Uphill Physics Problem: Which Side Requires Less Energy?

[erik]

hello, I would like to apologize for my ingnorance in advance.

I have a question.

If a person were going to walk up a hill and had the choice of going up either side, one side has a much steeper grade than the other. which side would require less energy? or would they both require the same amount?

again, I apologize for my ignorance and I appreciate any help that is given.

Thanks

 

[mengshuen]

E=mgh. if both sides would have the same eventual elevation, then the energy used would be the same.

 

[erik]

thanks, still not sure I understand?

because the person is using more muscles and a fuller range of motion with the muscles when traveling up the steeper side wouldn't that use up more energy?

thanks

 

[ZapperZ]

There is a difference between "work" as defined in the physics of mechanics, and "work" as defined in biology, and "work" as used in the pedestrian sense. You asked this in the physics section, and thus, it is assumed that the physics definition of work is what you were asking for.

Zz.

 

[erik]

sorry if I'm not getting it?

why isn't biology taken into consideration in the solution?

 

[ZapperZ]

sorry if I'm not getting it?

why isn't biology taken into consideration in the solution?

Because in mechanics, whether it is a person, or a ball, or a brick, or a vehicle, etc. going up the hill, it doesn't matter. If you have taken any lessons in mechanics, you'll notice that when you give a mass "m" to an object that is undergoing a particular dynamics, your instructor, or the text, doesn't specify that this is a person undergoing this process. As far as the physics of mechanics is concerned, that is irrelevant.

If you think you've asked this in the wrong forum, I can move it to the biology forum. Otherwise, this is something you might want to investigate further on your own first before proceeding any further. Go to the hyperphysics webpage for basic lessons in mechanics.

Zz.

 

[LURCH]

thanks, still not sure I understand?

because the person is using more muscles and a fuller range of motion with the muscles when traveling up the steeper side wouldn't that use up more energy?

thanks

No, because they are expending their energy (at a greater rate) over a sharter period of time, because the steeper side is a straighter line and therefore a shorter distance. If you take the greater amount of power (energy per second) required to go up the steep side, and divide it by the lesser number of seconds the trip would take (assuming two identical hikers walking at the same speed), you would find that the total amount of energy expended would be exactly the same.

Of course, the person going up the steeper side could take the same amount of time by not working so hard and going slower, but the total amount of energy spent would still be the same.

 

[WhyIsItSo]

erik,

Think of it like this. If you walk a mile and evenly climb to say, 100 feet above your starting point, you won't feel a great deal of effort because of the time it takes you to do the "work". If you climb a 45 degree slope to attain a gain of 100 feet, you only travel a little over 141 feet. Even if you move at about the same speed, you'll reach your destination feeling the "work" you just did much more intently because you did it much faster.

From a purely mechanical point of view, the "work" is the same; one would say you burn as many calories walking the mile or climbing the hill.

Your reference to biological factors is a good point; the human body behaves differently under these two situations. We know that to burn fat one needs to exercise in an aerobic fashion for example. But all exercise uses energy. I'm not certain of this, but I strongly suspect that when all is said and done, you will expend the same energy in both exercises; where your body draws that energy from (sugars or fat?) and how you feel afterwards will be all that changes.

Hope that helps.

 

[WhyIsItSo]

A caveat to what I just wrote. With all due respect to ZapperZ in particular, the steeper slope will require the lesser energy.

Friction.

In the simplified definition of "work", the results would be the same, however in the real world all machines (human or otherwise) have frictional forces to overcome, therefore energy is lost simply by moving. If you are at rest, start moving, go for a mile, return to rest, but have gained or lost no altitude, we might say you haven't done any "work", but we understand that energy has been used through this process.

So, erik, in the real world you have a point. ZapperZ is also correct because in the pure sense of mechanics, friction is not taken into account when determining "work".

 

[ZapperZ]

A caveat to what I just wrote. With all due respect to ZapperZ in particular, the steeper slope will require the lesser energy.

Friction.

In the simplified definition of "work", the results would be the same, however in the real world all machines (human or otherwise) have frictional forces to overcome, therefore energy is lost simply by moving. If you are at rest, start moving, go for a mile, return to rest, but have gained or lost no altitude, we might say you haven't done any "work", but we understand that energy has been used through this process.

So, erik, in the real world you have a point. ZapperZ is also correct because in the pure sense of mechanics, friction is not taken into account when determining "work".

But unless you're dragging something, friction doesn't play a role in any work done other than to provide traction. For an object of mass m sliding up a frictionless surface, the slope of that surface is irrelevant. The amount of energy expanded only depends on the height. You could also do the same thing for a ball rolling up the inclined without slipping. No work is done by friction here.

This is the definition of a conservative force, where only the starting and the end points matter. Now if you want to include friction when you drag things up the inclined, then we have a different problem than what I understand in the OP. However, if you notice, the problem the OP had was more to do with the "energy" expanded by the muscles, etc... which is not part of the mechanics of motion. Thus, "friction" wasn't part of the scenario that is being asked.

Zz.

 

[WhyIsItSo]

Zz,

You are correct, no question. What I'm trying to do is get behind where erik is coming from. In his second post, he said:

because the person is using more muscles and a fuller range of motion with the muscles when traveling up the steeper side wouldn't that use up more energy?

I can see where his thinking is, and my purpose was trying to connect the pure physics to the vagaries of real-world situations. A human model is not a simple system, and within erik's context of thought, he has a point. The human body is not terribly efficient, and that efficiency is not constant.

Still, your position is probably best. He did after all ask a physics question, and I suppose it is best to give him the exact answer and leave it to him to sort out any (seeming) discrepancies between his conceptualization and the physics model.

My apologies.

 

[rcgldr]

Taking into account kinematics (human motion), there's is probably a best angle of ascent where a human body takes the least amount of energy to get from the bottom of the hill to the top. There's been similar research into the design of stairs. You can do a web search for "kinematic stair" to find a few articles. I didn't get as many hits looking for kinematic ramp.