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Suppose I want to go from point A to Point B on a straight level road. I have 2 options: use a cycle or go walking. Now, which one of the 2 should I prefer if I want to minimise the amount of work done by myself and explain why .

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Consider forces acting on you when moving from A to B. The forces are gravity, normal reaction, friction, air resistance.

Now, gravity and normal reaction being perpendicular to the direction of motion, do zero work and air resistance would be same in both cycling and walking (approximately) Hence deciding factor is force of friction.

Now you may want to move with constant velocity or accelerate; for constant velocity:

When we walk, the friction force provides the horizontal force neccesary to move forward but your body would need to provide that force constantly over the course of your motion for constant velocity. For cycling, however, as your body does work peddling, the friction acting on wheels provide the horizontal velocity until rolling starts between wheels and road, after that friction becomes zero (assuming ideal case, practically value is very very small). Thus only some work has to be put in while cycling to reach desired speed, then it becomes comfortable riding at that speed(you may have observed this )(ideally, we won't have to any work after reaching desired speed)

For acceleration :

While walking, body would need to produce constant power like before but while cycling also we would need to provide power constantly but since friction on wheels would be much smaller, therefore work wasted in heating would be less and it would be better if you used cycle instead of walking in both cases.

While this is the answer in terms of physical analysis of forces, in reality, we would also require energy to keep our body in vertical posture while in cycling we just have to sit and that is more enegergetically favorable.

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    $\begingroup$ "air resistance would be same in both cycling and walking" this could hardly be further from the truth $\endgroup$ – LLlAMnYP Sep 15 '16 at 9:32
  • $\begingroup$ Assuming identical body surface area and equal velocity, air resistance would be same $\endgroup$ – Rishabh Sep 15 '16 at 9:35
  • $\begingroup$ Sure, but both assumptions are unfounded. A cyclists velocity is much higher, as is the effective surface area of a bicycle+human (not only because of the additional bicycle, but also the posture of the cyclist, etc) $\endgroup$ – LLlAMnYP Sep 15 '16 at 9:39
  • $\begingroup$ Sure, the surface area would matter but velocity is under our control and its not neccesary that velocity of cyclist is high and surface area alone is not enough to make considerable impact $\endgroup$ – Rishabh Sep 15 '16 at 9:42
  • $\begingroup$ Even inexperienced cyclists travel at a gentle jogging pace or above (i.e., about twice walking pace); a more experienced cyclist can easily travel at five times walking pace. That's hugely significant, given that air resistance scales quadratically with speed. $\endgroup$ – David Richerby Oct 2 '16 at 13:04

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