be corrected without a perfect memory of exactly what the original statement actually was, which we’re probably not going to get.
Less energy expended doing what?
You’d be correct, if. I don’t know why I got it into my head that the first 180 feet are all the same in the question but still I’m right.
Exceeeeepppt:
the last 10-20 (group A) feet require less energy than any of the previous 180-190(Group B) feet.
the 187th foot in group A will require more energy than the 188th foot of group B.
The question should not leave the wiggle room. “The last 20 feet require less energy than any previous 20 feet of the prvious 180 feet.” Would be the statement you’re looking for to allow us to answer yes.
Note that the reduction in energy expended to raise an object the next 20 ft (vs. the previous 20) is something like one part in 10[sup]12[/sup].
To say this is below what could be measured is a serious understatement. It’s dramatically less than the effects of even minor air currents, and probably something like that of the solar wind.
Another stupid and trivial and really dorky observation is that your automobile will have burned a little gas while climbing the first part of the hill, and so the engine has a little less weight (mass) to lift.
But if we have a nifty futuristic car that runs of “beamed energy,” never mind…
More realistically, there’s the observation that most hills aren’t pyramid-shaped, and level out as you approach the top.
Or sticky tires that pick up material leading to a heavier automobile, or degradation of the engine or other parts leading to a less efficient car, and so *more *energy being expended the nearer the top.
Won’t the same be true of the bottom of the hill?
It scales with the square of distance as measured from the center of the earth. So the base of the Great Pyramids is 4000 miles (21,120,000 ft) from the center of the earth, and the top of the tallest great pyramid is 481 feet higher than that - so 21,120, 481 feet from the center of the earth.
Gravity at the top will be 21,120,000[sup]2[/sup]/21,120,481[sup]2[/sup] time the gravity at the bottom, which works out to 99.9954% of the gravity at the bottom. So for the OP, his buddy was technically correct, although the change in gravity is not going to be noticed by someone who isn’t carrying extremely sensitive instrumentation with them.
If astronomical distances are involved, then it gets interesting. For example, in low-earth orbit (just 200 miles above sea level), gravity is about 91% of its sea-level value.
You could take your foot off the gas as you approached the top, and coast to a stop, using momentum for the last little way to deal with gravity.
A car is not necessarily part of the equation. Just pushing a load up.
But of course youa re right, if you are using a car.
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.”
Car or not, many self-propelled vehicles (including a human body) will have burned some fuel early in the trip, and thus be lighter at the end. Theoretically, if not measurably.
True. But if we change this to an elevator shaft pushing at a 45 angle it is not true. Only true if what is pushing also goes up the incline.
Canoes get heavier the further along the portage you go. Scientifically proven fact. :eek:
It’s also possible that the original statement, now corrupted by fallible memory, stated something about intervals of time, not intervals of distance.
Hi, everybody. Just got back to a computer.
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?
Thanks, everybody, for your responses.