As I was lugging all of my groceries up three flights of stairs, (One trip, of course) a question stuck me that has been bugging me all night: What happens to the Potential Energy of the food that we eat? Carrying the food up the stairs added Potential Energy to the food. But that PE is never converted into Kinetic Energy. I just eat the food and convert it into Chemical Energy. But since energy cannot be created or destroyed, the Potential Energy must have gone somewhere. But where?
Can my digestive system convert Potential Energy into Chemical energy? In other words, does an apple that I eat in my third-story apartment give me more energy than if I had eaten that same apple at ground level? That seems ridiculous to me, but I can't think of anything else right now. What happened to the PE of the apple?
Other Theories:
1) It is stored in fecal matter.
That might account for some of the Potential Energy, but it doesn't account for it all. The mass of the apple I eat is greater than the corresponding excrement. Therefore, the PE of the apple is greater than the PE of the excrement. That still leaves some PE unaccounted for. So I'm still left with the question: What happened to the PE?
2) The PE is converted into KE by the act of chewing.
This doesn't make sense, because I chew the same at ground level as I do in my apartment. If the PE was used by chewing, or any other part of digestion, it would be more difficult to accomplish at high altitudes, but this is not the case. The energy I use to digest my food at ground level is exactly equal to the energy I use in my apartment.
This is bugging me. Where is Bill Nye when you need him?
(Cartoon from http://xkcd.com/200/)
19 comments:
I don't see how carrying the food added potential energy to it.
The higher an object is off the ground, the more potential energy that object has. PE = MGH where M is the mass of the object, G is the force of gravity, and H is the height off of the ground.
But did your height really change? Where you stood at the base of your apartment building, your groceries might have been three feet from the ground. When you went to your third floor, your grocies were still 3 feet from the ground- of your apartment floor. I guess what I'm trying to say is, that as you went up, the height never really changes. You're still three feet from the ground. Now if you had a bottomless apartment, then I wonder.
Yes the height changes when I walk up the stairs! If I start from ground level, then the height increases as I increase in elevation. It doesn't matter what is between the ground and the object, not even if it's an apartment floor. But if it makes it easier for you to visualize, assume that I am eating my apple while perched on the railing of my balcony, and one slip could send the apple falling all three stories.
Haha, I'm still struggling seeing it! Here's what I just can't figure...
At the base of your apartment floor:
PE= ?
M= 4 pounds (for example purposes)
G= 9.8 meters/second squared (or so they say)
H= 3 feet from ground
So PE= 4 x 9.8 x 3
At the third floor of your apartment:
PE= ?
M= 4 pounds (same)
G= 9.8 meters/second squared (same)
H= 3 feet from ground (of your apartment floor)
So PE= 4 x 9.8 x 3
To me, having the third floor "ground" matters. That's what makes the PE equal in my mind.
Can we all agree on the PE at the base ground level (meaning we could use the formula I proposed at the top and the numerics I chose)? Now, what if there was a hole in the ground that dropped fifteen feet? The PE changes because the height changes, right? The ground is no longer 3 feet below the object, it's 15 feet. I think the same principle applies with the apartment floor/balcony. On the third floor the object is still 3 feet from the ground. If we move to the balcony and hold the object over the edge, then it's 15 feet from the ground and PE will change. But from where you stand in anywhere in your apartment (including the balcony), you are three feet from the ground, regardless if the ground you are on is elevated.
You are arguing with me over points that I took as given.
Here is a good defenition of (gravitational)Potential Energy:
"Energy stored by an object by virtue of its position. For example, an object raised above the ground acquires potential energy equal to the work done against the force of gravity"
http://www.answers.com/topic/potential-energy?cat=technology
The apartment floor is not creating gravity, the Earth is. This is why the height of the object, and therefore the PE, does indeed change when I walk up to my apartment. (Although technically all matter creates gravity, the gravity created by the apartment floor is negligible)
If I had no potential energy while lying on the floor of my apartment, (what you claim as height=0), then if someone in the apartment below me cut a hole around where I was lying, I wouldn't fall through; I would float!
So when do you ever have a height that's equal to 0? Can't the same arguement be said if you were standing ontop of ground and somebody dug a hole underneath you and you fell? You wouldn't float there either...
Arrgh! This is supposed to be the easy part!
You can set Height=0 anywhere you want. But you have to use like terms when comparing two systems. If you set h=0 at the ground to calculate PE, you can't compare that figure to a PE calcualted where h=0 is my apartment floor.
If you want to set my apartment floor as h=0 then anything below that is at a negative height. I have to admit, I don't even know if it's possible to construct a physics that includes objects with negative heights.
But OK, I'll use my apartment floor as h=0. The same question still exists! What happens to the PE when I climb up to the roof of my apartment, and eat my apple?
So what happens when you climb a mountain as the ground becomes elevated? Does the PE increase, even though the ground level increases?
"Ground level" can never increase. "Ground level" is h=0, normally set at the ground(to make life simple). I suppose you could set h=0 at different elevations for different problems, but once you set the line, h=0 is constant throughout the problem.
