### Thread: Work on an incline

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#### Work on an incline

Hello,
We went on a family hike today and I had a debate with my brother in law regarding a physics question.

There were two trails:

1) one that curved around and was much longer but less steep
2) the other trail was much steeper but shorter.

Both trails ended up at the same altitude and converged basically at the same spot.

Now I know from Physics the work = force x distance formula. My argument with him was he thinks the steeper trail takes more work because we were more tired from that trail than the longer, less steeper trail that curved around. I said that no matter which trail is chose if they ended up at the same height (altitude) the net work would be the same.

Thanks,

Ankur
2. Ignoring friction and using the physics definition of work, yes, they are equal regardless of the slope of the trail.

Now, which ones give you more of a workout could be different. Depends what kind of workout you're after.

---John Holmes...

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Agreed. Theoretically, it should be the same, but since this is the real world you might have to do more work on the steeper on. Take it to the extreme. If you made the steeper one 90 degrees, you might have hell of a time.
4. I think what's missing here is the concept of where the work is coming from. Going the force of gravity is working against you, but going down the force of gravity is working with you. In otherwords (note: only the scalar component, Direction will be covered with signs)

W = work done by you (variable)
G = work done by gravity (constant)
T = total work (constant)

Going up it's
T = W - G

Going down it's
T = W + G

So you're doing more work going up, but the total amount of work getting done is the same.

-MBirchmeier
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#### im full

Where'd you hike @?
I just got back from a very filling lunch and i think i need a hike if im ever gonna lose weight
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#### Physics

• gimp disagrees : (-0) Unlock!
7. Thanks for unlocking. Basically I asked for an unlock because keeping it open hurts nobody and may potentially benefit someone.

• ChiefWigs1982 agrees : You're welcome. ;)
8. [placeholder] ... I'm tired, but i'll be back

/edit, it's a real world scenario, so you can't ignore the forces of friction, and it's no longer a simple machine. One will have marginally more "work", but why ? I'm guessing the longer trek because of the amount of time taken indicates more energy expended against an assumed constant force of friction over a greater displacement.

I've got a nice diagram, but it's 20 years since the sin2Ѳ vs 2cosѲ days, so I'll check it over coffee tomorrow.

[thought for the day]You and you brother in law should have had a few beers and went bowling instead
Last edited by Axweildr; August 2nd, 2006 at 09:46 PM.
9. I'm going to need the coefficient of limiting friction for each track if you'd be so kind ...
10. Bear in mind also, Ax, the Earth is an oblate spheroid and not a flat plane :-P You'll get Pythagoras running about in circles ...
Last edited by medialint; August 2nd, 2006 at 09:59 PM.
11. Can I just say that 'coefficient of limiting friction' and 'oblate spheroid' mean absolutely bugger all to me and things like that just confuse me.
12. you may ... well you have already
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#### The real answer... from a guy who used to work at NASA and has a BS in Physics

The real answer is that the longer trail would definitely take more work.

The rise up to altitude is certainly just a matter of doing work against gravity up the vertical distance to get to your altitude. This is the exact same thing going the "long way" or the "steep way". You are going from altitude x to altitude y working against gravity. Both paths require the same work from that standpoint.

Where they differ is not really in a coefficient of friction, but more in the effort required to move legs in general and to stick your foot into dirt or rocks and pick it back out again. Each STEP is a huge effort, so the work done to take each step would add up in on the "longer" path.

This is why the longer path would require more work (or calories you ate) to get there.
14. You left a f*cking job at nasa? You dumb, dumb piece of sh*t.

(No offense)
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#### Ha ha ha!!

Ha ha ha! Yeah... I'm dumb. What happend is I sat next to a printer where I got to see a lot of stuff come out that I probably shouldn't have seen.

One day the payroll stats came out. I saw that the lead scientist... Old guy, PhD from the Max Planck institute for Physics in Germany... Brilliant guy... was pulling in \$65K a year.

I got greedy and went to work at a software company that paid more. In retrospect... there's one emoticon I see here on the side that fits the whole thing:

Originally Posted by gimp
You left a f*cking job at nasa? You dumb, dumb piece of sh*t.

(No offense)
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