This isn’t the question you’re expecting. Walking from the hotel to my client’s office dragging both my check-on sized roller bag luggage and laptop combined with boredom made me consider why I had spent the extra few seconds that morning to secure my heavy laptop from the roller bags “catch” having the laptop sit on the front of the roller bag closer to the ground. Normally I extend the retractable handle and hold the bag against it on top, higher than the bag and closer to my hand.
In my normal method the laptop’s weight makes covering any great distance a pain. The weight pushes down and makes me strain more. When I strap the bag lower the weigh is gone and rolling the bag is easy as pie.
I think I understand the basic physics of this. The laptop’s weight when strapped to the front is on the other side of the lever and this requires me to use a smaller force to balance it out. However, for the life of me I can’t figure out where the energy goes. It’s the same weight and the same basic machine but the normal method requirements a much more exertion on my part. Where does the energy go? I am now moving the same weight with much less energy. This is driving me nutty!
If I’m understanding you correctly it’s not that the energy “goes” somewhere, it’s that you aren’t using as much to begin with. So in the case of hauling something around that energy stays stored in your body ready to be used for something else like lifting your bag into the overhead compartment.
The reason it uses less is as you surmise - with the laptop closer to the wheels it’s on a shorter lever arm and so requires less force from your arm to keep the bag from tipping to the ground. Stack the laptop closer to the top and it’s got a longer lever arm (distance to the wheels) and so you have to exert more force.
ETA - yes, if the center of mass of the laptop is on the other side of the wheels from the center of mass of the rest of the bag then it will act as a counterbalance, again requiring less force from your arm.
In both instances I am moving the same amount of weight. A simple machine (or my understanding of one) does not reduce work just distributes it. The old block and tackle analogy, I can lift a much heavier weight but it takes more pulling.
In my laptop, roller back I exert less energy so I guess I should have said where does the “extra work” I had been doing go?
Thinking about this some more I guess it is similar to a packed merry-go-round. If a dozen kids were sitting on the ground I would have to exert much more energy to overcome gravity and friction to move them but when they are on the merry-go-round the friction has been reduced.
Ahh! I get it. When I put the laptop low and on the opposite end of the lever I can reduce my work because I’ve reduce the drag gravity was adding to the equation.
It may be clearer if you understand that supporting a weight, while it feels effortful, doesn’t use any energy. The energy you expend in rolling the luggage-laptop combo along on a flat surface is tiny. But you experience it as tiring because there is a force exerted through your arm to support the handle of the luggage. If you held the luggage off the ground at arms length in front of you while walking to the client’s office, it would quickly become very tiring indeed, but wouldn’t take any more energy!
If on the other hand you arrange the luggage so that the handle is over the centre of gravity, the load will seem very light, and the only force required is to overcome rolling resistance (and air resistance), and to raise the load if you’re walking uphill.
Wrong, I’m afraid. The real answer is that you haven’t reduced your work (in the sense of energy expended). You have reduced the force on your arm, which is tiring and feels like work, but doesn’t involve any expenditure of energy.
Can you expand on that? I am not confusing the tiring of my arm with work. When the bag is higher it takes more energy to start moving and more energy to continue moving or to deal with obstacles such as curbs. Going down hill also requires more braking power to reduced the increased forward momentum of the unbalanced bag vs the balanced scenario.
Can you provide a more detailed answer in regards to conservation of energy?
The fact that you are rolling the bags is a red herring.
Suppose you just stand in one place holding the laptop. Your arm is going to get tired and is using energy, even though there is no work being done with respect to movement of the bag[sup]1[/sup]. You are exerting a force on the laptop equal and opposite to the force of gravity. But “work” is force applied through a distance. No distance, no work. Now hang the laptop from your suitcase and stand next to it. That does the same amount of “work” (i.e., none) but your arm doesn’t get tired.
Now start the whole system moving on wheels and you haven’t really changed anything about the “missing” energy.
I got into a discussion like on the boards a while back and was instructed that there is work being done inside the structure of the arm, since work is directly related to energy (though they didn’t mention that when I studied physics 30 years ago :)). I am still pondering that one. See post #24 by Blake in this thread.
I agree that the distinction between energy in the physical sense, and effort that you feel yourself expending, is the problem here. For example you say that going downhill requires more braking power, as though that is an energy export on your part, whereas the rolling baggage is actually pumping energy into you when this happens.
There is also a description of this problem where we carefully account for all the physical energy in your participation, but that is strongly sensitive to the inefficiencies in your body. For example, you export no physical work (in the sense of force times distance) if you stand perfectly still, but you will spend significant energy to manage doing this, which will appear largely as heat around you. Defined this way your body is operating with zero efficiency. And, the rolling downhill situation has your body operating with a negative efficiency, consuming food calories to let the bag donate energy to you.
Conservation of energy isn’t really relevant to this situation. If you roll your luggage along, there is some energy lost to friction in the wheel bearings. This energy is transferred as heat to the environment. But that’s not really what you’re asking about, is it?
Earlier, I mistakenly said that “If on the other hand you arrange the luggage so that the handle is over the centre of gravity, the load will seem very light”. I should have said “if you arrange the load so that the centre of gravity is over the wheels…” But the point still stands.
You say that the unbalanced bag “takes more energy” to get moving or to continue moving or to lift onto a kerb. But you’re mistaken. It’s more difficult, but the amount of work done is the same in each case. It’s also a mistake to think that the unbalanced arrangement has more forward momentum, at a given speed, than the balanced arrangement.
Whenever the question is “where did the energy go?”, the answer is almost always heat. The other posters are correct that holding a weight at a constant height doesn’t do any work, but the way the human body is constructed, it does require an expenditure of energy. All of that energy is getting converted into heat.
Are you guys claiming that his body’s calorie expenditure would be the same if collapsed the extension handle on the roller-case and carried it at arm’s length off the ground like a briefcase over whatever distance he was traveling vs rolling it?
I’ve having trouble with that concept, surely the muscular strain involved uses calories. On a similar note Are you saying static isometric resistance exercises that build muscle would burn virtually no calories?
That’s incorrect. Holding a weight up does expend energy within your muscles, even if no work is done on the object being held. The internal structure of your muscles means that you are doing work even while holding a static load (unlike, say, a table) which is expended as heat. The simple fact that you get tired, heat up and sweat while holding up a heavy weight should be a refutation of your statement that there is no expenditure of energy.
Dervorin, chronos and astro are right; I was wrong to state that no energy is expended by a human supporting a load. I apologise for sowing confusion with my misleading posts in this thread.