Let me try a math analogy (because those work so well...). Think of the line h=0 like the X-axis on a cartesian coordiante system. The y-axis would correspond to height. So in the example, one side of the mountain could be given by the line y=x. (or y=2x or whatever slope you want to use)
As you move along the line y=x (i.e. climb the mountain) you gradually move farther and farther away from the x-axis. (i.e. you move higher, and therfore increase PE)
I like it in mathematical terms.
Why does h have to be constant throughout your problem? Why can't it change?
You are calculating the PE at two different points, why doesn't your height reset at these points as well? I mean, if you are six feet tall at ground level, you are still six feet tall on the third floor.
Two different points within the same system! Why can't all three points of a triangle intersect the x-axis? You can "reset" the x-axis anyway you want so that two points are on the x-axis, but never all three. That third point will always represent the height of the triangle. The question of "why" is a philosophical question on the nature of reality.
The height question is a semantic trick between height(elevation) and height (tallness)In terms of being six feet tall if you are standing on the x-axis, and you draw a line from the top of your head to the y-axis, that line will intersect the y-axis at 6. If you are standing in my apartment (the line say y=20), then draw a line from the top of my head to the y-axis, that line will intersect the y-axis at 26.
6-0=26-20. Your height (tallness) does remain the same. But your height(elevation) certainly changes, because the line y=20 does not equal the x-axis.
Explain to me why we can't use "tallness" height instead of "elevation" height? Where does it say that we have to use the elevation height?
I'm getting lost here...
Tallness is a property of the object itself. An apple is so many inches tall X so many inches wide X so many inches long. Since tallness is a property of the object, it will not change when the object is moving.
Elevation is property of location. An apple is so many feet above the ground. As the object moves away from the ground, the elevation does change.
The height used to calculate PE is distance away from the ground, not the height of the object itself.
Okay, I get it! It only took 14 comments, but I think I'm ready to look at your original post now! =)
So the gravitational potential energy increased as you brought the groceries up your stairs. I can finally accept that as our given. It is higher on your third floor than it was on the ground level.
There seems to be one really easy secenario that explains your question. You could take all of the bags of groceries you brought up to the third floor and drop them off your balcony. The potential energy is converted into kinetic energy.
Here are a couple of my thoughts:
1) You eat an apple. That apple is turned into two things: waste excrement and stored chemical potential energy. You are right; the apple you ate has a greater mass than the excrement. But part of the apples mass was taken away in the form of nutrients stored by your body. What's not needed is the excrement. The PE is thus transformed into stored chemical energy for later, and then kinetic energy (as strange as this sounds) as your excrement travels down through your body and into the septic tank.
2) What about a cereal box? Not necessarily the cereal, but the box that carried the cereal. It gained PE as you brought it up the stairs as well. Again, I think the gained PE is just stored until you either take it down to the trash dumpster, or drop it off your balcony.
Can you explain mechanical energy to me? I keep reading that mechanical energy is basicall that "when the work is done upon the object, that object gains energy." So when we lift bags of groceries from the ground to the 3rd floor, doesn't it gain mechanical energy as well? Where does that go?
Your idea about the PE of the food converting into a combination of PE in the excrement and Chemical Energy is probably correct.
The problem I have is imagining that the human body has a process to convert gravitational PE into chemical energy. (The fraction that is not stored in excrement) And if it does, then I ask my orginal question again. Does the body gain MORE chemical energy if you eat it in my apartment than if you eat it on the ground?
As for the cereal box, you are exactly right.
And I'm not positive, but I think mechanical energy is just a general term to describe both types of energy in a mechanical system. PE and kinetic energy combined make up the total mechanical energy of a given system. (I think)
As I know the term, it is used to differentiate between other types of energy, such as electro-magnetic or chemical.
No, it doesn't gain more chemical energy. You get the same amount of chemical energy regardless of where you eat it. The excrement is what makes the difference. Because you are on the third floor, the kinetic energy the excrement has is higher (going from the third floor to the septic tank) than it would be on the ground level (h=0 to the septic tank). So it's not a difference in chemical, but rather kinetic. But I agree with you, it's hard for me to imagine this process. Hell, I struggled just understanding PE in general.
The example I was looking at with mechanical energy was a person throwing a baseball. The person applied work to the baseball to make it move, and the baseball took the energy provided (the mechanical energy). You are right, it's the combination of kinetic and potential.
I guess I'm struggling with the properties of mechanical energy. When we are carrying bags up stairs, we are doing work to the bags. Thus our energy is transfered to the bags of food, right? Where does this energy go when we get to the top? Is the energy just the PE at the third floor plus the kinectic energy (0) at the third floor? Just a little confused...
Ok, that makes enough sense for me. At this point, I'm ready to just leave it alone.
And you're correct about the mechanical energy in the third floor bags. It's all in PE with no KE. If you dropped the bags from the balcony, halfway down the total mechanical energy would be 1/2 PE and 1/2 KE, and at impact it would be all KE with no PE.
Hahaha, words I thought you would never utter =).
I think we've come to an answer that makes sense for both of us.
Good discussion. The end.
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