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So, the question is as follows:

What is the difference in work exerted by the rider in the two following scenarios?

a) Rider + bike. Water carried in a holder on the frame
b) Rider + bike. Water carried in a backpack

(for simplicity, assumption that weight of holder = weight of backpack and backpack is perfectly aerodynamic, not increasing drag)

I would assume that in case a), as the weight is closer to the bike's centre of mass, it would require the least amount of extra work, compared to b), where the weight is more distant from the centre of mass.

Thanks in advance.

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3 Answers

Work in both cases is equal. Work (in physics sense of the meaning) is simply

$$W = \int \vec{F} \cdot \text{d}\vec{s}$$

and this does not depend on the relative position on the bicycle.

The problem is what we intuitively consider to be work and what is work in sense of physics. When you for example just hold an object on certain height, you obviously do no work, but your muscles are constantly contracting and expanding. So you are loosing chemical energy, but it does not go into the work done to the object, but into your own thermal energy.

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Pygmalion's answer is quite correct, however anyone who has carried heavy loads on a bicycle will know they are less work if they are mounted low on the frame.

I have never looked into the mechanics of this, but I would guess it is because it makes the moment of inertia lower if you consider the bicycle to be rotating sideways around the tyre-road contact. That means you need a lower torque and hence less work when you're manouvering the bicycle.

having said this, I'd regard this as a small effect. The majority of the work is expended in overcoming air resistance, and as Pygmalion says the mounting of the load will not affect this.

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I cycle regularly and apart for the fact it is harder to steer with heavy objects high regard to the ground, I never had a feeling I actually do more work... I am interested in your argumentation, but I do not understand what you mean about lower moment of inertia. Could you get into more detail? Thanks. –  Pygmalion May 25 '12 at 11:34
    
if you have a weight higher and the bike tilts you have to do more work to move your body weight to compensate and provide a force to move the bike bake to upright - doing work since you move the mass upward –  Martin Beckett May 25 '12 at 12:45
    
Yes that's what I meant. –  John Rennie May 25 '12 at 13:50
    
@MartinBeckett Yes, but if you do work by e.g. tilting right, you receive work by tilting left, so eventually total work tilting left and right equals zero. –  Pygmalion May 25 '12 at 16:25
    
@Pygmalion - you don't get work back into your body. Otherwise cycling over the mountain stages would take no effort! –  Martin Beckett May 25 '12 at 16:29
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When riding, it seems like the bike stays mostly stable, while the rider is moving up and down (unless you keep your butt planted to the seat the whole time), and side-to-side in relation to the bike and the direction of motion.

With that in mind, it seems like carrying a load on the rider would increase the energy needed to produce or compensate for that up-and-down or side-to-side motion. Whereas, carrying the load on the bike frame would add only to the overall weight of the bike + rider, but not to that secondary motion of the rider him/herself.

Thus, in my total layman-ignorance, it seems like carrying the load on the rider would require more energy. :)

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